MAYBE Problem: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Proof: DP Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt())) -> mark#(tt()) active#(U21(tt())) -> mark#(tt()) active#(U31(tt())) -> mark#(tt()) active#(U41(tt(),V2)) -> isNatIList#(V2) active#(U41(tt(),V2)) -> U42#(isNatIList(V2)) active#(U41(tt(),V2)) -> mark#(U42(isNatIList(V2))) active#(U42(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> isNatList#(V2) active#(U51(tt(),V2)) -> U52#(isNatList(V2)) active#(U51(tt(),V2)) -> mark#(U52(isNatList(V2))) active#(U52(tt())) -> mark#(tt()) active#(U61(tt(),V2)) -> isNatIList#(V2) active#(U61(tt(),V2)) -> U62#(isNatIList(V2)) active#(U61(tt(),V2)) -> mark#(U62(isNatIList(V2))) active#(U62(tt())) -> mark#(tt()) active#(U71(tt(),L,N)) -> isNat#(N) active#(U71(tt(),L,N)) -> U72#(isNat(N),L) active#(U71(tt(),L,N)) -> mark#(U72(isNat(N),L)) active#(U72(tt(),L)) -> length#(L) active#(U72(tt(),L)) -> s#(length(L)) active#(U72(tt(),L)) -> mark#(s(length(L))) active#(U81(tt())) -> mark#(nil()) active#(U91(tt(),IL,M,N)) -> isNat#(M) active#(U91(tt(),IL,M,N)) -> U92#(isNat(M),IL,M,N) active#(U91(tt(),IL,M,N)) -> mark#(U92(isNat(M),IL,M,N)) active#(U92(tt(),IL,M,N)) -> isNat#(N) active#(U92(tt(),IL,M,N)) -> U93#(isNat(N),IL,M,N) active#(U92(tt(),IL,M,N)) -> mark#(U93(isNat(N),IL,M,N)) active#(U93(tt(),IL,M,N)) -> take#(M,IL) active#(U93(tt(),IL,M,N)) -> cons#(N,take(M,IL)) active#(U93(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) active#(isNat(0())) -> mark#(tt()) active#(isNat(length(V1))) -> isNatList#(V1) active#(isNat(length(V1))) -> U11#(isNatList(V1)) active#(isNat(length(V1))) -> mark#(U11(isNatList(V1))) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> U21#(isNat(V1)) active#(isNat(s(V1))) -> mark#(U21(isNat(V1))) active#(isNatIList(V)) -> isNatList#(V) active#(isNatIList(V)) -> U31#(isNatList(V)) active#(isNatIList(V)) -> mark#(U31(isNatList(V))) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(V1,V2))) -> isNat#(V1) active#(isNatIList(cons(V1,V2))) -> U41#(isNat(V1),V2) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNat(V1),V2)) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> isNat#(V1) active#(isNatList(cons(V1,V2))) -> U51#(isNat(V1),V2) active#(isNatList(cons(V1,V2))) -> mark#(U51(isNat(V1),V2)) active#(isNatList(take(V1,V2))) -> isNat#(V1) active#(isNatList(take(V1,V2))) -> U61#(isNat(V1),V2) active#(isNatList(take(V1,V2))) -> mark#(U61(isNat(V1),V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> U71#(isNatList(L),L,N) active#(length(cons(N,L))) -> mark#(U71(isNatList(L),L,N)) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> U81#(isNatIList(IL)) active#(take(0(),IL)) -> mark#(U81(isNatIList(IL))) active#(take(s(M),cons(N,IL))) -> isNatIList#(IL) active#(take(s(M),cons(N,IL))) -> U91#(isNatIList(IL),IL,M,N) active#(take(s(M),cons(N,IL))) -> mark#(U91(isNatIList(IL),IL,M,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(X)) -> mark#(X) mark#(U11(X)) -> U11#(mark(X)) mark#(U11(X)) -> active#(U11(mark(X))) mark#(tt()) -> active#(tt()) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> U21#(mark(X)) mark#(U21(X)) -> active#(U21(mark(X))) mark#(U31(X)) -> mark#(X) mark#(U31(X)) -> U31#(mark(X)) mark#(U31(X)) -> active#(U31(mark(X))) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> U41#(mark(X1),X2) mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2)) mark#(U42(X)) -> mark#(X) mark#(U42(X)) -> U42#(mark(X)) mark#(U42(X)) -> active#(U42(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#(isNatList(X)) -> active#(isNatList(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> U71#(mark(X1),X2,X3) mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3)) mark#(U72(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> U72#(mark(X1),X2) mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) 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#(U81(X)) -> mark#(X) mark#(U81(X)) -> U81#(mark(X)) mark#(U81(X)) -> active#(U81(mark(X))) mark#(nil()) -> active#(nil()) mark#(U91(X1,X2,X3,X4)) -> mark#(X1) mark#(U91(X1,X2,X3,X4)) -> U91#(mark(X1),X2,X3,X4) mark#(U91(X1,X2,X3,X4)) -> active#(U91(mark(X1),X2,X3,X4)) mark#(U92(X1,X2,X3,X4)) -> mark#(X1) mark#(U92(X1,X2,X3,X4)) -> U92#(mark(X1),X2,X3,X4) mark#(U92(X1,X2,X3,X4)) -> active#(U92(mark(X1),X2,X3,X4)) mark#(U93(X1,X2,X3,X4)) -> mark#(X1) mark#(U93(X1,X2,X3,X4)) -> U93#(mark(X1),X2,X3,X4) mark#(U93(X1,X2,X3,X4)) -> active#(U93(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) 