MAYBE Problem: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Proof: DP Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt(),V1)) -> isNatIListKind#(V1) active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> isNatList#(V1) active#(U12(tt(),V1)) -> U13#(isNatList(V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) active#(U21(tt(),V1)) -> isNatKind#(V1) active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> isNat#(V1) active#(U22(tt(),V1)) -> U23#(isNat(V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) active#(U31(tt(),V)) -> isNatIListKind#(V) active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) active#(U32(tt(),V)) -> isNatList#(V) active#(U32(tt(),V)) -> U33#(isNatList(V)) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) active#(U33(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> isNatKind#(V1) active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) active#(U44(tt(),V1,V2)) -> isNat#(V1) active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) active#(U45(tt(),V2)) -> isNatIList#(V2) active#(U45(tt(),V2)) -> U46#(isNatIList(V2)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> isNatIListKind#(V2) active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) active#(U61(tt())) -> mark#(tt()) active#(U71(tt())) -> mark#(tt()) active#(U81(tt(),V1,V2)) -> isNatKind#(V1) active#(U81(tt(),V1,V2)) -> U82#(isNatKind(V1),V1,V2) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) active#(U82(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U82(tt(),V1,V2)) -> U83#(isNatIListKind(V2),V1,V2) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) active#(U83(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U83(tt(),V1,V2)) -> U84#(isNatIListKind(V2),V1,V2) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) active#(U84(tt(),V1,V2)) -> isNat#(V1) active#(U84(tt(),V1,V2)) -> U85#(isNat(V1),V2) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) active#(U85(tt(),V2)) -> isNatList#(V2) active#(U85(tt(),V2)) -> U86#(isNatList(V2)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) active#(U86(tt())) -> mark#(tt()) active#(U91(tt(),L,N)) -> isNatIListKind#(L) active#(U91(tt(),L,N)) -> U92#(isNatIListKind(L),L,N) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) -> isNat#(N) active#(U92(tt(),L,N)) -> U93#(isNat(N),L,N) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) active#(U93(tt(),L,N)) -> isNatKind#(N) active#(U93(tt(),L,N)) -> U94#(isNatKind(N),L) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) active#(U94(tt(),L)) -> length#(L) active#(U94(tt(),L)) -> s#(length(L)) active#(U94(tt(),L)) -> mark#(s(length(L))) active#(isNat(0())) -> mark#(tt()) active#(isNat(length(V1))) -> isNatIListKind#(V1) active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) active#(isNat(s(V1))) -> isNatKind#(V1) active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) active#(isNatIList(V)) -> isNatIListKind#(V) active#(isNatIList(V)) -> U31#(isNatIListKind(V),V) active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V)) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1) active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) active#(isNatIListKind(nil())) -> mark#(tt()) active#(isNatIListKind(zeros())) -> mark#(tt()) active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1) active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) active#(isNatKind(0())) -> mark#(tt()) active#(isNatKind(length(V1))) -> isNatIListKind#(V1) active#(isNatKind(length(V1))) -> U61#(isNatIListKind(V1)) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> isNatKind#(V1) active#(isNatKind(s(V1))) -> U71#(isNatKind(V1)) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> isNatKind#(V1) active#(isNatList(cons(V1,V2))) -> U81#(isNatKind(V1),V1,V2) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> U91#(isNatList(L),L,N) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) mark#(zeros()) -> active#(zeros()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(0()) -> active#(0()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> U12#(mark(X1),X2) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> U13#(mark(X)) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> U21#(mark(X1),X2) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> U22#(mark(X1),X2) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> U23#(mark(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(isNat(X)) -> active#(isNat(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> U32#(mark(X1),X2) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> U33#(mark(X)) mark#(U33(X)) -> active#(U33(mark(X))) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> U45#(mark(X1),X2) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> U46#(mark(X)) mark#(U46(X)) -> active#(U46(mark(X))) mark#(isNatIList(X)) -> active#(isNatIList(X)) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> U52#(mark(X)) mark#(U52(X)) -> active#(U52(mark(X))) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> U61#(mark(X)) mark#(U61(X)) -> active#(U61(mark(X))) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> U71#(mark(X)) mark#(U71(X)) -> active#(U71(mark(X))) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> U81#(mark(X1),X2,X3) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> U82#(mark(X1),X2,X3) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> U83#(mark(X1),X2,X3) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> U84#(mark(X1),X2,X3) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> U85#(mark(X1),X2) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> U86#(mark(X)) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> U91#(mark(X1),X2,X3) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> U92#(mark(X1),X2,X3) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> U93#(mark(X1),X2,X3) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> U94#(mark(X1),X2) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> mark#(X) mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> active#(length(mark(X))) mark#(nil()) -> active#(nil()) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) isNatIListKind#(mark(X)) -> isNatIListKind#(X) isNatIListKind#(active(X)) -> isNatIListKind#(X) U13#(mark(X)) -> U13#(X) U13#(active(X)) -> U13#(X) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) U32#(active(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) U33#(mark(X)) -> U33#(X) U33#(active(X)) -> U33#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) U45#(active(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) U46#(mark(X)) -> U46#(X) U46#(active(X)) -> U46#(X) isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) U61#(mark(X)) -> U61#(X) U61#(active(X)) -> U61#(X) U71#(mark(X)) -> U71#(X) U71#(active(X)) -> U71#(X) U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3) U81#(active(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,active(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3) U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3) U82#(active(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,active(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3) U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3) U83#(active(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,active(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3) U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3) U84#(active(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,active(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3) U85#(mark(X1),X2) -> U85#(X1,X2) U85#(X1,mark(X2)) -> U85#(X1,X2) U85#(active(X1),X2) -> U85#(X1,X2) U85#(X1,active(X2)) -> U85#(X1,X2) U86#(mark(X)) -> U86#(X) U86#(active(X)) -> U86#(X) U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3) U91#(active(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,active(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3) U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3) U92#(active(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,active(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3) U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3) U93#(active(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,active(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3) U94#(mark(X1),X2) -> U94#(X1,X2) U94#(X1,mark(X2)) -> U94#(X1,X2) U94#(active(X1),X2) -> U94#(X1,X2) U94#(X1,active(X2)) -> U94#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) TDG Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt(),V1)) -> isNatIListKind#(V1) active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> isNatList#(V1) active#(U12(tt(),V1)) -> U13#(isNatList(V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) active#(U21(tt(),V1)) -> isNatKind#(V1) active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> isNat#(V1) active#(U22(tt(),V1)) -> U23#(isNat(V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) active#(U31(tt(),V)) -> isNatIListKind#(V) active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) active#(U32(tt(),V)) -> isNatList#(V) active#(U32(tt(),V)) -> U33#(isNatList(V)) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) active#(U33(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> isNatKind#(V1) active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) active#(U44(tt(),V1,V2)) -> isNat#(V1) active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) active#(U45(tt(),V2)) -> isNatIList#(V2) active#(U45(tt(),V2)) -> U46#(isNatIList(V2)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> isNatIListKind#(V2) active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) active#(U61(tt())) -> mark#(tt()) active#(U71(tt())) -> mark#(tt()) active#(U81(tt(),V1,V2)) -> isNatKind#(V1) active#(U81(tt(),V1,V2)) -> U82#(isNatKind(V1),V1,V2) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) active#(U82(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U82(tt(),V1,V2)) -> U83#(isNatIListKind(V2),V1,V2) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) active#(U83(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U83(tt(),V1,V2)) -> U84#(isNatIListKind(V2),V1,V2) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) active#(U84(tt(),V1,V2)) -> isNat#(V1) active#(U84(tt(),V1,V2)) -> U85#(isNat(V1),V2) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) active#(U85(tt(),V2)) -> isNatList#(V2) active#(U85(tt(),V2)) -> U86#(isNatList(V2)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) active#(U86(tt())) -> mark#(tt()) active#(U91(tt(),L,N)) -> isNatIListKind#(L) active#(U91(tt(),L,N)) -> U92#(isNatIListKind(L),L,N) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) -> isNat#(N) active#(U92(tt(),L,N)) -> U93#(isNat(N),L,N) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) active#(U93(tt(),L,N)) -> isNatKind#(N) active#(U93(tt(),L,N)) -> U94#(isNatKind(N),L) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) active#(U94(tt(),L)) -> length#(L) active#(U94(tt(),L)) -> s#(length(L)) active#(U94(tt(),L)) -> mark#(s(length(L))) active#(isNat(0())) -> mark#(tt()) active#(isNat(length(V1))) -> isNatIListKind#(V1) active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) active#(isNat(s(V1))) -> isNatKind#(V1) active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) active#(isNatIList(V)) -> isNatIListKind#(V) active#(isNatIList(V)) -> U31#(isNatIListKind(V),V) active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V)) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1) active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) active#(isNatIListKind(nil())) -> mark#(tt()) active#(isNatIListKind(zeros())) -> mark#(tt()) active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1) active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) active#(isNatKind(0())) -> mark#(tt()) active#(isNatKind(length(V1))) -> isNatIListKind#(V1) active#(isNatKind(length(V1))) -> U61#(isNatIListKind(V1)) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> isNatKind#(V1) active#(isNatKind(s(V1))) -> U71#(isNatKind(V1)) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> isNatKind#(V1) active#(isNatList(cons(V1,V2))) -> U81#(isNatKind(V1),V1,V2) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> U91#(isNatList(L),L,N) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) mark#(zeros()) -> active#(zeros()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(0()) -> active#(0()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> U12#(mark(X1),X2) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> U13#(mark(X)) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> U21#(mark(X1),X2) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> U22#(mark(X1),X2) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> U23#(mark(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(isNat(X)) -> active#(isNat(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> U32#(mark(X1),X2) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> U33#(mark(X)) mark#(U33(X)) -> active#(U33(mark(X))) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> U45#(mark(X1),X2) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> U46#(mark(X)) mark#(U46(X)) -> active#(U46(mark(X))) mark#(isNatIList(X)) -> active#(isNatIList(X)) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> U52#(mark(X)) mark#(U52(X)) -> active#(U52(mark(X))) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> U61#(mark(X)) mark#(U61(X)) -> active#(U61(mark(X))) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> U71#(mark(X)) mark#(U71(X)) -> active#(U71(mark(X))) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> U81#(mark(X1),X2,X3) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> U82#(mark(X1),X2,X3) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> U83#(mark(X1),X2,X3) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> U84#(mark(X1),X2,X3) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> U85#(mark(X1),X2) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> U86#(mark(X)) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> U91#(mark(X1),X2,X3) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> U92#(mark(X1),X2,X3) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> U93#(mark(X1),X2,X3) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> U94#(mark(X1),X2) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> mark#(X) mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> active#(length(mark(X))) mark#(nil()) -> active#(nil()) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) isNatIListKind#(mark(X)) -> isNatIListKind#(X) isNatIListKind#(active(X)) -> isNatIListKind#(X) U13#(mark(X)) -> U13#(X) U13#(active(X)) -> U13#(X) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) U32#(active(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) U33#(mark(X)) -> U33#(X) U33#(active(X)) -> U33#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) U45#(active(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) U46#(mark(X)) -> U46#(X) U46#(active(X)) -> U46#(X) isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) U61#(mark(X)) -> U61#(X) U61#(active(X)) -> U61#(X) U71#(mark(X)) -> U71#(X) U71#(active(X)) -> U71#(X) U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3) U81#(active(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,active(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3) U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3) U82#(active(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,active(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3) U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3) U83#(active(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,active(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3) U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3) U84#(active(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,active(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3) U85#(mark(X1),X2) -> U85#(X1,X2) U85#(X1,mark(X2)) -> U85#(X1,X2) U85#(active(X1),X2) -> U85#(X1,X2) U85#(X1,active(X2)) -> U85#(X1,X2) U86#(mark(X)) -> U86#(X) U86#(active(X)) -> U86#(X) U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3) U91#(active(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,active(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3) U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3) U92#(active(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,active(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3) U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3) U93#(active(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,active(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3) U94#(mark(X1),X2) -> U94#(X1,X2) U94#(X1,mark(X2)) -> U94#(X1,X2) U94#(active(X1),X2) -> U94#(X1,X2) U94#(X1,active(X2)) -> U94#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) graph: ... SCC Processor: #sccs: 38 #rules: 259 #arcs: 13527/123904 DPs: mark#(nil()) -> active#(nil()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) mark#(0()) -> active#(0()) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) mark#(tt()) -> active#(tt()) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) active#(U33(tt())) -> mark#(tt()) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) active#(isNatIList(zeros())) -> mark#(tt()) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 1, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 1, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 1, [active](x0) = 0, [zeros] = 1 orientation: mark#(nil()) = 1 >= 1 = active#(nil()) active#(zeros()) = 1 >= 1 = mark#(cons(0(),zeros())) mark#(zeros()) = 1 >= 1 = active#(zeros()) active#(U11(tt(),V1)) = 1 >= 1 = mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) = 1 >= 1 = mark#(X1) mark#(cons(X1,X2)) = 1 >= 0 = active#(cons(mark(X1),X2)) active#(U12(tt(),V1)) = 1 >= 1 = mark#(U13(isNatList(V1))) mark#(0()) = 1 >= 1 = active#(0()) active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) mark#(tt()) = 1 >= 1 = active#(tt()) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) active#(U32(tt(),V)) = 1 >= 1 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) active#(U33(tt())) = 1 >= 1 = mark#(tt()) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 1 >= 1 = mark#(tt()) mark#(U32(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U32(X1,X2)) = 1 >= 1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = 1 >= 1 = mark#(X) mark#(U33(X)) = 1 >= 1 = active#(U33(mark(X))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 1 >= 1 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) active#(isNatIList(V)) = 1 >= 1 = mark#(U31(isNatIListKind(V),V)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) active#(isNatIList(zeros())) = 1 >= 1 = mark#(tt()) mark#(U91(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) mark#(s(X)) = 1 >= 1 = active#(s(mark(X))) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = mark#(X) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 1 >= 1 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(nil())) = 1 >= 1 = mark#(0()) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 1 >= 1 = U33(X) U33(active(X)) = 1 >= 1 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: mark#(nil()) -> active#(nil()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) -> mark#(X1) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) mark#(0()) -> active#(0()) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) mark#(tt()) -> active#(tt()) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) active#(U33(tt())) -> mark#(tt()) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) active#(isNatIList(zeros())) -> mark#(tt()) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = x0, [U94](x0, x1) = x0 + x1, [U93](x0, x1, x2) = x0 + x1, [U92](x0, x1, x2) = x0 + x1, [U91](x0, x1, x2) = x0 + x1, [U86](x0) = x0, [U85](x0, x1) = x0, [U84](x0, x1, x2) = x0, [U83](x0, x1, x2) = x0, [U82](x0, x1, x2) = x0, [U81](x0, x1, x2) = x0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 1, [U45](x0, x1) = x0 + 1, [U44](x0, x1, x2) = x0 + 1, [U43](x0, x1, x2) = x0 + 1, [U42](x0, x1, x2) = x0 + 1, [U41](x0, x1, x2) = x0 + 1, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = x0, [isNatKind](x0) = 0, [U21](x0, x1) = x0, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = x0, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: mark#(nil()) = 0 >= 0 = active#(nil()) active#(zeros()) = 0 >= 0 = mark#(cons(0(),zeros())) mark#(zeros()) = 0 >= 0 = active#(zeros()) active#(U11(tt(),V1)) = 0 >= 0 = mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1) active#(U12(tt(),V1)) = 0 >= 0 = mark#(U13(isNatList(V1))) mark#(0()) = 0 >= 0 = active#(0()) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) mark#(tt()) = 0 >= 0 = active#(tt()) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) active#(U32(tt(),V)) = 0 >= 0 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) active#(U33(tt())) = 0 >= 0 = mark#(tt()) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 >= X1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = X >= X = mark#(X) mark#(U33(X)) = X >= X = active#(U33(mark(X))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = X1 + 1 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = X1 + 1 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = X1 + 1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = X1 + 1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L >= L = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L >= L = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L >= L = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 >= X1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L >= L = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 >= X1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 >= X1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 0 >= 0 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 >= X1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 >= X1 = active#(U85(mark(X1),X2)) active#(isNatIList(V)) = 1 >= 0 = mark#(U31(isNatIListKind(V),V)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) active#(isNatIList(zeros())) = 1 >= 0 = mark#(tt()) mark#(U91(X1,X2,X3)) = X1 + X2 >= X1 = mark#(X1) mark#(U91(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X1 + X2 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X1 + X2 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U94(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = active#(s(mark(X))) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X >= X = mark#(X) mark#(length(X)) = X >= X = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 0 >= 0 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(nil())) = 0 >= 0 = mark#(0()) active#(length(cons(N,L))) = L + N >= L = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L >= L = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L >= L = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L >= L = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L >= L = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = L + N >= L = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 >= X1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 >= X1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = X1 >= X1 = active(U32(mark(X1),X2)) mark(U33(X)) = X >= X = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = X1 + 1 >= X1 + 1 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 >= X1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 >= X1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 >= X1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 >= X1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 >= X1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X1 + X2 >= X1 + X2 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,mark(X2)) = X1 >= X1 = U12(X1,X2) U12(active(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,active(X2)) = X1 >= X1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,mark(X2)) = X1 >= X1 = U21(X1,X2) U21(active(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,active(X2)) = X1 >= X1 = U21(X1,X2) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X1),X2) = X1 >= X1 = U32(X1,X2) U32(X1,mark(X2)) = X1 >= X1 = U32(X1,X2) U32(active(X1),X2) = X1 >= X1 = U32(X1,X2) U32(X1,active(X2)) = X1 >= X1 = U32(X1,X2) U33(mark(X)) = X >= X = U33(X) U33(active(X)) = X >= X = U33(X) U41(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 + 1 >= X1 + 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 + 1 >= X1 + 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 + 1 >= X1 + 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 + 1 >= X1 + 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 + 1 >= X1 + 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X1 + 1 >= X1 + 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X1 + 1 >= X1 + 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X1 + 1 >= X1 + 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X1 + 1 >= X1 + 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X1 + 1 >= X1 + 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = X1 + 1 >= X1 + 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = X1 + 1 >= X1 + 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = X1 + 1 >= X1 + 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = X1 + 1 >= X1 + 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = X1 + 1 >= X1 + 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = X1 + 1 >= X1 + 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = X1 + 1 >= X1 + 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = X1 + 1 >= X1 + 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = X1 + 1 >= X1 + 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = X1 + 1 >= X1 + 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = X1 + 1 >= X1 + 1 = U44(X1,X2,X3) U45(mark(X1),X2) = X1 + 1 >= X1 + 1 = U45(X1,X2) U45(X1,mark(X2)) = X1 + 1 >= X1 + 1 = U45(X1,X2) U45(active(X1),X2) = X1 + 1 >= X1 + 1 = U45(X1,X2) U45(X1,active(X2)) = X1 + 1 >= X1 + 1 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 >= X1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 >= X1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 >= X1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 >= X1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 >= X1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 >= X1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 >= X1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 >= X1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,mark(X2)) = X1 >= X1 = U85(X1,X2) U85(active(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,active(X2)) = X1 >= X1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U94(mark(X1),X2) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(active(X1),X2) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(X1,active(X2)) = X1 + X2 >= X1 + X2 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) problem: DPs: mark#(nil()) -> active#(nil()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) -> mark#(X1) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) mark#(0()) -> active#(0()) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) mark#(tt()) -> active#(tt()) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) active#(U33(tt())) -> mark#(tt()) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 1, [s](x0) = x0, [length](x0) = x0, [U94](x0, x1) = x0 + x1, [U93](x0, x1, x2) = x0 + x1, [U92](x0, x1, x2) = x0 + x1, [U91](x0, x1, x2) = x0 + x1, [U86](x0) = x0, [U85](x0, x1) = x0, [U84](x0, x1, x2) = x0, [U83](x0, x1, x2) = x0, [U82](x0, x1, x2) = x0, [U81](x0, x1, x2) = x0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = x0, [isNatKind](x0) = 0, [U21](x0, x1) = x0, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = x0, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: mark#(nil()) = 1 >= 1 = active#(nil()) active#(zeros()) = 0 >= 0 = mark#(cons(0(),zeros())) mark#(zeros()) = 0 >= 0 = active#(zeros()) active#(U11(tt(),V1)) = 0 >= 0 = mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1) active#(U12(tt(),V1)) = 0 >= 0 = mark#(U13(isNatList(V1))) mark#(0()) = 0 >= 0 = active#(0()) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) mark#(tt()) = 0 >= 0 = active#(tt()) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) active#(U32(tt(),V)) = 0 >= 0 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) active#(U33(tt())) = 0 >= 0 = mark#(tt()) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 >= X1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 >= X1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = X >= X = mark#(X) mark#(U33(X)) = X >= X = active#(U33(mark(X))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L >= L = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L >= L = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L >= L = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 >= X1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L >= L = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 >= X1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 >= X1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 0 >= 0 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 >= X1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 >= X1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X1 + X2 >= X1 = mark#(X1) mark#(U91(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X1 + X2 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X1 + X2 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U94(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = active#(s(mark(X))) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X >= X = mark#(X) mark#(length(X)) = X >= X = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 0 >= 0 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(nil())) = 1 >= 0 = mark#(0()) active#(length(cons(N,L))) = L + N >= L = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L >= L = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L >= L = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L >= L = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L >= L = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N >= L = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 >= X1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 >= X1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = X1 >= X1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = X1 >= X1 = active(U32(mark(X1),X2)) mark(U33(X)) = X >= X = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 >= X1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 >= X1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 >= X1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 >= X1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 >= X1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X1 + X2 >= X1 + X2 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,mark(X2)) = X1 >= X1 = U12(X1,X2) U12(active(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,active(X2)) = X1 >= X1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,mark(X2)) = X1 >= X1 = U21(X1,X2) U21(active(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,active(X2)) = X1 >= X1 = U21(X1,X2) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,mark(X2)) = X1 >= X1 = U31(X1,X2) U31(active(X1),X2) = X1 >= X1 = U31(X1,X2) U31(X1,active(X2)) = X1 >= X1 = U31(X1,X2) U32(mark(X1),X2) = X1 >= X1 = U32(X1,X2) U32(X1,mark(X2)) = X1 >= X1 = U32(X1,X2) U32(active(X1),X2) = X1 >= X1 = U32(X1,X2) U32(X1,active(X2)) = X1 >= X1 = U32(X1,X2) U33(mark(X)) = X >= X = U33(X) U33(active(X)) = X >= X = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 >= X1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 >= X1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 >= X1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 >= X1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 >= X1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 >= X1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 >= X1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 >= X1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,mark(X2)) = X1 >= X1 = U85(X1,X2) U85(active(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,active(X2)) = X1 >= X1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U94(mark(X1),X2) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(active(X1),X2) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(X1,active(X2)) = X1 + X2 >= X1 + X2 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) problem: DPs: mark#(nil()) -> active#(nil()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) -> mark#(X1) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) mark#(0()) -> active#(0()) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) mark#(tt()) -> active#(tt()) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) active#(U33(tt())) -> mark#(tt()) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 1, [0] = 1, [active](x0) = 0, [zeros] = 1 orientation: mark#(nil()) = 1 >= 0 = active#(nil()) active#(zeros()) = 1 >= 1 = mark#(cons(0(),zeros())) mark#(zeros()) = 1 >= 1 = active#(zeros()) active#(U11(tt(),V1)) = 1 >= 1 = mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) = 1 >= 1 = mark#(X1) active#(U12(tt(),V1)) = 1 >= 1 = mark#(U13(isNatList(V1))) mark#(0()) = 1 >= 1 = active#(0()) active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) mark#(tt()) = 1 >= 0 = active#(tt()) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) active#(U32(tt(),V)) = 1 >= 1 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) active#(U33(tt())) = 1 >= 1 = mark#(tt()) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 1 >= 1 = mark#(tt()) mark#(U32(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U32(X1,X2)) = 1 >= 1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = 1 >= 1 = mark#(X) mark#(U33(X)) = 1 >= 1 = active#(U33(mark(X))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 1 >= 1 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) mark#(s(X)) = 1 >= 1 = active#(s(mark(X))) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = mark#(X) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 1 >= 1 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 1 >= 1 = U33(X) U33(active(X)) = 1 >= 1 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) -> mark#(X1) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) mark#(0()) -> active#(0()) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) active#(U33(tt())) -> mark#(tt()) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = 0, [zeros] = 1 orientation: active#(zeros()) = 1 >= 1 = mark#(cons(0(),zeros())) mark#(zeros()) = 1 >= 1 = active#(zeros()) active#(U11(tt(),V1)) = 1 >= 1 = mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) = 1 >= 1 = mark#(X1) active#(U12(tt(),V1)) = 1 >= 1 = mark#(U13(isNatList(V1))) mark#(0()) = 1 >= 0 = active#(0()) active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) active#(U32(tt(),V)) = 1 >= 1 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) active#(U33(tt())) = 1 >= 1 = mark#(tt()) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 1 >= 1 = mark#(tt()) mark#(U32(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U32(X1,X2)) = 1 >= 1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = 1 >= 1 = mark#(X) mark#(U33(X)) = 1 >= 1 = active#(U33(mark(X))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 1 >= 1 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) mark#(s(X)) = 1 >= 0 = active#(s(mark(X))) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = mark#(X) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 1 >= 1 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 1 >= 1 = U33(X) U33(active(X)) = 1 >= 1 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) -> mark#(X1) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) active#(U33(tt())) -> mark#(tt()) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 1, [s](x0) = x0, [length](x0) = x0, [U94](x0, x1) = x0 + x1, [U93](x0, x1, x2) = x0 + x1, [U92](x0, x1, x2) = x0 + x1 + x2, [U91](x0, x1, x2) = x0 + x1 + x2, [U86](x0) = x0, [U85](x0, x1) = x0, [U84](x0, x1, x2) = x0, [U83](x0, x1, x2) = x0, [U82](x0, x1, x2) = x0, [U81](x0, x1, x2) = x0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = x0 + 1, [U32](x0, x1) = x0 + 1, [U31](x0, x1) = x0 + 1, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = x0, [isNatKind](x0) = 0, [U21](x0, x1) = x0, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = x0, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(zeros()) = 0 >= 0 = mark#(cons(0(),zeros())) mark#(zeros()) = 0 >= 0 = active#(zeros()) active#(U11(tt(),V1)) = 0 >= 0 = mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1) active#(U12(tt(),V1)) = 0 >= 0 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) active#(U32(tt(),V)) = 1 >= 1 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) active#(U33(tt())) = 1 >= 0 = mark#(tt()) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 >= X1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U31(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = X + 1 >= X = mark#(X) mark#(U33(X)) = X + 1 >= X + 1 = active#(U33(mark(X))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + N >= L + N = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + N >= L = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L >= L = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 >= X1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L >= L = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 >= X1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 >= X1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 0 >= 0 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 >= X1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 >= X1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U91(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X1 + X2 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U94(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X >= X = mark#(X) mark#(length(X)) = X >= X = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 0 >= 0 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N >= L + N = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + N >= L + N = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + N >= L = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L >= L = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L >= L = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N >= L + N = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 >= X1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 >= X1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = X1 + 1 >= X1 + 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = X1 + 1 >= X1 + 1 = active(U32(mark(X1),X2)) mark(U33(X)) = X + 1 >= X + 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 >= X1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 >= X1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 >= X1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 >= X1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 >= X1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X1 + X2 >= X1 + X2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X1 + X2 >= X1 + X2 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,mark(X2)) = X1 >= X1 = U12(X1,X2) U12(active(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,active(X2)) = X1 >= X1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,mark(X2)) = X1 >= X1 = U21(X1,X2) U21(active(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,active(X2)) = X1 >= X1 = U21(X1,X2) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(X1,mark(X2)) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(active(X1),X2) = X1 + 1 >= X1 + 1 = U31(X1,X2) U31(X1,active(X2)) = X1 + 1 >= X1 + 1 = U31(X1,X2) U32(mark(X1),X2) = X1 + 1 >= X1 + 1 = U32(X1,X2) U32(X1,mark(X2)) = X1 + 1 >= X1 + 1 = U32(X1,X2) U32(active(X1),X2) = X1 + 1 >= X1 + 1 = U32(X1,X2) U32(X1,active(X2)) = X1 + 1 >= X1 + 1 = U32(X1,X2) U33(mark(X)) = X + 1 >= X + 1 = U33(X) U33(active(X)) = X + 1 >= X + 1 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 >= X1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 >= X1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 >= X1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 >= X1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 >= X1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 >= X1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 >= X1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 >= X1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,mark(X2)) = X1 >= X1 = U85(X1,X2) U85(active(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,active(X2)) = X1 >= X1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X1 + X2 >= X1 + X2 = U93(X1,X2,X3) U94(mark(X1),X2) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(active(X1),X2) = X1 + X2 >= X1 + X2 = U94(X1,X2) U94(X1,active(X2)) = X1 + X2 >= X1 + X2 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) problem: DPs: active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) -> mark#(X1) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> mark#(X1) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = x0 + 1, [U94](x0, x1) = x0 + x1 + 1, [U93](x0, x1, x2) = x0 + x1 + 1, [U92](x0, x1, x2) = x0 + x1 + 1, [U91](x0, x1, x2) = x0 + x1 + 1, [U86](x0) = x0, [U85](x0, x1) = x0, [U84](x0, x1, x2) = x0, [U83](x0, x1, x2) = x0, [U82](x0, x1, x2) = x0, [U81](x0, x1, x2) = x0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = x0, [isNatKind](x0) = 0, [U21](x0, x1) = x0, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = x0, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(zeros()) = 0 >= 0 = mark#(cons(0(),zeros())) mark#(zeros()) = 0 >= 0 = active#(zeros()) active#(U11(tt(),V1)) = 0 >= 0 = mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1) active#(U12(tt(),V1)) = 0 >= 0 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) active#(U32(tt(),V)) = 0 >= 0 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 >= X1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 0 >= 0 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = 0 >= 0 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = 0 >= 0 = active#(U33(mark(X))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + 1 >= L + 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + 1 >= L + 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L + 1 >= L + 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 >= X1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L + 1 >= L + 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 >= X1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 >= X1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 0 >= 0 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 >= X1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 >= X1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U91(X1,X2,X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U94(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X + 1 >= X = mark#(X) mark#(length(X)) = X + 1 >= X + 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 0 >= 0 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N + 1 >= L + 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + 1 >= L + 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + 1 >= L + 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L + 1 >= L + 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L + 1 >= L + 1 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N + 1 >= L + 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 >= X1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 >= X1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 >= X1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 >= X1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 >= X1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 >= X1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 >= X1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X + 1 >= X + 1 