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(X)) -> U11#(X) U11#(active(X)) -> U11#(X) U21#(mark(X)) -> U21#(X) U21#(active(X)) -> U21#(X) U31#(mark(X)) -> U31#(X) U31#(active(X)) -> U31#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U41#(X1,mark(X2)) -> U41#(X1,X2) U41#(active(X1),X2) -> U41#(X1,X2) U41#(X1,active(X2)) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U42#(active(X)) -> U42#(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) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) U72#(active(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) U81#(mark(X)) -> U81#(X) U81#(active(X)) -> U81#(X) U91#(mark(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,mark(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,mark(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,mark(X4)) -> U91#(X1,X2,X3,X4) U91#(active(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,active(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,active(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,active(X4)) -> U91#(X1,X2,X3,X4) U92#(mark(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,mark(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,mark(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,mark(X4)) -> U92#(X1,X2,X3,X4) U92#(active(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,active(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,active(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,active(X4)) -> U92#(X1,X2,X3,X4) U93#(mark(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,mark(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,mark(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,mark(X4)) -> U93#(X1,X2,X3,X4) U93#(active(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,active(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,active(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,active(X4)) -> U93#(X1,X2,X3,X4) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) TDG Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt())) -> mark#(tt()) active#(U21(tt())) -> mark#(tt()) active#(U31(tt())) -> mark#(tt()) active#(U41(tt(),V2)) -> isNatIList#(V2) active#(U41(tt(),V2)) -> U42#(isNatIList(V2)) active#(U41(tt(),V2)) -> mark#(U42(isNatIList(V2))) active#(U42(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> isNatList#(V2) active#(U51(tt(),V2)) -> U52#(isNatList(V2)) active#(U51(tt(),V2)) -> mark#(U52(isNatList(V2))) active#(U52(tt())) -> mark#(tt()) active#(U61(tt(),V2)) -> isNatIList#(V2) active#(U61(tt(),V2)) -> U62#(isNatIList(V2)) active#(U61(tt(),V2)) -> mark#(U62(isNatIList(V2))) active#(U62(tt())) -> mark#(tt()) active#(U71(tt(),L,N)) -> isNat#(N) active#(U71(tt(),L,N)) -> U72#(isNat(N),L) active#(U71(tt(),L,N)) -> mark#(U72(isNat(N),L)) active#(U72(tt(),L)) -> length#(L) active#(U72(tt(),L)) -> s#(length(L)) active#(U72(tt(),L)) -> mark#(s(length(L))) active#(U81(tt())) -> mark#(nil()) active#(U91(tt(),IL,M,N)) -> isNat#(M) active#(U91(tt(),IL,M,N)) -> U92#(isNat(M),IL,M,N) active#(U91(tt(),IL,M,N)) -> mark#(U92(isNat(M),IL,M,N)) active#(U92(tt(),IL,M,N)) -> isNat#(N) active#(U92(tt(),IL,M,N)) -> U93#(isNat(N),IL,M,N) active#(U92(tt(),IL,M,N)) -> mark#(U93(isNat(N),IL,M,N)) active#(U93(tt(),IL,M,N)) -> take#(M,IL) active#(U93(tt(),IL,M,N)) -> cons#(N,take(M,IL)) active#(U93(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) active#(isNat(0())) -> mark#(tt()) active#(isNat(length(V1))) -> isNatList#(V1) active#(isNat(length(V1))) -> U11#(isNatList(V1)) active#(isNat(length(V1))) -> mark#(U11(isNatList(V1))) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> U21#(isNat(V1)) active#(isNat(s(V1))) -> mark#(U21(isNat(V1))) active#(isNatIList(V)) -> isNatList#(V) active#(isNatIList(V)) -> U31#(isNatList(V)) active#(isNatIList(V)) -> mark#(U31(isNatList(V))) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(V1,V2))) -> isNat#(V1) active#(