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,mark(X2)) = X1 >= X1 = U12(X1,X2) U12(active(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,active(X2)) = X1 >= X1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,mark(X2)) = X1 >= X1 = U21(X1,X2) U21(active(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,active(X2)) = X1 >= X1 = U21(X1,X2) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 >= X1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 >= X1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 >= X1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 >= X1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 >= X1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 >= X1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 >= X1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 >= X1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,mark(X2)) = X1 >= X1 = U85(X1,X2) U85(active(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,active(X2)) = X1 >= X1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = U93(X1,X2,X3) U94(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U94(X1,X2) U94(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U94(X1,X2) U94(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U94(X1,X2) U94(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X + 1 >= X + 1 = length(X) length(active(X)) = X + 1 >= X + 1 = length(X) problem: DPs: active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) -> mark#(X1) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [active#](x0) = x0 + 1, [nil] = 0, [s](x0) = x0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = x0, [U85](x0, x1) = x0, [U84](x0, x1, x2) = x0, [U83](x0, x1, x2) = x0, [U82](x0, x1, x2) = x0, [U81](x0, x1, x2) = x0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = x0, [isNatKind](x0) = 0, [U21](x0, x1) = x0, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = x0, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + 1, [0] = 0, [active](x0) = x0, [zeros] = 1 orientation: active#(zeros()) = 2 >= 2 = mark#(cons(0(),zeros())) mark#(zeros()) = 2 >= 2 = active#(zeros()) active#(U11(tt(),V1)) = 1 >= 1 = mark#(U12(isNatIListKind(V1),V1)) mark#(cons(X1,X2)) = X1 + 2 >= X1 + 1 = mark#(X1) active#(U12(tt(),V1)) = 1 >= 1 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U11(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U12(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = X + 1 >= X + 1 = mark#(X) mark#(U13(X)) = X + 1 >= X + 1 = active#(U13(mark(X))) active#(U32(tt(),V)) = 1 >= 1 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U21(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 2 >= 2 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U22(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 2 >= 2 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 2 >= 2 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X + 1 >= X + 1 = mark#(X) mark#(U23(X)) = X + 1 >= X + 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 2 >= 2 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 2 >= 2 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 1 >= 1 = mark#(tt()) mark#(U32(X1,X2)) = 1 >= 1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = 1 >= 1 = active#(U33(mark(X))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 2 >= 2 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 2 >= 2 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 2 >= 2 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 2 >= 2 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 2 >= 2 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X + 1 >= X + 1 = mark#(X) mark#(U46(X)) = X + 1 >= X + 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 2 >= 2 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U51(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = X + 1 >= X + 1 = mark#(X) mark#(U52(X)) = X + 1 >= X + 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X + 1 >= X + 1 = mark#(X) mark#(U61(X)) = X + 1 >= X + 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X + 1 >= X + 1 = mark#(X) mark#(U71(X)) = X + 1 >= X + 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 1 >= 1 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 + 1 >= X1 + 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U85(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X + 1 >= X + 1 = mark#(X) mark#(U86(X)) = X + 1 >= X + 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 2 >= 2 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X + 1 >= X + 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 1 >= 1 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X1 + 1 >= X1 + 1 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 >= X1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 >= X1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 >= X1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 >= X1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 >= X1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 >= X1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 >= X1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = X1 + 1 >= X1 + 1 = cons(X1,X2) cons(X1,mark(X2)) = X1 + 1 >= X1 + 1 = cons(X1,X2) cons(active(X1),X2) = X1 + 1 >= X1 + 1 = cons(X1,X2) cons(X1,active(X2)) = X1 + 1 >= X1 + 1 = cons(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,mark(X2)) = X1 >= X1 = U12(X1,X2) U12(active(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,active(X2)) = X1 >= X1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,mark(X2)) = X1 >= X1 = U21(X1,X2) U21(active(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,active(X2)) = X1 >= X1 = U21(X1,X2) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 >= X1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 >= X1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 >= X1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 >= X1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 >= X1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 >= X1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 >= X1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 >= X1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,mark(X2)) = X1 >= X1 = U85(X1,X2) U85(active(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,active(X2)) = X1 >= X1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U33(X)) -> active#(U33(mark(X))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = 0, [zeros] = 1 orientation: active#(zeros()) = 1 >= 1 = mark#(cons(0(),zeros())) mark#(zeros()) = 1 >= 1 = active#(zeros()) active#(U11(tt(),V1)) = 1 >= 1 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = 1 >= 1 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 1 >= 1 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) active#(U32(tt(),V)) = 1 >= 1 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 1 >= 1 = mark#(tt()) mark#(U32(X1,X2)) = 1 >= 1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) mark#(U33(X)) = 1 >= 0 = active#(U33(mark(X))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 1 >= 1 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 1 >= 1 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = 0, [nil] = 1, [s](x0) = x0, [length](x0) = 0, [U94](x0, x1) = x0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = 0, [U86](x0) = x0, [U85](x0, x1) = x0, [U84](x0, x1, x2) = x0, [U83](x0, x1, x2) = x0, [U82](x0, x1, x2) = x0, [U81](x0, x1, x2) = x0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = x0, [isNatKind](x0) = 0, [U21](x0, x1) = x0, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = x0, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0, [zeros] = 1 orientation: active#(zeros()) = 0 >= 0 = mark#(cons(0(),zeros())) mark#(zeros()) = 1 >= 0 = active#(zeros()) active#(U11(tt(),V1)) = 0 >= 0 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = 0 >= 0 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= 0 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= 0 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= 0 = active#(U13(mark(X))) active#(U32(tt(),V)) = 0 >= 0 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 >= 0 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= 0 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= 0 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 0 >= 0 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = 0 >= 0 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = X1 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = X1 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = X1 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= 0 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= 0 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= 0 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 0 >= 0 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= 0 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 0 >= 0 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= 0 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 0 >= 0 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 0 >= 0 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 >= 0 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 >= 0 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 0 >= 0 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= 0 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 0 >= 0 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X1 >= 0 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = 0 >= 0 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X1 >= 0 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = 0 >= 0 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 0 >= 0 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 0 >= 0 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 >= X1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 >= X1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X1 >= X1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = X1 >= X1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = X1 >= X1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 >= X1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 >= X1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 >= X1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 >= X1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 >= X1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X1 >= X1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X1 >= X1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,mark(X2)) = X1 >= X1 = U12(X1,X2) U12(active(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,active(X2)) = X1 >= X1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,mark(X2)) = X1 >= X1 = U21(X1,X2) U21(active(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,active(X2)) = X1 >= X1 = U21(X1,X2) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X1 >= X1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X1 >= X1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X1 >= X1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = X1 >= X1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = X1 >= X1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = X1 >= X1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = X1 >= X1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = X1 >= X1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = X1 >= X1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = X1 >= X1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = X1 >= X1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = X1 >= X1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = X1 >= X1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = X1 >= X1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = X1 >= X1 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 >= X1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 >= X1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 >= X1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 >= X1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 >= X1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 >= X1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 >= X1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 >= X1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,mark(X2)) = X1 >= X1 = U85(X1,X2) U85(active(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,active(X2)) = X1 >= X1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X1 >= X1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X1 >= X1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X1 >= X1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X1 >= X1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X1 >= X1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X1 >= X1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = X1 >= X1 = U94(X1,X2) U94(X1,mark(X2)) = X1 >= X1 = U94(X1,X2) U94(active(X1),X2) = X1 >= X1 = U94(X1,X2) U94(X1,active(X2)) = X1 >= X1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 0, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = 0, [zeros] = 1 orientation: active#(zeros()) = 1 >= 0 = mark#(cons(0(),zeros())) active#(U11(tt(),V1)) = 0 >= 0 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = 0 >= 0 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U11(X1,X2)) = 0 >= 0 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U12(X1,X2)) = 0 >= 0 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 0 >= 0 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = 0 >= 0 = mark#(X) mark#(U13(X)) = 0 >= 0 = active#(U13(mark(X))) active#(U32(tt(),V)) = 0 >= 0 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U21(X1,X2)) = 0 >= 0 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 0 >= 0 = mark#(X) mark#(U23(X)) = 0 >= 0 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 0 >= 0 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = 0 >= 0 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 0 >= 0 = mark#(X) mark#(U46(X)) = 0 >= 0 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U51(X1,X2)) = 0 >= 0 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = 0 >= 0 = mark#(X) mark#(U52(X)) = 0 >= 0 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 0 >= 0 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 0 >= 0 = mark#(X) mark#(U61(X)) = 0 >= 0 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 0 >= 0 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 0 >= 0 = mark#(X) mark#(U71(X)) = 0 >= 0 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 0 >= 0 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 0 >= 0 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 0 >= 0 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 0 >= 0 = mark#(X) mark#(U86(X)) = 0 >= 0 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 0 >= 0 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 0 >= 0 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = 0 >= 0 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = 0 >= 0 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 0 >= 0 = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = 0 >= 0 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 0 >= 0 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 0 >= 0 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = x0, [U85](x0, x1) = x0, [U84](x0, x1, x2) = x0, [U83](x0, x1, x2) = x0, [U82](x0, x1, x2) = x0, [U81](x0, x1, x2) = x0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = x0, [isNatKind](x0) = 0, [U21](x0, x1) = x0, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = x0, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0, [zeros] = 1 orientation: active#(U11(tt(),V1)) = 0 >= 0 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = 0 >= 0 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) active#(U31(tt(),V)) = 1 >= 0 = mark#(U32(isNatIListKind(V),V)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) active#(U32(tt(),V)) = 0 >= 0 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 >= X1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 1 >= 1 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = 0 >= 0 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 0 >= 0 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 0 >= 0 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 0 >= 0 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 >= X1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 0 >= 0 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 >= X1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 >= X1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 0 >= 0 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 >= X1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 >= X1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 0 >= 0 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 0 >= 0 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = 0 >= 0 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = 0 >= 0 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = 0 >= 0 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 0 >= 0 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 0 >= 0 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 >= X1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 >= X1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 >= X1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 >= X1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 >= X1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 >= X1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 >= X1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,mark(X2)) = X1 >= X1 = U12(X1,X2) U12(active(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,active(X2)) = X1 >= X1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,mark(X2)) = X1 >= X1 = U21(X1,X2) U21(active(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,active(X2)) = X1 >= X1 = U21(X1,X2) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 >= X1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 >= X1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 >= X1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 >= X1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 >= X1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 >= X1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 >= X1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 >= X1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,mark(X2)) = X1 >= X1 = U85(X1,X2) U85(active(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,active(X2)) = X1 >= X1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 0, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = 0, [zeros] = 0 orientation: active#(U11(tt(),V1)) = 1 >= 1 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = 1 >= 1 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) active#(U32(tt(),V)) = 1 >= 1 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) mark#(U31(X1,X2)) = 1 >= 0 = active#(U31(mark(X1),X2)) active#(U46(tt())) = 1 >= 1 = mark#(tt()) mark#(U32(X1,X2)) = 1 >= 1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 1 >= 1 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 1 >= 1 = mark#(tt()) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 1, [s](x0) = x0, [length](x0) = x0, [U94](x0, x1) = x1, [U93](x0, x1, x2) = x1, [U92](x0, x1, x2) = x1, [U91](x0, x1, x2) = x1, [U86](x0) = x0, [U85](x0, x1) = x0 + x1, [U84](x0, x1, x2) = x0 + x1 + x2, [U83](x0, x1, x2) = x0 + x1 + x2, [U82](x0, x1, x2) = x0 + x1 + x2, [U81](x0, x1, x2) = x0 + x1 + x2, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = x0, [U22](x0, x1) = x0 + x1, [isNatKind](x0) = 0, [U21](x0, x1) = x0 + x1, [U13](x0) = x0, [isNatList](x0) = x0, [U12](x0, x1) = x0 + x1, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(U11(tt(),V1)) = V1 >= V1 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = V1 >= V1 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = V1 >= V1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = V1 >= V1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) active#(U32(tt(),V)) = 0 >= 0 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = X >= X = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = X >= X = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = 0 >= 0 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = V2 >= V2 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L >= L = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L >= L = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L >= L = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L >= L = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = V1 >= V1 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = V1 >= V1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 >= X2 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 >= X2 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X2 >= X2 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X2 >= X2 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X >= X = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(nil())) = 1 >= 0 = mark#(tt()) active#(isNatList(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N >= L = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = V1 >= V1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = V1 >= V1 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = V1 >= V1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = V1 >= V1 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = V2 >= V2 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L >= L = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L >= L = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L >= L = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L >= L = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = V1 >= V1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N >= L = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = X >= X = active(isNatList(X)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = X >= X = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 + X2 >= X1 + X2 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 >= X2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 >= X2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 >= X2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 >= X2 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X1),X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(active(X1),X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(X1,active(X2)) = X1 + X2 >= X1 + X2 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(active(X1),X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(X1,active(X2)) = X1 + X2 >= X1 + X2 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 >= X2 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 >= X2 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 >= X2 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 >= X2 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 >= X2 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 >= X2 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 >= X2 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 >= X2 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 >= X2 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 >= X2 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 >= X2 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 >= X2 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 >= X2 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 >= X2 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 >= X2 = U94(X1,X2) U94(X1,mark(X2)) = X2 >= X2 = U94(X1,X2) U94(active(X1),X2) = X2 >= X2 = U94(X1,X2) U94(X1,active(X2)) = X2 >= X2 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) problem: DPs: active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 1, [s](x0) = x0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = x0, [U85](x0, x1) = x0, [U84](x0, x1, x2) = x0, [U83](x0, x1, x2) = x0, [U82](x0, x1, x2) = x0, [U81](x0, x1, x2) = x0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = x0, [isNatKind](x0) = 0, [U21](x0, x1) = x0, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = x0, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0, [zeros] = 1 orientation: active#(U11(tt(),V1)) = 0 >= 0 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = 0 >= 0 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 >= X1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) active#(U32(tt(),V)) = 1 >= 0 = mark#(U33(isNatList(V))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 >= X1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = 1 >= 1 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 0 >= 0 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 0 >= 0 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 0 >= 0 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 >= X1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 0 >= 0 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 >= X1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 >= X1 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = 0 >= 0 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 >= X1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 >= X1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 0 >= 0 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 0 >= 0 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = 0 >= 0 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = 0 >= 0 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = 0 >= 0 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 0 >= 0 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 >= X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 >= X1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 >= X1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 >= X1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 >= X1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 >= X1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 >= X1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 >= X1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 >= X1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 >= X1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 >= X2 = cons(X1,X2) U11(mark(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,mark(X2)) = X1 >= X1 = U11(X1,X2) U11(active(X1),X2) = X1 >= X1 = U11(X1,X2) U11(X1,active(X2)) = X1 >= X1 = U11(X1,X2) U12(mark(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,mark(X2)) = X1 >= X1 = U12(X1,X2) U12(active(X1),X2) = X1 >= X1 = U12(X1,X2) U12(X1,active(X2)) = X1 >= X1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,mark(X2)) = X1 >= X1 = U21(X1,X2) U21(active(X1),X2) = X1 >= X1 = U21(X1,X2) U21(X1,active(X2)) = X1 >= X1 = U21(X1,X2) U22(mark(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,mark(X2)) = X1 >= X1 = U22(X1,X2) U22(active(X1),X2) = X1 >= X1 = U22(X1,X2) U22(X1,active(X2)) = X1 >= X1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 >= X1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 >= X1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 >= X1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 >= X1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 >= X1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 >= X1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 >= X1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 >= X1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 >= X1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 >= X1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 >= X1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 >= X1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,mark(X2)) = X1 >= X1 = U85(X1,X2) U85(active(X1),X2) = X1 >= X1 = U85(X1,X2) U85(X1,active(X2)) = X1 >= X1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = x0 + 1, [U94](x0, x1) = x1 + 1, [U93](x0, x1, x2) = x1 + 1, [U92](x0, x1, x2) = x1 + 1, [U91](x0, x1, x2) = x1 + 1, [U86](x0) = x0, [U85](x0, x1) = x0 + x1, [U84](x0, x1, x2) = x0 + x1 + x2, [U83](x0, x1, x2) = x0 + x1 + x2, [U82](x0, x1, x2) = x0 + x1 + x2, [U81](x0, x1, x2) = x0 + x1 + x2, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = x0, [U22](x0, x1) = x0 + x1, [isNatKind](x0) = 0, [U21](x0, x1) = x0 + x1, [U13](x0) = x0, [isNatList](x0) = x0, [U12](x0, x1) = x0 + x1, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0 + x1, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(U11(tt(),V1)) = V1 >= V1 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = V1 >= V1 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = V1 >= V1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = V1 >= V1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) mark#(isNatList(X)) = X >= X = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = X >= X = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) mark#(U32(X1,X2)) = 0 >= 0 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = V2 >= V2 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + 1 >= L + 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + 1 >= L + 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L + 1 >= L + 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L + 1 >= L + 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U83(mark(X1),X2,X3)) active#(isNat(length(V1))) = V1 + 1 >= V1 = mark#(U11(isNatIListKind(V1),V1)) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = V1 >= V1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X + 1 >= X + 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N + 1 >= L + 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = V1 >= V1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = V1 >= V1 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = V1 >= V1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = V1 >= V1 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = V2 >= V2 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + 1 >= L + 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + 1 >= L + 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L + 1 >= L + 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L + 1 >= L + 1 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = V1 + 1 >= V1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N + 1 >= L + 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = X >= X = active(isNatList(X)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = X >= X = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 + X2 >= X1 + X2 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X + 1 >= X + 1 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 >= X1 + X2 = U11(X1,X2) U12(mark(X1),X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(active(X1),X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(X1,active(X2)) = X1 + X2 >= X1 + X2 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(active(X1),X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(X1,active(X2)) = X1 + X2 >= X1 + X2 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(active(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,active(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X + 1 >= X + 1 = length(X) length(active(X)) = X + 1 >= X + 1 = length(X) problem: DPs: active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = 0, [zeros] = 0 orientation: active#(U11(tt(),V1)) = 1 >= 1 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = 1 >= 1 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 1 >= 1 = mark#(tt()) mark#(U32(X1,X2)) = 1 >= 0 = active#(U32(mark(X1),X2)) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = x0 + 1, [U94](x0, x1) = x1 + 1, [U93](x0, x1, x2) = x1 + 1, [U92](x0, x1, x2) = x1 + 1, [U91](x0, x1, x2) = x1 + 1, [U86](x0) = x0, [U85](x0, x1) = x0 + x1, [U84](x0, x1, x2) = x0 + x1 + x2, [U83](x0, x1, x2) = x0 + x1 + x2, [U82](x0, x1, x2) = x0 + x1 + x2, [U81](x0, x1, x2) = x0 + x1 + x2, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = x0, [U22](x0, x1) = x0 + x1, [isNatKind](x0) = 0, [U21](x0, x1) = x0 + x1, [U13](x0) = x0, [isNatList](x0) = x0, [U12](x0, x1) = x0 + x1, [isNatIListKind](x0) = 0, [U11](x0, x1) = x0 + x1 + 1, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(U11(tt(),V1)) = V1 + 1 >= V1 = mark#(U12(isNatIListKind(V1),V1)) active#(U12(tt(),V1)) = V1 >= V1 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = V1 >= V1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = V1 >= V1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) mark#(isNatList(X)) = X >= X = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = X >= X = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = V2 >= V2 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + 1 >= L + 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + 1 >= L + 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L + 1 >= L + 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L + 1 >= L + 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = V1 >= V1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X + 1 >= X + 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N + 1 >= L + 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = V1 + 1 >= V1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = V1 >= V1 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = V1 >= V1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = V1 >= V1 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = V2 >= V2 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + 1 >= L + 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + 1 >= L + 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L + 1 >= L + 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L + 1 >= L + 1 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = V1 + 1 >= V1 + 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N + 1 >= L + 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = X >= X = active(isNatList(X)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = X >= X = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 + X2 >= X1 + X2 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X + 1 >= X + 1 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) U11(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) U11(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) U11(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) U12(mark(X1),X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(active(X1),X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) U12(X1,active(X2)) = X1 + X2 >= X1 + X2 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(active(X1),X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(X1,active(X2)) = X1 + X2 >= X1 + X2 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(active(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,active(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X + 1 >= X + 1 = length(X) length(active(X)) = X + 1 >= X + 1 = length(X) problem: DPs: active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = x0 + 1, [U94](x0, x1) = x1 + 1, [U93](x0, x1, x2) = x1 + 1, [U92](x0, x1, x2) = x1 + 1, [U91](x0, x1, x2) = x1 + 1, [U86](x0) = x0, [U85](x0, x1) = x0 + x1, [U84](x0, x1, x2) = x0 + x1 + x2, [U83](x0, x1, x2) = x0 + x1 + x2, [U82](x0, x1, x2) = x0 + x1 + x2, [U81](x0, x1, x2) = x0 + x1 + x2, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = x0, [U22](x0, x1) = x0 + x1, [isNatKind](x0) = 0, [U21](x0, x1) = x0 + x1, [U13](x0) = x0, [isNatList](x0) = x0, [U12](x0, x1) = x0 + x1 + 1, [isNatIListKind](x0) = 0, [U11](x0, x1) = x1 + 1, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(U12(tt(),V1)) = V1 + 1 >= V1 = mark#(U13(isNatList(V1))) active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = V1 >= V1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = V1 >= V1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) mark#(isNatList(X)) = X >= X = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = X >= X = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = V2 >= V2 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + 1 >= L + 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + 1 >= L + 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L + 1 >= L + 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L + 1 >= L + 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = V1 >= V1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X + 1 >= X + 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N + 1 >= L + 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = V1 + 1 >= V1 + 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = V1 + 1 >= V1 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = V1 >= V1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = V1 >= V1 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = V1 + V2 >= V1 + V2 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = V2 >= V2 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + 1 >= L + 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + 1 >= L + 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L + 1 >= L + 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L + 1 >= L + 1 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = V1 + 1 >= V1 + 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N + 1 >= L + 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = X >= X = active(isNatList(X)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = X >= X = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 + X2 >= X1 + X2 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X + 1 >= X + 1 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(active(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,active(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U12(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(X1,X2) U12(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(X1,X2) U12(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(X1,X2) U12(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(active(X1),X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) U85(X1,active(X2)) = X1 + X2 >= X1 + X2 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(active(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,active(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X + 1 >= X + 1 = length(X) length(active(X)) = X + 1 >= X + 1 = length(X) problem: DPs: active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = x0 + 1, [U94](x0, x1) = x1 + 1, [U93](x0, x1, x2) = x1 + 1, [U92](x0, x1, x2) = x1 + 1, [U91](x0, x1, x2) = x1 + 1, [U86](x0) = x0, [U85](x0, x1) = x0 + x1 + 1, [U84](x0, x1, x2) = x0 + x1 + x2 + 1, [U83](x0, x1, x2) = x0 + x1 + x2 + 1, [U82](x0, x1, x2) = x0 + x1 + x2 + 1, [U81](x0, x1, x2) = x0 + x1 + x2 + 1, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = x0, [U22](x0, x1) = x0 + x1, [isNatKind](x0) = 0, [U21](x0, x1) = x0 + x1, [U13](x0) = x0, [isNatList](x0) = x0 + 1, [U12](x0, x1) = x1 + 1, [isNatIListKind](x0) = 0, [U11](x0, x1) = x1 + 1, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(U13(tt())) = 0 >= 0 = mark#(tt()) mark#(U11(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = V1 >= V1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = V1 >= V1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) mark#(isNatList(X)) = X + 1 >= X + 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = X >= X = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = V2 + 1 >= V2 + 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + 1 >= L + 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + 1 >= L + 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L + 1 >= L + 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U81(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L + 1 >= L + 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U82(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 0 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U83(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U84(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = V1 >= V1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U85(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X + 1 >= X + 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N + 1 >= L + 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = V1 + 1 >= V1 + 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = V1 + 1 >= V1 + 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = V1 >= V1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = V1 >= V1 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = V2 + 1 >= V2 + 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + 1 >= L + 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + 1 >= L + 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L + 1 >= L + 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L + 1 >= L + 1 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = V1 + 1 >= V1 + 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N + 1 >= L + 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = X2 + 1 >= X2 + 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = X + 1 >= X + 1 = active(isNatList(X)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = X >= X = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X + 1 >= X + 1 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(active(X1),X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) U11(X1,active(X2)) = X2 + 1 >= X2 + 1 = U11(X1,X2) U12(mark(X1),X2) = X2 + 1 >= X2 + 1 = U12(X1,X2) U12(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U12(X1,X2) U12(active(X1),X2) = X2 + 1 >= X2 + 1 = U12(X1,X2) U12(X1,active(X2)) = X2 + 1 >= X2 + 1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = X + 1 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 1 >= X + 1 = isNatList(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U84(X1,X2,X3) U85(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U85(X1,X2) U85(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U85(X1,X2) U85(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U85(X1,X2) U85(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(active(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,active(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X + 1 >= X + 1 = length(X) length(active(X)) = X + 1 >= X + 1 = length(X) problem: DPs: active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 1, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = 0, [zeros] = 0 orientation: active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = 1 >= 1 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) mark#(U12(X1,X2)) = 1 >= 0 = active#(U12(mark(X1),X2)) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 1 >= 1 = U33(X) U33(active(X)) = 1 >= 1 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U13(tt())) -> mark#(tt()) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 1, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = 0, [zeros] = 0 orientation: active#(U13(tt())) = 1 >= 1 = mark#(tt()) mark#(U11(X1,X2)) = 1 >= 0 = active#(U11(mark(X1),X2)) active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 1 = mark#(tt()) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 1 >= 1 = U33(X) U33(active(X)) = 1 >= 1 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U13(tt())) -> mark#(tt()) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 1, [s](x0) = x0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = x0, [U22](x0, x1) = x0 + x1, [isNatKind](x0) = 0, [U21](x0, x1) = x0 + x1, [U13](x0) = x0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0, [0] = 1, [active](x0) = x0, [zeros] = 1 orientation: active#(U13(tt())) = 0 >= 0 = mark#(tt()) active#(U21(tt(),V1)) = V1 >= V1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = V1 >= V1 = mark#(U23(isNat(V1))) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(U13(X)) = X >= X = mark#(X) mark#(U13(X)) = X >= X = active#(U13(mark(X))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = X >= X = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) active#(isNat(0())) = 1 >= 0 = mark#(tt()) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = V1 >= V1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = V1 >= V1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = V1 >= V1 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 0 = mark(tt()) active(isNat(length(V1))) = 1 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X1 >= X1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X >= X = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = X >= X = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X1 >= X1 = cons(X1,X2) cons(X1,mark(X2)) = X1 >= X1 = cons(X1,X2) cons(active(X1),X2) = X1 >= X1 = cons(X1,X2) cons(X1,active(X2)) = X1 >= X1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X >= X = U13(X) U13(active(X)) = X >= X = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U13(tt())) -> mark#(tt()) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = x0, [U22](x0, x1) = x0 + x1, [isNatKind](x0) = 0, [U21](x0, x1) = x0 + x1, [U13](x0) = x0 + 1, [isNatList](x0) = 0, [U12](x0, x1) = 1, [isNatIListKind](x0) = 0, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0, [zeros] = 1 orientation: active#(U13(tt())) = 1 >= 0 = mark#(tt()) active#(U21(tt(),V1)) = V1 >= V1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = V1 >= V1 = mark#(U23(isNat(V1))) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(U13(X)) = X + 1 >= X = mark#(X) mark#(U13(X)) = X + 1 >= X + 1 = active#(U13(mark(X))) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = X >= X = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 >= X1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = V1 >= V1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 0 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 0 = mark(tt()) active(U21(tt(),V1)) = V1 >= V1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = V1 >= V1 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = X + 1 >= X + 1 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = X >= X = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = X + 1 >= X + 1 = U13(X) U13(active(X)) = X + 1 >= X + 1 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(active(X1),X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) U21(X1,active(X2)) = X1 + X2 >= X1 + X2 = U21(X1,X2) U22(mark(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(active(X1),X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) U22(X1,active(X2)) = X1 + X2 >= X1 + X2 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 1, [active#](x0) = x0 + 1, [nil] = 0, [s](x0) = x0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 1, [U22](x0, x1) = x0 + 1, [isNatKind](x0) = 0, [U21](x0, x1) = x0 + 1, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0, [zeros] = 1 orientation: active#(U21(tt(),V1)) = 2 >= 2 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 2 >= 2 = mark#(U23(isNat(V1))) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) mark#(U13(X)) = 1 >= 1 = active#(U13(mark(X))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = X1 + 2 >= X1 + 1 = mark#(X1) mark#(U21(X1,X2)) = X1 + 2 >= X1 + 2 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 2 >= 2 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = X1 + 2 >= X1 + 1 = mark#(X1) mark#(U22(X1,X2)) = X1 + 2 >= X1 + 2 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 2 >= 2 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 2 >= 2 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X + 1 >= X + 1 = mark#(X) mark#(U23(X)) = X + 1 >= X + 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 2 >= 2 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 2 >= 2 = active#(isNat(X)) active#(U45(tt(),V2)) = 2 >= 2 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 2 >= 2 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 2 >= 2 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 2 >= 2 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 2 >= 2 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 2 >= 2 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X + 1 >= X + 1 = mark#(X) mark#(U46(X)) = X + 1 >= X + 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 2 >= 2 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U51(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = X + 1 >= X + 1 = mark#(X) mark#(U52(X)) = X + 1 >= X + 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X + 1 >= X + 1 = mark#(X) mark#(U61(X)) = X + 1 >= X + 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X + 1 >= X + 1 = mark#(X) mark#(U71(X)) = X + 1 >= X + 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 2 >= 2 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X + 1 >= X + 1 = mark#(X) mark#(U86(X)) = X + 1 >= X + 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 2 >= 2 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X + 1 >= X + 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 1 >= 0 = mark(tt()) active(isNat(length(V1))) = 1 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = X1 + 1 >= X1 + 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = X1 + 1 >= X1 + 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 >= X1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = X1 + 1 >= X1 + 1 = U21(X1,X2) U21(X1,mark(X2)) = X1 + 1 >= X1 + 1 = U21(X1,X2) U21(active(X1),X2) = X1 + 1 >= X1 + 1 = U21(X1,X2) U21(X1,active(X2)) = X1 + 1 >= X1 + 1 = U21(X1,X2) U22(mark(X1),X2) = X1 + 1 >= X1 + 1 = U22(X1,X2) U22(X1,mark(X2)) = X1 + 1 >= X1 + 1 = U22(X1,X2) U22(active(X1),X2) = X1 + 1 >= X1 + 1 = U22(X1,X2) U22(X1,active(X2)) = X1 + 1 >= X1 + 1 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,mark(X2)) = X1 >= X1 = U51(X1,X2) U51(active(X1),X2) = X1 >= X1 = U51(X1,X2) U51(X1,active(X2)) = X1 >= X1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 1, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 1, [0] = 0, [active](x0) = 0, [zeros] = 0 orientation: active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) mark#(U13(X)) = 1 >= 0 = active#(U13(mark(X))) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 1 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 1 = mark#(X) mark#(U61(X)) = 1 >= 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 1 = mark#(tt()) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 1 = mark#(tt()) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 1 >= 1 = U33(X) U33(active(X)) = 1 >= 1 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 1 >= 1 = U61(X) U61(active(X)) = 1 >= 1 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 1, [s](x0) = x0, [length](x0) = x0, [U94](x0, x1) = x1, [U93](x0, x1, x2) = x1 + x2, [U92](x0, x1, x2) = x1 + x2, [U91](x0, x1, x2) = x1 + x2, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0 + x1, [U46](x0) = x0, [isNatIList](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = x0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = X >= X = active#(isNatIListKind(X)) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = 0 >= 0 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = V2 >= V2 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = V2 >= V2 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = X >= X = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = V2 >= V2 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = V2 >= V2 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = V2 >= V2 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = V2 >= V2 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = X3 >= X3 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = X3 >= X3 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = X3 >= X3 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = X3 >= X3 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = X2 >= X2 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = X >= X = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + N >= L + N = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + N >= L + N = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L + N >= L = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L >= L = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = V1 + V2 >= V2 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(nil())) = 1 >= 0 = mark#(tt()) mark#(U93(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 0 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X2 >= X2 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X >= X = active#(length(mark(X))) active#(isNatKind(length(V1))) = V1 >= V1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = V1 >= V1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N >= L + N = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = V2 >= V2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 >= V2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = V2 >= V2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = V2 >= V2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = V2 >= V2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = V2 >= V2 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + N >= L + N = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + N >= L + N = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L + N >= L = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L >= L = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = V1 + V2 >= V2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = V1 >= V1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = V1 >= V1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N >= L + N = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X >= X = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X >= X = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 >= X3 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 >= X3 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = X3 >= X3 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = X3 >= X3 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = X2 >= X2 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = X >= X = active(isNatIList(X)) mark(U51(X1,X2)) = X1 + X2 >= X1 + X2 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 >= X2 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X >= X = isNatIListKind(X) isNatIListKind(active(X)) = X >= X = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = X >= X = isNatKind(X) isNatKind(active(X)) = X >= X = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = X3 >= X3 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = X3 >= X3 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = X3 >= X3 = U43(X1,X2,X3) U43(active(X1),X2,X3) = X3 >= X3 = U43(X1,X2,X3) U43(X1,active(X2),X3) = X3 >= X3 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = X3 >= X3 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = X3 >= X3 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = X3 >= X3 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = X3 >= X3 = U44(X1,X2,X3) U44(active(X1),X2,X3) = X3 >= X3 = U44(X1,X2,X3) U44(X1,active(X2),X3) = X3 >= X3 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = X3 >= X3 = U44(X1,X2,X3) U45(mark(X1),X2) = X2 >= X2 = U45(X1,X2) U45(X1,mark(X2)) = X2 >= X2 = U45(X1,X2) U45(active(X1),X2) = X2 >= X2 = U45(X1,X2) U45(X1,active(X2)) = X2 >= X2 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = X >= X = isNatIList(X) isNatIList(active(X)) = X >= X = isNatIList(X) U51(mark(X1),X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(active(X1),X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(X1,active(X2)) = X1 + X2 >= X1 + X2 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 >= X2 = U94(X1,X2) U94(X1,mark(X2)) = X2 >= X2 = U94(X1,X2) U94(active(X1),X2) = X2 >= X2 = U94(X1,X2) U94(X1,active(X2)) = X2 >= X2 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 1, [s](x0) = x0, [length](x0) = x0, [U94](x0, x1) = x1, [U93](x0, x1, x2) = x1, [U92](x0, x1, x2) = x1 + x2, [U91](x0, x1, x2) = x1 + x2, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0 + x1, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = x0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 1 orientation: active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = X >= X = active#(isNatIListKind(X)) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = 0 >= 0 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = X >= X = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = V2 >= V2 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 0 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + N >= L + N = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X >= X = mark#(X) mark#(U61(X)) = X >= X = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + N >= L = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L >= L = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L >= L = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) = X2 >= X2 = active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) = 1 >= 0 = mark#(tt()) mark#(U94(X1,X2)) = X2 >= X2 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X >= X = active#(length(mark(X))) active#(isNatKind(length(V1))) = V1 >= V1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = V1 >= V1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N >= L + N = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = V2 >= V2 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + N >= L + N = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + N >= L = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L >= L = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L >= L = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = V1 >= V1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = V1 >= V1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N >= L + N = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X >= X = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X >= X = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 + X2 >= X1 + X2 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X >= X = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 + X3 >= X2 + X3 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 >= X2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 >= X2 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X >= X = isNatIListKind(X) isNatIListKind(active(X)) = X >= X = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = X >= X = isNatKind(X) isNatKind(active(X)) = X >= X = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(active(X1),X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(X1,active(X2)) = X1 + X2 >= X1 + X2 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X >= X = U61(X) U61(active(X)) = X >= X = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 >= X2 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 >= X2 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 >= X2 = U94(X1,X2) U94(X1,mark(X2)) = X2 >= X2 = U94(X1,X2) U94(active(X1),X2) = X2 >= X2 = U94(X1,X2) U94(X1,active(X2)) = X2 >= X2 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U61(tt())) -> mark#(tt()) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> mark#(X) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = x0 + 1, [U94](x0, x1) = x1 + 1, [U93](x0, x1, x2) = x1 + 1, [U92](x0, x1, x2) = x1 + 1, [U91](x0, x1, x2) = x1 + 1, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = x0 + 1, [U52](x0) = x0, [U51](x0, x1) = x0 + x1, [U46](x0) = x0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = x0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x0 + x1, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = X >= X = active#(isNatIListKind(X)) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = 0 >= 0 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = X >= X = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = V2 >= V2 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) active#(U61(tt())) = 1 >= 0 = mark#(tt()) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 + X2 >= X1 + X2 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L + 1 >= L + 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = X + 1 >= X = mark#(X) mark#(U61(X)) = X + 1 >= X + 1 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = L + 1 >= L + 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L + 1 >= L + 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L + 1 >= L + 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = X + 1 >= X + 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = V1 + 1 >= V1 + 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = V1 >= V1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L + N + 1 >= L + 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = V2 >= V2 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 1 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L + 1 >= L + 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L + 1 >= L + 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L + 1 >= L + 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L + 1 >= L + 1 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V1 + V2 >= V1 + V2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = V1 + 1 >= V1 + 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = V1 >= V1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = L + N + 1 >= L + 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X >= X = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X >= X = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 + X2 >= X1 + X2 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = X + 1 >= X + 1 = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 + 1 >= X2 + 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 + 1 >= X2 + 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X + 1 >= X + 1 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X >= X = isNatIListKind(X) isNatIListKind(active(X)) = X >= X = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = X >= X = isNatKind(X) isNatKind(active(X)) = X >= X = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 1 >= 1 = U33(X) U33(active(X)) = 1 >= 1 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(X1,mark(X2)) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(active(X1),X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) U51(X1,active(X2)) = X1 + X2 >= X1 + X2 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = X + 1 >= X + 1 = U61(X) U61(active(X)) = X + 1 >= X + 1 = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 + 1 >= X2 + 1 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,mark(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(active(X1),X2) = X2 + 1 >= X2 + 1 = U94(X1,X2) U94(X1,active(X2)) = X2 + 1 >= X2 + 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X + 1 >= X + 1 = length(X) length(active(X)) = X + 1 >= X + 1 = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) -> active#(U61(mark(X))) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 1, [active#](x0) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 1, [U85](x0, x1) = 1, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 1, [U61](x0) = 0, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 1, [isNat](x0) = 1, [U22](x0, x1) = 1, [isNatKind](x0) = 1, [U21](x0, x1) = 1, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = 0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = 0, [zeros] = 0 orientation: active#(U21(tt(),V1)) = 1 >= 1 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 1 >= 1 = mark#(U23(isNat(V1))) active#(U23(tt())) = 1 >= 1 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) mark#(isNatList(X)) = 1 >= 1 = active#(isNatList(X)) mark#(U21(X1,X2)) = 1 >= 1 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 1 >= 1 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 1 >= 1 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 1 >= 1 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 1 >= 1 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 1 >= 1 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U23(X)) = 1 >= 1 = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 1 >= 1 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 1 >= 1 = active#(isNat(X)) active#(U45(tt(),V2)) = 1 >= 1 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 1 >= 1 = mark#(tt()) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 1 >= 1 = mark#(tt()) mark#(U41(X1,X2,X3)) = 1 >= 1 = active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) = 1 >= 1 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 1 >= 1 = mark#(tt()) mark#(U43(X1,X2,X3)) = 1 >= 1 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 1 >= 1 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 1 >= 1 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 1 >= 1 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 1 >= 1 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 1 >= 1 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U46(X)) = 1 >= 1 = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 1 >= 1 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 1 >= 1 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 1 >= 1 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2)) = 1 >= 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 1 >= 1 = mark#(tt()) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U52(X)) = 1 >= 1 = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) mark#(U61(X)) = 1 >= 0 = active#(U61(mark(X))) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 1 >= 1 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 1 >= 1 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 1 >= 1 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 1 >= 1 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 1 >= 1 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 1 >= 1 = active#(U85(mark(X1),X2)) mark#(U86(X)) = 1 >= 1 = mark#(X) mark#(U86(X)) = 1 >= 1 = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 1 >= 1 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = 1 >= 1 = mark#(X) active#(isNatKind(0())) = 1 >= 1 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 1 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 1 >= 