isNatIList(cons(V1,V2))) -> U41#(isNat(V1),V2) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNat(V1),V2)) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> isNat#(V1) active#(isNatList(cons(V1,V2))) -> U51#(isNat(V1),V2) active#(isNatList(cons(V1,V2))) -> mark#(U51(isNat(V1),V2)) active#(isNatList(take(V1,V2))) -> isNat#(V1) active#(isNatList(take(V1,V2))) -> U61#(isNat(V1),V2) active#(isNatList(take(V1,V2))) -> mark#(U61(isNat(V1),V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> U71#(isNatList(L),L,N) active#(length(cons(N,L))) -> mark#(U71(isNatList(L),L,N)) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> U81#(isNatIList(IL)) active#(take(0(),IL)) -> mark#(U81(isNatIList(IL))) active#(take(s(M),cons(N,IL))) -> isNatIList#(IL) active#(take(s(M),cons(N,IL))) -> U91#(isNatIList(IL),IL,M,N) active#(take(s(M),cons(N,IL))) -> mark#(U91(isNatIList(IL),IL,M,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(X)) -> mark#(X) mark#(U11(X)) -> U11#(mark(X)) mark#(U11(X)) -> active#(U11(mark(X))) mark#(tt()) -> active#(tt()) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> U21#(mark(X)) mark#(U21(X)) -> active#(U21(mark(X))) mark#(U31(X)) -> mark#(X) mark#(U31(X)) -> U31#(mark(X)) mark#(U31(X)) -> active#(U31(mark(X))) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> U41#(mark(X1),X2) mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2)) mark#(U42(X)) -> mark#(X) mark#(U42(X)) -> U42#(mark(X)) mark#(U42(X)) -> active#(U42(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#(isNatList(X)) -> active#(isNatList(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> U71#(mark(X1),X2,X3) mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3)) mark#(U72(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> U72#(mark(X1),X2) mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) 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#(U81(X)) -> mark#(X) mark#(U81(X)) -> U81#(mark(X)) mark#(U81(X)) -> active#(U81(mark(X))) mark#(nil()) -> active#(nil()) mark#(U91(X1,X2,X3,X4)) -> mark#(X1) mark#(U91(X1,X2,X3,X4)) -> U91#(mark(X1),X2,X3,X4) mark#(U91(X1,X2,X3,X4)) -> active#(U91(mark(X1),X2,X3,X4)) mark#(U92(X1,X2,X3,X4)) -> mark#(X1) mark#(U92(X1,X2,X3,X4)) -> U92#(mark(X1),X2,X3,X4) mark#(U92(X1,X2,X3,X4)) -> active#(U92(mark(X1),X2,X3,X4)) mark#(U93(X1,X2,X3,X4)) -> mark#(X1) mark#(U93(X1,X2,X3,X4)) -> U93#(mark(X1),X2,X3,X4) mark#(U93(X1,X2,X3,X4)) -> active#(U93(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) 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(X)) -> U11#(X) U11#(active(X)) -> U11#(X) U21#(mark(X)) -> U21#(X) U21#(active(X)) -> U21#(X) U31#(mark(X)) -> U31#(X) U31#(active(X)) -> U31#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U41#(X1,mark(X2)) -> U41#(X1,X2) U41#(active(X1),X2) -> U41#(X1,X2) U41#(X1,active(X2)) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U42#(active(X)) -> U42#(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) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) U72#(active(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) U81#(mark(X)) -> U81#(X) U81#(active(X)) -> U81#(X) U91#(mark(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,mark(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,mark(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,mark(X4)) -> U91#(X1,X2,X3,X4) U91#(active(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,active(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,active(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,active(X4)) -> U91#(X1,X2,X3,X4) U92#(mark(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,mark(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,mark(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,mark(X4)) -> U92#(X1,X2,X3,X4) U92#(active(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,active(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,active(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,active(X4)) -> U92#(X1,X2,X3,X4) U93#(mark(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,mark(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,mark(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,mark(X4)) -> U93#(X1,X2,X3,X4) U93#(active(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,active(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,active(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,active(X4)) -> U93#(X1,X2,X3,X4) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) graph: ... EDG Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt())) -> mark#(tt()) active#(U21(tt())) -> mark#(tt()) active#(U31(tt())) -> mark#(tt()) active#(U41(tt(),V2)) -> isNatIList#(V2) active#(U41(tt(),V2)) -> U42#(isNatIList(V2)) active#(U41(tt(),V2)) -> mark#(U42(isNatIList(V2))) active#(U42(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> isNatList#(V2) active#(U51(tt(),V2)) -> U52#(isNatList(V2)) active#(U51(tt(),V2)) -> mark#(U52(isNatList(V2))) active#(U52(tt())) -> mark#(tt()) active#(U61(tt(),V2)) -> isNatIList#(V2) active#(U61(tt(),V2)) -> U62#(isNatIList(V2)) active#(U61(tt(),V2)) -> mark#(U62(isNatIList(V2))) active#(U62(tt())) -> mark#(tt()) active#(U71(tt(),L,N)) -> isNat#(N) active#(U71(tt(),L,N)) -> U72#(isNat(N),L) active#(U71(tt(),L,N)) -> mark#(U72(isNat(N),L)) active#(U72(tt(),L)) -> length#(L) active#(U72(tt(),L)) -> s#(length(L)) active#(U72(tt(),L)) -> mark#(s(length(L))) active#(U81(tt())) -> mark#(nil()) active#(U91(tt(),IL,M,N)) -> isNat#(M) active#(U91(tt(),IL,M,N)) -> U92#(isNat(M),IL,M,N) active#(U91(tt(),IL,M,N)) -> mark#(U92(isNat(M),IL,M,N)) active#(U92(tt(),IL,M,N)) -> isNat#(N) active#(U92(tt(),IL,M,N)) -> U93#(isNat(N),IL,M,N) active#(U92(tt(),IL,M,N)) -> mark#(U93(isNat(N),IL,M,N)) active#(U93(tt(),IL,M,N)) -> take#(M,IL) active#(U93(tt(),IL,M,N)) -> cons#(N,take(M,IL)) active#(U93(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) active#(isNat(0())) -> mark#(tt()) active#(isNat(length(V1))) -> isNatList#(V1) active#(isNat(length(V1))) -> U11#(isNatList(V1)) active#(isNat(length(V1))) -> mark#(U11(isNatList(V1))) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> U21#(isNat(V1)) active#(isNat(s(V1))) -> mark#(U21(isNat(V1))) active#(isNatIList(V)) -> isNatList#(V) active#(isNatIList(V)) -> U31#(isNatList(V)) active#(isNatIList(V)) -> mark#(U31(isNatList(V))) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(V1,V2))) -> isNat#(V1) active#(isNatIList(cons(V1,V2))) -> U41#(isNat(V1),V2) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNat(V1),V2)) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> isNat#(V1) active#(isNatList(cons(V1,V2))) -> U51#(isNat(V1),V2) active#(isNatList(cons(V1,V2))) -> mark#(U51(isNat(V1),V2)) active#(isNatList(take(V1,V2))) -> isNat#(V1) active#(isNatList(take(V1,V2))) -> U61#(isNat(V1),V2) active#(isNatList(take(V1,V2))) -> mark#(U61(isNat(V1),V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> U71#(isNatList(L),L,N) active#(length(cons(N,L))) -> mark#(U71(isNatList(L),L,N)) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> U81#(isNatIList(IL)) active#(take(0(),IL)) -> mark#(U81(isNatIList(IL))) active#(take(s(M),cons(N,IL))) -> isNatIList#(IL) active#(take(s(M),cons(N,IL))) -> U91#(isNatIList(IL),IL,M,N) active#(take(s(M),cons(N,IL))) -> mark#(U91(isNatIList(IL),IL,M,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(X)) -> mark#(X) mark#(U11(X)) -> U11#(mark(X)) mark#(U11(X)) -> active#(U11(mark(X))) mark#(tt()) -> active#(tt()) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> U21#(mark(X)) mark#(U21(X)) -> active#(U21(mark(X))) mark#(U31(X)) -> mark#(X) mark#(U31(X)) -> U31#(mark(X)) mark#(U31(X)) -> active#(U31(mark(X))) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> U41#(mark(X1),X2) mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2)) mark#(U42(X)) -> mark#(X) mark#(U42(X)) -> U42#(mark(X)) mark#(U42(X)) -> active#(U42(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#(isNatList(X)) -> active#(isNatList(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> U71#(mark(X1),X2,X3) mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3)) mark#(U72(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> U72#(mark(X1),X2) mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) 