1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 1 >= 1 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = 0 >= 0 = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = 0 >= 0 = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = 0 >= 0 = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = 0 >= 0 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = 0 >= 0 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = 0 >= 0 = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = 1 >= 1 = isNatKind(X) isNatKind(active(X)) = 1 >= 1 = isNatKind(X) U23(mark(X)) = 1 >= 1 = U23(X) U23(active(X)) = 1 >= 1 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 1 >= 1 = U52(X) U52(active(X)) = 1 >= 1 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 1 >= 1 = U71(X) U71(active(X)) = 1 >= 1 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,mark(X2)) = 1 >= 1 = U85(X1,X2) U85(active(X1),X2) = 1 >= 1 = U85(X1,X2) U85(X1,active(X2)) = 1 >= 1 = U85(X1,X2) U86(mark(X)) = 1 >= 1 = U86(X) U86(active(X)) = 1 >= 1 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = 0, [U52](x0) = x0, [U51](x0, x1) = x0 + 1, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0, [zeros] = 1 orientation: active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 1 >= 1 = active#(isNatIListKind(X)) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = 0 >= 0 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = 0 >= 0 = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = 1 >= 1 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U51(X1,X2)) = X1 + 1 >= X1 + 1 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 0 >= 0 = mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) = 0 >= 0 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 0 >= 0 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 0 >= 0 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 0 >= 0 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 0 >= 0 = active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) = 0 >= 0 = active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) = 0 >= 0 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = 0 >= 0 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 0 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = 0 >= 0 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 0 >= 0 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 1 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 0 >= 0 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 0 >= 0 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 0 >= 0 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 0 >= 0 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 0 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 0 >= 0 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 0 >= 0 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 0 >= 0 = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 + 1 >= X1 + 1 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 0 >= 0 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 0 >= 0 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 0 >= 0 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 0 >= 0 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 0 >= 0 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = X1 + 1 >= X1 + 1 = U51(X1,X2) U51(X1,mark(X2)) = X1 + 1 >= X1 + 1 = U51(X1,X2) U51(active(X1),X2) = X1 + 1 >= X1 + 1 = U51(X1,X2) U51(X1,active(X2)) = X1 + 1 >= X1 + 1 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(length(V1))) -> mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 0, [s](x0) = x0, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = 0, [U52](x0) = x0, [U51](x0, x1) = 0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = x0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0, [zeros] = 0 orientation: active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = 0 >= 0 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = X >= X = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 0 >= 0 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = 1 >= 1 = mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) = 1 >= 1 = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = 1 >= 1 = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = 1 >= 1 = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = 1 >= 1 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = 1 >= 1 = active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) = 1 >= 1 = active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) = 1 >= 1 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 0 >= 0 = mark#(tt()) mark#(length(X)) = 1 >= 1 = active#(length(mark(X))) active#(isNatKind(length(V1))) = 1 >= 0 = mark#(U61(isNatIListKind(V1))) active#(isNatKind(s(V1))) = V1 >= V1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = 1 >= 1 = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 0 >= 0 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = V1 >= V1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 0 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 0 >= 0 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X >= X = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = X >= X = isNatKind(X) isNatKind(active(X)) = X >= X = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) active#(isNatKind(0())) -> mark#(tt()) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [nil] = 1, [s](x0) = x0, [length](x0) = x0, [U94](x0, x1) = x1, [U93](x0, x1, x2) = x1, [U92](x0, x1, x2) = x1, [U91](x0, x1, x2) = x1, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = x0, [U61](x0) = 0, [U52](x0) = x0, [U51](x0, x1) = 0, [U46](x0) = x0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = x0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0, [zeros] = 0 orientation: active#(U21(tt(),V1)) = 0 >= 0 = mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) = 0 >= 0 = mark#(U23(isNat(V1))) active#(U23(tt())) = 0 >= 0 = mark#(tt()) mark#(isNatIListKind(X)) = 0 >= 0 = active#(isNatIListKind(X)) mark#(isNatList(X)) = 0 >= 0 = active#(isNatList(X)) mark#(U21(X1,X2)) = 0 >= 0 = active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) = 0 >= 0 = mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) = 0 >= 0 = active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) = 0 >= 0 = mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) = X >= X = active#(isNatKind(X)) active#(U43(tt(),V1,V2)) = 0 >= 0 = mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) = X >= X = mark#(X) mark#(U23(X)) = X >= X = active#(U23(mark(X))) active#(U44(tt(),V1,V2)) = 0 >= 0 = mark#(U45(isNat(V1),V2)) mark#(isNat(X)) = 0 >= 0 = active#(isNat(X)) active#(U45(tt(),V2)) = 0 >= 0 = mark#(U46(isNatIList(V2))) active#(U46(tt())) = 0 >= 0 = mark#(tt()) active#(U51(tt(),V2)) = 0 >= 0 = mark#(U52(isNatIListKind(V2))) active#(U52(tt())) = 0 >= 0 = mark#(tt()) mark#(U41(X1,X2,X3)) = 0 >= 0 = active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) = 0 >= 0 = active#(U42(mark(X1),X2,X3)) active#(U71(tt())) = 0 >= 0 = mark#(tt()) mark#(U43(X1,X2,X3)) = 0 >= 0 = active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) = 0 >= 0 = mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) = 0 >= 0 = active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) = 0 >= 0 = mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) = 0 >= 0 = active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) = 0 >= 0 = mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = active#(U46(mark(X))) active#(U84(tt(),V1,V2)) = 0 >= 0 = mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) = 0 >= 0 = active#(isNatIList(X)) active#(U85(tt(),V2)) = 0 >= 0 = mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) = 0 >= 0 = active#(U51(mark(X1),X2)) active#(U86(tt())) = 0 >= 0 = mark#(tt()) mark#(U52(X)) = X >= X = mark#(X) mark#(U52(X)) = X >= X = active#(U52(mark(X))) active#(U91(tt(),L,N)) = L >= L = mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) = L >= L = mark#(U93(isNat(N),L,N)) mark#(U71(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = active#(U71(mark(X))) active#(U93(tt(),L,N)) = L >= L = mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) = 0 >= 0 = active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) = L >= L = mark#(s(length(L))) mark#(U82(X1,X2,X3)) = 0 >= 0 = active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) = 0 >= 0 = active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) = 0 >= 0 = active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) = 0 >= 0 = mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) = 0 >= 0 = active#(U85(mark(X1),X2)) mark#(U86(X)) = X >= X = mark#(X) mark#(U86(X)) = X >= X = active#(U86(mark(X))) mark#(U91(X1,X2,X3)) = X2 >= X2 = active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) = 0 >= 0 = mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) = X2 >= X2 = active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) = X2 >= X2 = active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) = X2 >= X2 = active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark#(U51(isNatKind(V1),V2)) mark#(s(X)) = X >= X = mark#(X) active#(isNatKind(0())) = 1 >= 0 = mark#(tt()) mark#(length(X)) = X >= X = active#(length(mark(X))) active#(isNatKind(s(V1))) = V1 >= V1 = mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) = 0 >= 0 = mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) = L >= L = mark#(U91(isNatList(L),L,N)) active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 0 >= 0 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 0 >= 0 = mark(U13(isNatList(V1))) active(U13(tt())) = 0 >= 0 = mark(tt()) active(U21(tt(),V1)) = 0 >= 0 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 0 >= 0 = mark(U23(isNat(V1))) active(U23(tt())) = 0 >= 0 = mark(tt()) active(U31(tt(),V)) = 0 >= 0 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 0 >= 0 = mark(U33(isNatList(V))) active(U33(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V1,V2)) = 0 >= 0 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 0 >= 0 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 0 >= 0 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 0 >= 0 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 0 >= 0 = mark(U46(isNatIList(V2))) active(U46(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 0 >= 0 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt())) = 0 >= 0 = mark(tt()) active(U71(tt())) = 0 >= 0 = mark(tt()) active(U81(tt(),V1,V2)) = 0 >= 0 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 0 >= 0 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 0 >= 0 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 0 >= 0 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 0 >= 0 = mark(U86(isNatList(V2))) active(U86(tt())) = 0 >= 0 = mark(tt()) active(U91(tt(),L,N)) = L >= L = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = L >= L = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = L >= L = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = L >= L = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 0 >= 0 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 0 >= 0 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 0 >= 0 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 0 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 0 >= 0 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 0 >= 0 = mark(tt()) active(isNatIListKind(zeros())) = 0 >= 0 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 0 >= 0 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 0 = mark(tt()) active(isNatKind(length(V1))) = V1 >= 0 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = V1 >= V1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 0 >= 0 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = L >= L = mark(U91(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X2 >= X2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 0 >= 0 = active(U11(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2)) = 0 >= 0 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 0 >= 0 = active(isNatIListKind(X)) mark(U13(X)) = 0 >= 0 = active(U13(mark(X))) mark(isNatList(X)) = 0 >= 0 = active(isNatList(X)) mark(U21(X1,X2)) = 0 >= 0 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 0 >= 0 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X >= X = active(isNatKind(X)) mark(U23(X)) = X >= X = active(U23(mark(X))) mark(isNat(X)) = 0 >= 0 = active(isNat(X)) mark(U31(X1,X2)) = 0 >= 0 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 0 >= 0 = active(U32(mark(X1),X2)) mark(U33(X)) = 0 >= 0 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 0 >= 0 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 0 >= 0 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 0 >= 0 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 0 >= 0 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 0 >= 0 = active(U45(mark(X1),X2)) mark(U46(X)) = X >= X = active(U46(mark(X))) mark(isNatIList(X)) = 0 >= 0 = active(isNatIList(X)) mark(U51(X1,X2)) = 0 >= 0 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(U61(X)) = 0 >= 0 = active(U61(mark(X))) mark(U71(X)) = X >= X = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 0 >= 0 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 0 >= 0 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 0 >= 0 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 0 >= 0 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 0 >= 0 = active(U85(mark(X1),X2)) mark(U86(X)) = X >= X = active(U86(mark(X))) mark(U91(X1,X2,X3)) = X2 >= X2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = X2 >= X2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = X2 >= X2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = X2 >= X2 = active(U94(mark(X1),X2)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = X >= X = isNatKind(X) isNatKind(active(X)) = X >= X = isNatKind(X) U23(mark(X)) = X >= X = U23(X) U23(active(X)) = X >= X = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = X >= X = U46(X) U46(active(X)) = X >= X = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = X >= X = U71(X) U71(active(X)) = X >= X = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = X >= X = U86(X) U86(active(X)) = X >= X = U86(X) U91(mark(X1),X2,X3) = X2 >= X2 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = X2 >= X2 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = X2 >= X2 = U91(X1,X2,X3) U91(active(X1),X2,X3) = X2 >= X2 = U91(X1,X2,X3) U91(X1,active(X2),X3) = X2 >= X2 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = X2 >= X2 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = X2 >= X2 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = X2 >= X2 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = X2 >= X2 = U92(X1,X2,X3) U92(active(X1),X2,X3) = X2 >= X2 = U92(X1,X2,X3) U92(X1,active(X2),X3) = X2 >= X2 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = X2 >= X2 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = X2 >= X2 = U93(X1,X2,X3) U93(active(X1),X2,X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,active(X2),X3) = X2 >= X2 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = X2 >= X2 = U93(X1,X2,X3) U94(mark(X1),X2) = X2 >= X2 = U94(X1,X2) U94(X1,mark(X2)) = X2 >= X2 = U94(X1,X2) U94(active(X1),X2) = X2 >= X2 = U94(X1,X2) U94(X1,active(X2)) = X2 >= X2 = U94(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) problem: DPs: active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(isNat(X)) -> active#(isNat(X)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U71(tt())) -> mark#(tt()) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U81(tt(),V1,V2)) -> mark#(U82(isNatKind(V1),V1,V2)) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U82(tt(),V1,V2)) -> mark#(U83(isNatIListKind(V2),V1,V2)) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U83(tt(),V1,V2)) -> mark#(U84(isNatIListKind(V2),V1,V2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U84(tt(),V1,V2)) -> mark#(U85(isNat(V1),V2)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U85(tt(),V2)) -> mark#(U86(isNatList(V2))) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U86(tt())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(U91(tt(),L,N)) -> mark#(U92(isNatIListKind(L),L,N)) active#(U92(tt(),L,N)) -> mark#(U93(isNat(N),L,N)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(U93(tt(),L,N)) -> mark#(U94(isNatKind(N),L)) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(U94(tt(),L)) -> mark#(s(length(L))) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U85(X1,X2)) -> active#(U85(mark(X1),X2)) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> active#(U86(mark(X))) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2)) -> active#(U94(mark(X1),X2)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(s(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatKind(s(V1))) -> mark#(U71(isNatKind(V1))) active#(isNatList(cons(V1,V2))) -> mark#(U81(isNatKind(V1),V1,V2)) active#(length(cons(N,L))) -> mark#(U91(isNatList(L),L,N)) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Open DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [cons#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: cons#(mark(X1),X2) = X1 + 1 >= X1 = cons#(X1,X2) cons#(X1,mark(X2)) = X1 >= X1 = cons#(X1,X2) cons#(active(X1),X2) = X1 + 1 >= X1 = cons#(X1,X2) cons#(X1,active(X2)) = X1 >= X1 = cons#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [cons#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: cons#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = cons#(X1,X2) cons#(X1,active(X2)) = X2 + 2 >= X2 + 1 = cons#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: isNatIListKind#(mark(X)) -> isNatIListKind#(X) isNatIListKind#(active(X)) -> isNatIListKind#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [isNatIListKind#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: isNatIListKind#(mark(X)) = X + 1 >= X = isNatIListKind#(X) isNatIListKind#(active(X)) = X + 1 >= X = isNatIListKind#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U12#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U12#(mark(X1),X2) = X1 + 1 >= X1 = U12#(X1,X2) U12#(X1,mark(X2)) = X1 >= X1 = U12#(X1,X2) U12#(active(X1),X2) = X1 + 1 >= X1 = U12#(X1,X2) U12#(X1,active(X2)) = X1 >= X1 = U12#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U12#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U12#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U12#(X1,X2) U12#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U12#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [isNatList#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: isNatList#(mark(X)) = X + 1 >= X = isNatList#(X) isNatList#(active(X)) = X + 1 >= X = isNatList#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U13#(mark(X)) -> U13#(X) U13#(active(X)) -> U13#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U13#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U13#(mark(X)) = X + 1 >= X = U13#(X) U13#(active(X)) = X + 1 >= X = U13#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [isNatKind#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: isNatKind#(mark(X)) = X + 1 >= X = isNatKind#(X) isNatKind#(active(X)) = X + 1 >= X = isNatKind#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U22#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U22#(mark(X1),X2) = X1 + 1 >= X1 = U22#(X1,X2) U22#(X1,mark(X2)) = X1 >= X1 = U22#(X1,X2) U22#(active(X1),X2) = X1 + 1 >= X1 = U22#(X1,X2) U22#(X1,active(X2)) = X1 >= X1 = U22#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U22#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U22#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U22#(X1,X2) U22#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U22#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [isNat#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: isNat#(mark(X)) = X + 1 >= X = isNat#(X) isNat#(active(X)) = X + 1 >= X = isNat#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U23#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U23#(mark(X)) = X + 1 >= X = U23#(X) U23#(active(X)) = X + 1 >= X = U23#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) U32#(active(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U32#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U32#(mark(X1),X2) = X1 + 1 >= X1 = U32#(X1,X2) U32#(X1,mark(X2)) = X1 >= X1 = U32#(X1,X2) U32#(active(X1),X2) = X1 + 1 >= X1 = U32#(X1,X2) U32#(X1,active(X2)) = X1 >= X1 = U32#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U32#(X1,mark(X2)) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U32#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U32#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U32#(X1,X2) U32#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U32#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U33#(mark(X)) -> U33#(X) U33#(active(X)) -> U33#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U33#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U33#(mark(X)) = X + 1 >= X = U33#(X) U33#(active(X)) = X + 1 >= X = U33#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U42#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U42#(mark(X1),X2,X3) = X2 >= X2 = U42#(X1,X2,X3) U42#(X1,mark(X2),X3) = X2 + 1 >= X2 = U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) = X2 >= X2 = U42#(X1,X2,X3) U42#(active(X1),X2,X3) = X2 >= X2 = U42#(X1,X2,X3) U42#(X1,active(X2),X3) = X2 + 1 >= X2 = U42#(X1,X2,X3) U42#(X1,X2,active(X3)) = X2 >= X2 = U42#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U42#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U42#(mark(X1),X2,X3) = X3 >= X3 = U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42#(X1,X2,X3) U42#(active(X1),X2,X3) = X3 >= X3 = U42#(X1,X2,X3) U42#(X1,X2,active(X3)) = X3 + 1 >= X3 = U42#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U42#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U42#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U42#(X1,X2,X3) U42#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U42#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U43#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U43#(mark(X1),X2,X3) = X2 >= X2 = U43#(X1,X2,X3) U43#(X1,mark(X2),X3) = X2 + 1 >= X2 = U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) = X2 >= X2 = U43#(X1,X2,X3) U43#(active(X1),X2,X3) = X2 >= X2 = U43#(X1,X2,X3) U43#(X1,active(X2),X3) = X2 + 1 >= X2 = U43#(X1,X2,X3) U43#(X1,X2,active(X3)) = X2 >= X2 = U43#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U43#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U43#(mark(X1),X2,X3) = X3 >= X3 = U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U43#(X1,X2,X3) U43#(active(X1),X2,X3) = X3 >= X3 = U43#(X1,X2,X3) U43#(X1,X2,active(X3)) = X3 + 1 >= X3 = U43#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U43#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U43#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U43#(X1,X2,X3) U43#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U43#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U44#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U44#(mark(X1),X2,X3) = X2 >= X2 = U44#(X1,X2,X3) U44#(X1,mark(X2),X3) = X2 + 1 >= X2 = U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) = X2 >= X2 = U44#(X1,X2,X3) U44#(active(X1),X2,X3) = X2 >= X2 = U44#(X1,X2,X3) U44#(X1,active(X2),X3) = X2 + 1 >= X2 = U44#(X1,X2,X3) U44#(X1,X2,active(X3)) = X2 >= X2 = U44#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U44#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U44#(mark(X1),X2,X3) = X3 >= X3 = U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U44#(X1,X2,X3) U44#(active(X1),X2,X3) = X3 >= X3 = U44#(X1,X2,X3) U44#(X1,X2,active(X3)) = X3 + 1 >= X3 = U44#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U44#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U44#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U44#(X1,X2,X3) U44#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U44#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) U45#(active(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U45#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U45#(mark(X1),X2) = X1 + 1 >= X1 = U45#(X1,X2) U45#(X1,mark(X2)) = X1 >= X1 = U45#(X1,X2) U45#(active(X1),X2) = X1 + 1 >= X1 = U45#(X1,X2) U45#(X1,active(X2)) = X1 >= X1 = U45#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U45#(X1,mark(X2)) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U45#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U45#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U45#(X1,X2) U45#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U45#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [isNatIList#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: isNatIList#(mark(X)) = X + 1 >= X = isNatIList#(X) isNatIList#(active(X)) = X + 1 >= X = isNatIList#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U46#(mark(X)) -> U46#(X) U46#(active(X)) -> U46#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U46#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U46#(mark(X)) = X + 1 >= X = U46#(X) U46#(active(X)) = X + 1 >= X = U46#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U52#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U52#(mark(X)) = X + 1 >= X = U52#(X) U52#(active(X)) = X + 1 >= X = U52#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3) U82#(active(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,active(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U82#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U82#(mark(X1),X2,X3) = X2 >= X2 = U82#(X1,X2,X3) U82#(X1,mark(X2),X3) = X2 + 1 >= X2 = U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) = X2 >= X2 = U82#(X1,X2,X3) U82#(active(X1),X2,X3) = X2 >= X2 = U82#(X1,X2,X3) U82#(X1,active(X2),X3) = X2 + 1 >= X2 = U82#(X1,X2,X3) U82#(X1,X2,active(X3)) = X2 >= X2 = U82#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3) U82#(active(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U82#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U82#(mark(X1),X2,X3) = X3 >= X3 = U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U82#(X1,X2,X3) U82#(active(X1),X2,X3) = X3 >= X3 = U82#(X1,X2,X3) U82#(X1,X2,active(X3)) = X3 + 1 >= X3 = U82#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3) U82#(active(X1),X2,X3) -> U82#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U82#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U82#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U82#(X1,X2,X3) U82#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U82#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3) U83#(active(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,active(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U83#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U83#(mark(X1),X2,X3) = X2 >= X2 = U83#(X1,X2,X3) U83#(X1,mark(X2),X3) = X2 + 1 >= X2 = U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) = X2 >= X2 = U83#(X1,X2,X3) U83#(active(X1),X2,X3) = X2 >= X2 = U83#(X1,X2,X3) U83#(X1,active(X2),X3) = X2 + 1 >= X2 = U83#(X1,X2,X3) U83#(X1,X2,active(X3)) = X2 >= X2 = U83#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3) U83#(active(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U83#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U83#(mark(X1),X2,X3) = X3 >= X3 = U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U83#(X1,X2,X3) U83#(active(X1),X2,X3) = X3 >= X3 = U83#(X1,X2,X3) U83#(X1,X2,active(X3)) = X3 + 1 >= X3 = U83#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3) U83#(active(X1),X2,X3) -> U83#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U83#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U83#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U83#(X1,X2,X3) U83#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U83#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3) U84#(active(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,active(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U84#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U84#(mark(X1),X2,X3) = X2 >= X2 = U84#(X1,X2,X3) U84#(X1,mark(X2),X3) = X2 + 1 >= X2 = U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) = X2 >= X2 = U84#(X1,X2,X3) U84#(active(X1),X2,X3) = X2 >= X2 = U84#(X1,X2,X3) U84#(X1,active(X2),X3) = X2 + 1 >= X2 = U84#(X1,X2,X3) U84#(X1,X2,active(X3)) = X2 >= X2 = U84#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3) U84#(active(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U84#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U84#(mark(X1),X2,X3) = X3 >= X3 = U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U84#(X1,X2,X3) U84#(active(X1),X2,X3) = X3 >= X3 = U84#(X1,X2,X3) U84#(X1,X2,active(X3)) = X3 + 1 >= X3 = U84#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3) U84#(active(X1),X2,X3) -> U84#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U84#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U84#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U84#(X1,X2,X3) U84#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U84#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U85#(mark(X1),X2) -> U85#(X1,X2) U85#(X1,mark(X2)) -> U85#(X1,X2) U85#(active(X1),X2) -> U85#(X1,X2) U85#(X1,active(X2)) -> U85#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U85#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U85#(mark(X1),X2) = X1 + 1 >= X1 = U85#(X1,X2) U85#(X1,mark(X2)) = X1 >= X1 = U85#(X1,X2) U85#(active(X1),X2) = X1 + 1 >= X1 = U85#(X1,X2) U85#(X1,active(X2)) = X1 >= X1 = U85#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U85#(X1,mark(X2)) -> U85#(X1,X2) U85#(X1,active(X2)) -> U85#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U85#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U85#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U85#(X1,X2) U85#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U85#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U86#(mark(X)) -> U86#(X) U86#(active(X)) -> U86#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U86#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U86#(mark(X)) = X + 1 >= X = U86#(X) U86#(active(X)) = X + 1 >= X = U86#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3) U92#(active(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,active(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U92#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U92#(mark(X1),X2,X3) = X2 >= X2 = U92#(X1,X2,X3) U92#(X1,mark(X2),X3) = X2 + 1 >= X2 = U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) = X2 >= X2 = U92#(X1,X2,X3) U92#(active(X1),X2,X3) = X2 >= X2 = U92#(X1,X2,X3) U92#(X1,active(X2),X3) = X2 + 1 >= X2 = U92#(X1,X2,X3) U92#(X1,X2,active(X3)) = X2 >= X2 = U92#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3) U92#(active(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U92#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U92#(mark(X1),X2,X3) = X3 >= X3 = U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U92#(X1,X2,X3) U92#(active(X1),X2,X3) = X3 >= X3 = U92#(X1,X2,X3) U92#(X1,X2,active(X3)) = X3 + 1 >= X3 = U92#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3) U92#(active(X1),X2,X3) -> U92#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U92#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U92#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U92#(X1,X2,X3) U92#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U92#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3) U93#(active(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,active(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U93#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U93#(mark(X1),X2,X3) = X2 >= X2 = U93#(X1,X2,X3) U93#(X1,mark(X2),X3) = X2 + 1 >= X2 = U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) = X2 >= X2 = U93#(X1,X2,X3) U93#(active(X1),X2,X3) = X2 >= X2 = U93#(X1,X2,X3) U93#(X1,active(X2),X3) = X2 + 1 >= X2 = U93#(X1,X2,X3) U93#(X1,X2,active(X3)) = X2 >= X2 = U93#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3) U93#(active(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U93#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U93#(mark(X1),X2,X3) = X3 >= X3 = U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U93#(X1,X2,X3) U93#(active(X1),X2,X3) = X3 >= X3 = U93#(X1,X2,X3) U93#(X1,X2,active(X3)) = X3 + 1 >= X3 = U93#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3) U93#(active(X1),X2,X3) -> U93#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U93#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U93#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U93#(X1,X2,X3) U93#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U93#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U94#(mark(X1),X2) -> U94#(X1,X2) U94#(X1,mark(X2)) -> U94#(X1,X2) U94#(active(X1),X2) -> U94#(X1,X2) U94#(X1,active(X2)) -> U94#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U94#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U94#(mark(X1),X2) = X1 + 1 >= X1 = U94#(X1,X2) U94#(X1,mark(X2)) = X1 >= X1 = U94#(X1,X2) U94#(active(X1),X2) = X1 + 1 >= X1 = U94#(X1,X2) U94#(X1,active(X2)) = X1 >= X1 = U94#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U94#(X1,mark(X2)) -> U94#(X1,X2) U94#(X1,active(X2)) -> U94#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U94#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U94#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U94#(X1,X2) U94#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U94#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [length#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: length#(mark(X)) = X + 1 >= X = length#(X) length#(active(X)) = X + 1 >= X = length#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [s#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: s#(mark(X)) = X + 1 >= X = s#(X) s#(active(X)) = X + 1 >= X = s#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U11#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U11#(mark(X1),X2) = X1 + 1 >= X1 = U11#(X1,X2) U11#(X1,mark(X2)) = X1 >= X1 = U11#(X1,X2) U11#(active(X1),X2) = X1 + 1 >= X1 = U11#(X1,X2) U11#(X1,active(X2)) = X1 >= X1 = U11#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U11#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U11#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U11#(X1,X2) U11#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U11#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U21#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U21#(mark(X1),X2) = X1 + 1 >= X1 = U21#(X1,X2) U21#(X1,mark(X2)) = X1 >= X1 = U21#(X1,X2) U21#(active(X1),X2) = X1 + 1 >= X1 = U21#(X1,X2) U21#(X1,active(X2)) = X1 >= X1 = U21#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U21#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U21#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U21#(X1,X2) U21#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U21#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U31#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U31#(mark(X1),X2) = X1 + 1 >= X1 = U31#(X1,X2) U31#(X1,mark(X2)) = X1 >= X1 = U31#(X1,X2) U31#(active(X1),X2) = X1 + 1 >= X1 = U31#(X1,X2) U31#(X1,active(X2)) = X1 >= X1 = U31#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U31#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U31#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U31#(X1,X2) U31#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U31#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U41#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U41#(mark(X1),X2,X3) = X2 >= X2 = U41#(X1,X2,X3) U41#(X1,mark(X2),X3) = X2 + 1 >= X2 = U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) = X2 >= X2 = U41#(X1,X2,X3) U41#(active(X1),X2,X3) = X2 >= X2 = U41#(X1,X2,X3) U41#(X1,active(X2),X3) = X2 + 1 >= X2 = U41#(X1,X2,X3) U41#(X1,X2,active(X3)) = X2 >= X2 = U41#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U41#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U41#(mark(X1),X2,X3) = X3 >= X3 = U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41#(X1,X2,X3) U41#(active(X1),X2,X3) = X3 >= X3 = U41#(X1,X2,X3) U41#(X1,X2,active(X3)) = X3 + 1 >= X3 = U41#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U41#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U41#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U41#(X1,X2,X3) U41#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U41#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U51#](x0, x1) = x0, [nil] = 0, [s](x0) = 0, [length](x0) = 1, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = x0 + 1, [U22](x0, x1) = 1, [isNatKind](x0) = x0, [U21](x0, x1) = 1, [U13](x0) = 1, [isNatList](x0) = x0 + 1, [U12](x0, x1) = 1, [isNatIListKind](x0) = 1, [U11](x0, x1) = 1, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 1, [active](x0) = x0 + 1, [zeros] = 1 orientation: U51#(mark(X1),X2) = X1 + 1 >= X1 = U51#(X1,X2) U51#(X1,mark(X2)) = X1 >= X1 = U51#(X1,X2) U51#(active(X1),X2) = X1 + 1 >= X1 = U51#(X1,X2) U51#(X1,active(X2)) = X1 >= X1 = U51#(X1,X2) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 2 >= 2 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 2 >= 2 = mark(U13(isNatList(V1))) active(U13(tt())) = 2 >= 1 = mark(tt()) active(U21(tt(),V1)) = 2 >= 2 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 2 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 3 >= 1 = mark(tt()) active(isNat(length(V1))) = 3 >= 2 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 2 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 2 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 2 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 2 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 2 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = V2 + 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 2 >= 2 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 2 >= 2 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 2 >= 2 = active(isNatIListKind(X)) mark(U13(X)) = 2 >= 2 = active(U13(mark(X))) mark(isNatList(X)) = X + 2 >= X + 2 = active(isNatList(X)) mark(U21(X1,X2)) = 2 >= 2 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 2 >= 2 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = X + 1 >= X + 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = X + 2 >= X + 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,mark(X2)) = 1 >= 1 = U11(X1,X2) U11(active(X1),X2) = 1 >= 1 = U11(X1,X2) U11(X1,active(X2)) = 1 >= 1 = U11(X1,X2) U12(mark(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,mark(X2)) = 1 >= 1 = U12(X1,X2) U12(active(X1),X2) = 1 >= 1 = U12(X1,X2) U12(X1,active(X2)) = 1 >= 1 = U12(X1,X2) isNatIListKind(mark(X)) = 1 >= 1 = isNatIListKind(X) isNatIListKind(active(X)) = 1 >= 1 = isNatIListKind(X) U13(mark(X)) = 1 >= 1 = U13(X) U13(active(X)) = 1 >= 1 = U13(X) isNatList(mark(X)) = X + 2 >= X + 1 = isNatList(X) isNatList(active(X)) = X + 2 >= X + 1 = isNatList(X) U21(mark(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,mark(X2)) = 1 >= 1 = U21(X1,X2) U21(active(X1),X2) = 1 >= 1 = U21(X1,X2) U21(X1,active(X2)) = 1 >= 1 = U21(X1,X2) U22(mark(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,mark(X2)) = 1 >= 1 = U22(X1,X2) U22(active(X1),X2) = 1 >= 1 = U22(X1,X2) U22(X1,active(X2)) = 1 >= 1 = U22(X1,X2) isNatKind(mark(X)) = X + 1 >= X = isNatKind(X) isNatKind(active(X)) = X + 1 >= X = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = X + 2 >= X + 1 = isNat(X) isNat(active(X)) = X + 2 >= X + 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U51#](x0, x1) = x1 + 1, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U51#(X1,mark(X2)) = X2 + 2 >= X2 + 1 = U51#(X1,X2) U51#(X1,active(X2)) = X2 + 2 >= X2 + 1 = U51#(X1,X2) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U61#(mark(X)) -> U61#(X) U61#(active(X)) -> U61#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U61#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U61#(mark(X)) = X + 1 >= X = U61#(X) U61#(active(X)) = X + 1 >= X = U61#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U71#(mark(X)) -> U71#(X) U71#(active(X)) -> U71#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U71#](x0) = x0, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U71#(mark(X)) = X + 1 >= X = U71#(X) U71#(active(X)) = X + 1 >= X = U71#(X) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 1 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 1 >= X + 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 1 >= X = isNatIList(X) isNatIList(active(X)) = X + 1 >= X = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3) U81#(active(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,active(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U81#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U81#(mark(X1),X2,X3) = X2 >= X2 = U81#(X1,X2,X3) U81#(X1,mark(X2),X3) = X2 + 1 >= X2 = U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) = X2 >= X2 = U81#(X1,X2,X3) U81#(active(X1),X2,X3) = X2 >= X2 = U81#(X1,X2,X3) U81#(X1,active(X2),X3) = X2 + 1 >= X2 = U81#(X1,X2,X3) U81#(X1,X2,active(X3)) = X2 >= X2 = U81#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3) U81#(active(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U81#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U81#(mark(X1),X2,X3) = X3 >= X3 = U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U81#(X1,X2,X3) U81#(active(X1),X2,X3) = X3 >= X3 = U81#(X1,X2,X3) U81#(X1,X2,active(X3)) = X3 + 1 >= X3 = U81#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3) U81#(active(X1),X2,X3) -> U81#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U81#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U81#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U81#(X1,X2,X3) U81#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U81#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3) U91#(active(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,active(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U91#](x0, x1, x2) = x1, [nil] = 0, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [isNatIList](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 1 orientation: U91#(mark(X1),X2,X3) = X2 >= X2 = U91#(X1,X2,X3) U91#(X1,mark(X2),X3) = X2 + 1 >= X2 = U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) = X2 >= X2 = U91#(X1,X2,X3) U91#(active(X1),X2,X3) = X2 >= X2 = U91#(X1,X2,X3) U91#(X1,active(X2),X3) = X2 + 1 >= X2 = U91#(X1,X2,X3) U91#(X1,X2,active(X3)) = X2 >= X2 = U91#(X1,X2,X3) active(zeros()) = 2 >= 2 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 2 >= 2 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 2 >= 2 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 2 >= 2 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 2 >= 2 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 2 >= 2 = mark(U46(isNatIList(V2))) active(U46(tt())) = 2 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 2 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 2 >= 2 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = 2 >= 2 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 2 >= 2 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 2 >= 2 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 2 >= 2 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 2 >= 2 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 2 >= 2 = active(U45(mark(X1),X2)) mark(U46(X)) = 2 >= 2 = active(U46(mark(X))) mark(isNatIList(X)) = 2 >= 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,mark(X2)) = 1 >= 1 = cons(X1,X2) cons(active(X1),X2) = 1 >= 1 = cons(X1,X2) cons(X1,active(X2)) = 1 >= 1 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 1 >= 1 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 1 >= 1 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 1 >= 1 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 1 >= 1 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 1 >= 1 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 1 >= 1 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 1 >= 1 