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#(U81(X)) -> mark#(X) mark#(U81(X)) -> U81#(mark(X)) mark#(U81(X)) -> active#(U81(mark(X))) mark#(nil()) -> active#(nil()) mark#(U91(X1,X2,X3,X4)) -> mark#(X1) mark#(U91(X1,X2,X3,X4)) -> U91#(mark(X1),X2,X3,X4) mark#(U91(X1,X2,X3,X4)) -> active#(U91(mark(X1),X2,X3,X4)) mark#(U92(X1,X2,X3,X4)) -> mark#(X1) mark#(U92(X1,X2,X3,X4)) -> U92#(mark(X1),X2,X3,X4) mark#(U92(X1,X2,X3,X4)) -> active#(U92(mark(X1),X2,X3,X4)) mark#(U93(X1,X2,X3,X4)) -> mark#(X1) mark#(U93(X1,X2,X3,X4)) -> U93#(mark(X1),X2,X3,X4) mark#(U93(X1,X2,X3,X4)) -> active#(U93(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) 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(X)) -> U11#(X) U11#(active(X)) -> U11#(X) U21#(mark(X)) -> U21#(X) U21#(active(X)) -> U21#(X) U31#(mark(X)) -> U31#(X) U31#(active(X)) -> U31#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U41#(X1,mark(X2)) -> U41#(X1,X2) U41#(active(X1),X2) -> U41#(X1,X2) U41#(X1,active(X2)) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U42#(active(X)) -> U42#(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) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) U72#(active(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) U81#(mark(X)) -> U81#(X) U81#(active(X)) -> U81#(X) U91#(mark(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,mark(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,mark(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,mark(X4)) -> U91#(X1,X2,X3,X4) U91#(active(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,active(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,active(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,active(X4)) -> U91#(X1,X2,X3,X4) U92#(mark(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,mark(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,mark(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,mark(X4)) -> U92#(X1,X2,X3,X4) U92#(active(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,active(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,active(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,active(X4)) -> U92#(X1,X2,X3,X4) U93#(mark(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,mark(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,mark(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,mark(X4)) -> U93#(X1,X2,X3,X4) U93#(active(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,active(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,active(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,active(X4)) -> U93#(X1,X2,X3,X4) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) graph: ... Restore Modifier: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt())) -> mark#(tt()) active#(U21(tt())) -> mark#(tt()) active#(U31(tt())) -> mark#(tt()) active#(U41(tt(),V2)) -> isNatIList#(V2) active#(U41(tt(),V2)) -> U42#(isNatIList(V2)) active#(U41(tt(),V2)) -> mark#(U42(isNatIList(V2))) active#(U42(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> isNatList#(V2) active#(U51(tt(),V2)) -> U52#(isNatList(V2)) active#(U51(tt(),V2)) -> mark#(U52(isNatList(V2))) active#(U52(tt())) -> mark#(tt()) active#(U61(tt(),V2)) -> isNatIList#(V2) active#(U61(tt(),V2)) -> U62#(isNatIList(V2)) active#(U61(tt(),V2)) -> mark#(U62(isNatIList(V2))) active#(U62(tt())) -> mark#(tt()) active#(U71(tt(),L,N)) -> isNat#(N) active#(U71(tt(),L,N)) -> U72#(isNat(N),L) active#(U71(tt(),L,N)) -> mark#(U72(isNat(N),L)) active#(U72(tt(),L)) -> length#(L) active#(U72(tt(),L)) -> s#(length(L)) active#(U72(tt(),L)) -> mark#(s(length(L))) active#(U81(tt())) -> mark#(nil()) active#(U91(tt(),IL,M,N)) -> isNat#(M) active#(U91(tt(),IL,M,N)) -> U92#(isNat(M),IL,M,N) active#(U91(tt(),IL,M,N)) -> mark#(U92(isNat(M),IL,M,N)) active#(U92(tt(),IL,M,N)) -> isNat#(N) active#(U92(tt(),IL,M,N)) -> U93#(isNat(N),IL,M,N) active#(U92(tt(),IL,M,N)) -> mark#(U93(isNat(N),IL,M,N)) active#(U93(tt(),IL,M,N)) -> take#(M,IL) active#(U93(tt(),IL,M,N)) -> cons#(N,take(M,IL)) active#(U93(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) active#(isNat(0())) -> mark#(tt()) active#(isNat(length(V1))) -> isNatList#(V1) active#(isNat(length(V1))) -> U11#(isNatList(V1)) active#(isNat(length(V1))) -> mark#(U11(isNatList(V1))) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> U21#(isNat(V1)) active#(isNat(s(V1))