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 1 >= 1 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 1 >= 1 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 1 >= 1 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 1 >= 1 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 1 >= 1 = U44(X1,X2,X3) U45(mark(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,mark(X2)) = 1 >= 1 = U45(X1,X2) U45(active(X1),X2) = 1 >= 1 = U45(X1,X2) U45(X1,active(X2)) = 1 >= 1 = U45(X1,X2) U46(mark(X)) = 1 >= 1 = U46(X) U46(active(X)) = 1 >= 1 = U46(X) isNatIList(mark(X)) = 1 >= 1 = isNatIList(X) isNatIList(active(X)) = 1 >= 1 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3) U91#(active(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U91#](x0, x1, x2) = x2, [nil] = 1, [s](x0) = 0, [length](x0) = 0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 1, [U83](x0, x1, x2) = 1, [U82](x0, x1, x2) = 1, [U81](x0, x1, x2) = 1, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 1, [U46](x0) = 0, [isNatIList](x0) = x0 + 1, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [isNat](x0) = 1, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 1, [U12](x0, x1) = 0, [isNatIListKind](x0) = x0 + 1, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = x1, [0] = 0, [active](x0) = x0 + 1, [zeros] = 0 orientation: U91#(mark(X1),X2,X3) = X3 >= X3 = U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) = X3 + 1 >= X3 = U91#(X1,X2,X3) U91#(active(X1),X2,X3) = X3 >= X3 = U91#(X1,X2,X3) U91#(X1,X2,active(X3)) = X3 + 1 >= X3 = U91#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 2 >= 2 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 2 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = V2 + 1 >= V2 + 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = V2 + 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 2 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 2 >= 2 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 2 >= 2 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 2 >= 2 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 2 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 1 >= 1 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 1 >= 1 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 1 >= 1 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 1 >= 1 = mark(s(length(L))) active(isNat(0())) = 2 >= 1 = mark(tt()) active(isNat(length(V1))) = 2 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 2 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = V + 2 >= 2 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 2 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = V2 + 2 >= V2 + 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 3 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 2 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = V2 + 2 >= 2 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 2 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 2 >= 2 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(N,L))) = 1 >= 1 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = X2 + 1 >= X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 1 >= 1 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = X + 2 >= X + 2 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 2 >= 2 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 2 >= 2 = active(isNat(X)) mark(U31(X1,X2)) = 2 >= 2 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 2 >= 2 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = X + 2 >= X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 2 >= 2 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 2 >= 2 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 2 >= 2 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 2 >= 2 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 2 >= 2 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 1 >= 1 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 1 >= 1 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 1 >= 1 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 1 >= 1 = active(U94(mark(X1),X2)) mark(s(X)) = 1 >= 1 = active(s(mark(X))) mark(length(X)) = 1 >= 1 = active(length(mark(X))) mark(nil()) = 2 >= 2 = active(nil()) cons(mark(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,mark(X2)) = X2 + 1 >= X2 = cons(X1,X2) cons(active(X1),X2) = X2 >= X2 = cons(X1,X2) cons(X1,active(X2)) = X2 + 1 >= X2 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = X + 2 >= X + 1 = isNatIListKind(X) isNatIListKind(active(X)) = X + 2 >= X + 1 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 1 >= 1 = isNatList(X) isNatList(active(X)) = 1 >= 1 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 1 >= 1 = isNat(X) isNat(active(X)) = 1 >= 1 = isNat(X) U31(mark(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,mark(X2)) = 1 >= 1 = U31(X1,X2) U31(active(X1),X2) = 1 >= 1 = U31(X1,X2) U31(X1,active(X2)) = 1 >= 1 = U31(X1,X2) U32(mark(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,mark(X2)) = 1 >= 1 = U32(X1,X2) U32(active(X1),X2) = 1 >= 1 = U32(X1,X2) U32(X1,active(X2)) = 1 >= 1 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U41(active(X1),X2,X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,active(X2),X3) = X3 >= X3 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = X3 + 1 >= X3 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U42(active(X1),X2,X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,active(X2),X3) = X3 >= X3 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = X3 + 1 >= X3 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = X + 2 >= X + 1 = isNatIList(X) isNatIList(active(X)) = X + 2 >= X + 1 = isNatIList(X) U51(mark(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,mark(X2)) = 1 >= 1 = U51(X1,X2) U51(active(X1),X2) = 1 >= 1 = U51(X1,X2) U51(X1,active(X2)) = 1 >= 1 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 1 >= 1 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 1 >= 1 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 1 >= 1 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 1 >= 1 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 1 >= 1 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 1 >= 1 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 1 >= 1 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 1 >= 1 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 1 >= 1 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 1 >= 1 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 1 >= 1 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 1 >= 1 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 0 >= 0 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 0 >= 0 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 0 >= 0 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 0 >= 0 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 0 >= 0 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 0 >= 0 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 0 >= 0 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 0 >= 0 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 0 >= 0 = U93(X1,X2,X3) U94(mark(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,mark(X2)) = 0 >= 0 = U94(X1,X2) U94(active(X1),X2) = 0 >= 0 = U94(X1,X2) U94(X1,active(X2)) = 0 >= 0 = U94(X1,X2) s(mark(X)) = 0 >= 0 = s(X) s(active(X)) = 0 >= 0 = s(X) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3) U91#(active(X1),X2,X3) -> U91#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dimension: 1 interpretation: [U91#](x0, x1, x2) = x0 + 1, [nil] = 0, [s](x0) = 1, [length](x0) = 1, [U94](x0, x1) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U86](x0) = 0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [isNatIList](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [isNat](x0) = 0, [U22](x0, x1) = 0, [isNatKind](x0) = 0, [U21](x0, x1) = 0, [U13](x0) = 0, [isNatList](x0) = 0, [U12](x0, x1) = 0, [isNatIListKind](x0) = 0, [U11](x0, x1) = 0, [tt] = 0, [mark](x0) = x0 + 1, [cons](x0, x1) = 0, [0] = 1, [active](x0) = x0 + 1, [zeros] = 0 orientation: U91#(mark(X1),X2,X3) = X1 + 2 >= X1 + 1 = U91#(X1,X2,X3) U91#(active(X1),X2,X3) = X1 + 2 >= X1 + 1 = U91#(X1,X2,X3) active(zeros()) = 1 >= 1 = mark(cons(0(),zeros())) active(U11(tt(),V1)) = 1 >= 1 = mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) = 1 >= 1 = mark(U13(isNatList(V1))) active(U13(tt())) = 1 >= 1 = mark(tt()) active(U21(tt(),V1)) = 1 >= 1 = mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) = 1 >= 1 = mark(U23(isNat(V1))) active(U23(tt())) = 1 >= 1 = mark(tt()) active(U31(tt(),V)) = 1 >= 1 = mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) = 1 >= 1 = mark(U33(isNatList(V))) active(U33(tt())) = 1 >= 1 = mark(tt()) active(U41(tt(),V1,V2)) = 1 >= 1 = mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) = 1 >= 1 = mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) = 1 >= 1 = mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) = 1 >= 1 = mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) = 1 >= 1 = mark(U46(isNatIList(V2))) active(U46(tt())) = 1 >= 1 = mark(tt()) active(U51(tt(),V2)) = 1 >= 1 = mark(U52(isNatIListKind(V2))) active(U52(tt())) = 1 >= 1 = mark(tt()) active(U61(tt())) = 1 >= 1 = mark(tt()) active(U71(tt())) = 1 >= 1 = mark(tt()) active(U81(tt(),V1,V2)) = 1 >= 1 = mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) = 1 >= 1 = mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) = 1 >= 1 = mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) = 1 >= 1 = mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) = 1 >= 1 = mark(U86(isNatList(V2))) active(U86(tt())) = 1 >= 1 = mark(tt()) active(U91(tt(),L,N)) = 2 >= 2 = mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) = 2 >= 2 = mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) = 2 >= 2 = mark(U94(isNatKind(N),L)) active(U94(tt(),L)) = 2 >= 2 = mark(s(length(L))) active(isNat(0())) = 1 >= 1 = mark(tt()) active(isNat(length(V1))) = 1 >= 1 = mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) = 1 >= 1 = mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) = 1 >= 1 = mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) = 1 >= 1 = mark(tt()) active(isNatIList(cons(V1,V2))) = 1 >= 1 = mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) = 1 >= 1 = mark(tt()) active(isNatIListKind(zeros())) = 1 >= 1 = mark(tt()) active(isNatIListKind(cons(V1,V2))) = 1 >= 1 = mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) = 1 >= 1 = mark(tt()) active(isNatKind(length(V1))) = 1 >= 1 = mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) = 1 >= 1 = mark(U71(isNatKind(V1))) active(isNatList(nil())) = 1 >= 1 = mark(tt()) active(isNatList(cons(V1,V2))) = 1 >= 1 = mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) = 2 >= 2 = mark(0()) active(length(cons(N,L))) = 2 >= 2 = mark(U91(isNatList(L),L,N)) mark(zeros()) = 1 >= 1 = active(zeros()) mark(cons(X1,X2)) = 1 >= 1 = active(cons(mark(X1),X2)) mark(0()) = 2 >= 2 = active(0()) mark(U11(X1,X2)) = 1 >= 1 = active(U11(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2)) = 1 >= 1 = active(U12(mark(X1),X2)) mark(isNatIListKind(X)) = 1 >= 1 = active(isNatIListKind(X)) mark(U13(X)) = 1 >= 1 = active(U13(mark(X))) mark(isNatList(X)) = 1 >= 1 = active(isNatList(X)) mark(U21(X1,X2)) = 1 >= 1 = active(U21(mark(X1),X2)) mark(U22(X1,X2)) = 1 >= 1 = active(U22(mark(X1),X2)) mark(isNatKind(X)) = 1 >= 1 = active(isNatKind(X)) mark(U23(X)) = 1 >= 1 = active(U23(mark(X))) mark(isNat(X)) = 1 >= 1 = active(isNat(X)) mark(U31(X1,X2)) = 1 >= 1 = active(U31(mark(X1),X2)) mark(U32(X1,X2)) = 1 >= 1 = active(U32(mark(X1),X2)) mark(U33(X)) = 1 >= 1 = active(U33(mark(X))) mark(U41(X1,X2,X3)) = 1 >= 1 = active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) = 1 >= 1 = active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) = 1 >= 1 = active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) = 1 >= 1 = active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) = 1 >= 1 = active(U45(mark(X1),X2)) mark(U46(X)) = 1 >= 1 = active(U46(mark(X))) mark(isNatIList(X)) = 1 >= 1 = active(isNatIList(X)) mark(U51(X1,X2)) = 1 >= 1 = active(U51(mark(X1),X2)) mark(U52(X)) = 1 >= 1 = active(U52(mark(X))) mark(U61(X)) = 1 >= 1 = active(U61(mark(X))) mark(U71(X)) = 1 >= 1 = active(U71(mark(X))) mark(U81(X1,X2,X3)) = 1 >= 1 = active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) = 1 >= 1 = active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) = 1 >= 1 = active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) = 1 >= 1 = active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) = 1 >= 1 = active(U85(mark(X1),X2)) mark(U86(X)) = 1 >= 1 = active(U86(mark(X))) mark(U91(X1,X2,X3)) = 2 >= 2 = active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) = 2 >= 2 = active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) = 2 >= 2 = active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) = 2 >= 2 = active(U94(mark(X1),X2)) mark(s(X)) = 2 >= 2 = active(s(mark(X))) mark(length(X)) = 2 >= 2 = active(length(mark(X))) mark(nil()) = 1 >= 1 = active(nil()) cons(mark(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,mark(X2)) = 0 >= 0 = cons(X1,X2) cons(active(X1),X2) = 0 >= 0 = cons(X1,X2) cons(X1,active(X2)) = 0 >= 0 = cons(X1,X2) U11(mark(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,mark(X2)) = 0 >= 0 = U11(X1,X2) U11(active(X1),X2) = 0 >= 0 = U11(X1,X2) U11(X1,active(X2)) = 0 >= 0 = U11(X1,X2) U12(mark(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,mark(X2)) = 0 >= 0 = U12(X1,X2) U12(active(X1),X2) = 0 >= 0 = U12(X1,X2) U12(X1,active(X2)) = 0 >= 0 = U12(X1,X2) isNatIListKind(mark(X)) = 0 >= 0 = isNatIListKind(X) isNatIListKind(active(X)) = 0 >= 0 = isNatIListKind(X) U13(mark(X)) = 0 >= 0 = U13(X) U13(active(X)) = 0 >= 0 = U13(X) isNatList(mark(X)) = 0 >= 0 = isNatList(X) isNatList(active(X)) = 0 >= 0 = isNatList(X) U21(mark(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,mark(X2)) = 0 >= 0 = U21(X1,X2) U21(active(X1),X2) = 0 >= 0 = U21(X1,X2) U21(X1,active(X2)) = 0 >= 0 = U21(X1,X2) U22(mark(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,mark(X2)) = 0 >= 0 = U22(X1,X2) U22(active(X1),X2) = 0 >= 0 = U22(X1,X2) U22(X1,active(X2)) = 0 >= 0 = U22(X1,X2) isNatKind(mark(X)) = 0 >= 0 = isNatKind(X) isNatKind(active(X)) = 0 >= 0 = isNatKind(X) U23(mark(X)) = 0 >= 0 = U23(X) U23(active(X)) = 0 >= 0 = U23(X) isNat(mark(X)) = 0 >= 0 = isNat(X) isNat(active(X)) = 0 >= 0 = isNat(X) U31(mark(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,mark(X2)) = 0 >= 0 = U31(X1,X2) U31(active(X1),X2) = 0 >= 0 = U31(X1,X2) U31(X1,active(X2)) = 0 >= 0 = U31(X1,X2) U32(mark(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,mark(X2)) = 0 >= 0 = U32(X1,X2) U32(active(X1),X2) = 0 >= 0 = U32(X1,X2) U32(X1,active(X2)) = 0 >= 0 = U32(X1,X2) U33(mark(X)) = 0 >= 0 = U33(X) U33(active(X)) = 0 >= 0 = U33(X) U41(mark(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,mark(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,mark(X3)) = 0 >= 0 = U41(X1,X2,X3) U41(active(X1),X2,X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,active(X2),X3) = 0 >= 0 = U41(X1,X2,X3) U41(X1,X2,active(X3)) = 0 >= 0 = U41(X1,X2,X3) U42(mark(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,mark(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,mark(X3)) = 0 >= 0 = U42(X1,X2,X3) U42(active(X1),X2,X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,active(X2),X3) = 0 >= 0 = U42(X1,X2,X3) U42(X1,X2,active(X3)) = 0 >= 0 = U42(X1,X2,X3) U43(mark(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,mark(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,mark(X3)) = 0 >= 0 = U43(X1,X2,X3) U43(active(X1),X2,X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,active(X2),X3) = 0 >= 0 = U43(X1,X2,X3) U43(X1,X2,active(X3)) = 0 >= 0 = U43(X1,X2,X3) U44(mark(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,mark(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,mark(X3)) = 0 >= 0 = U44(X1,X2,X3) U44(active(X1),X2,X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,active(X2),X3) = 0 >= 0 = U44(X1,X2,X3) U44(X1,X2,active(X3)) = 0 >= 0 = U44(X1,X2,X3) U45(mark(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,mark(X2)) = 0 >= 0 = U45(X1,X2) U45(active(X1),X2) = 0 >= 0 = U45(X1,X2) U45(X1,active(X2)) = 0 >= 0 = U45(X1,X2) U46(mark(X)) = 0 >= 0 = U46(X) U46(active(X)) = 0 >= 0 = U46(X) isNatIList(mark(X)) = 0 >= 0 = isNatIList(X) isNatIList(active(X)) = 0 >= 0 = isNatIList(X) U51(mark(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,mark(X2)) = 0 >= 0 = U51(X1,X2) U51(active(X1),X2) = 0 >= 0 = U51(X1,X2) U51(X1,active(X2)) = 0 >= 0 = U51(X1,X2) U52(mark(X)) = 0 >= 0 = U52(X) U52(active(X)) = 0 >= 0 = U52(X) U61(mark(X)) = 0 >= 0 = U61(X) U61(active(X)) = 0 >= 0 = U61(X) U71(mark(X)) = 0 >= 0 = U71(X) U71(active(X)) = 0 >= 0 = U71(X) U81(mark(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,mark(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,mark(X3)) = 0 >= 0 = U81(X1,X2,X3) U81(active(X1),X2,X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,active(X2),X3) = 0 >= 0 = U81(X1,X2,X3) U81(X1,X2,active(X3)) = 0 >= 0 = U81(X1,X2,X3) U82(mark(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,mark(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,mark(X3)) = 0 >= 0 = U82(X1,X2,X3) U82(active(X1),X2,X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,active(X2),X3) = 0 >= 0 = U82(X1,X2,X3) U82(X1,X2,active(X3)) = 0 >= 0 = U82(X1,X2,X3) U83(mark(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,mark(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,mark(X3)) = 0 >= 0 = U83(X1,X2,X3) U83(active(X1),X2,X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,active(X2),X3) = 0 >= 0 = U83(X1,X2,X3) U83(X1,X2,active(X3)) = 0 >= 0 = U83(X1,X2,X3) U84(mark(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,mark(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,mark(X3)) = 0 >= 0 = U84(X1,X2,X3) U84(active(X1),X2,X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,active(X2),X3) = 0 >= 0 = U84(X1,X2,X3) U84(X1,X2,active(X3)) = 0 >= 0 = U84(X1,X2,X3) U85(mark(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,mark(X2)) = 0 >= 0 = U85(X1,X2) U85(active(X1),X2) = 0 >= 0 = U85(X1,X2) U85(X1,active(X2)) = 0 >= 0 = U85(X1,X2) U86(mark(X)) = 0 >= 0 = U86(X) U86(active(X)) = 0 >= 0 = U86(X) U91(mark(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,mark(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,mark(X3)) = 1 >= 1 = U91(X1,X2,X3) U91(active(X1),X2,X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,active(X2),X3) = 1 >= 1 = U91(X1,X2,X3) U91(X1,X2,active(X3)) = 1 >= 1 = U91(X1,X2,X3) U92(mark(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,mark(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,mark(X3)) = 1 >= 1 = U92(X1,X2,X3) U92(active(X1),X2,X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,active(X2),X3) = 1 >= 1 = U92(X1,X2,X3) U92(X1,X2,active(X3)) = 1 >= 1 = U92(X1,X2,X3) U93(mark(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,mark(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,mark(X3)) = 1 >= 1 = U93(X1,X2,X3) U93(active(X1),X2,X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,active(X2),X3) = 1 >= 1 = U93(X1,X2,X3) U93(X1,X2,active(X3)) = 1 >= 1 = U93(X1,X2,X3) U94(mark(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,mark(X2)) = 1 >= 1 = U94(X1,X2) U94(active(X1),X2) = 1 >= 1 = U94(X1,X2) U94(X1,active(X2)) = 1 >= 1 = U94(X1,X2) s(mark(X)) = 1 >= 1 = s(X) s(active(X)) = 1 >= 1 = s(X) length(mark(X)) = 1 >= 1 = length(X) length(active(X)) = 1 >= 1 = length(X) problem: DPs: TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),V1)) -> mark(U12(isNatIListKind(V1),V1)) active(U12(tt(),V1)) -> mark(U13(isNatList(V1))) active(U13(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V)) -> mark(U32(isNatIListKind(V),V)) active(U32(tt(),V)) -> mark(U33(isNatList(V))) active(U33(tt())) -> mark(tt()) active(U41(tt(),V1,V2)) -> mark(U42(isNatKind(V1),V1,V2)) active(U42(tt(),V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2)) active(U43(tt(),V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2)) active(U44(tt(),V1,V2)) -> mark(U45(isNat(V1),V2)) active(U45(tt(),V2)) -> mark(U46(isNatIList(V2))) active(U46(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatIListKind(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt())) -> mark(tt()) active(U71(tt())) -> mark(tt()) active(U81(tt(),V1,V2)) -> mark(U82(isNatKind(V1),V1,V2)) active(U82(tt(),V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2)) active(U83(tt(),V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2)) active(U84(tt(),V1,V2)) -> mark(U85(isNat(V1),V2)) active(U85(tt(),V2)) -> mark(U86(isNatList(V2))) active(U86(tt())) -> mark(tt()) active(U91(tt(),L,N)) -> mark(U92(isNatIListKind(L),L,N)) active(U92(tt(),L,N)) -> mark(U93(isNat(N),L,N)) active(U93(tt(),L,N)) -> mark(U94(isNatKind(N),L)) active(U94(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNatKind(V1),V1,V2)) active(isNatIListKind(nil())) -> mark(tt()) active(isNatIListKind(zeros())) -> mark(tt()) active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1))) active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U23(X)) -> active(U23(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X)) -> active(U61(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(U85(X1,X2)) -> active(U85(mark(X1),X2)) mark(U86(X)) -> active(U86(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2)) -> active(U94(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X)) -> U61(X) U61(active(X)) -> U61(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) U85(mark(X1),X2) -> U85(X1,X2) U85(X1,mark(X2)) -> U85(X1,X2) U85(active(X1),X2) -> U85(X1,X2) U85(X1,active(X2)) -> U85(X1,X2) U86(mark(X)) -> U86(X) U86(active(X)) -> U86(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2) -> U94(X1,X2) U94(X1,mark(X2)) -> U94(X1,X2) U94(active(X1),X2) -> U94(X1,X2) U94(X1,active(X2)) -> U94(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed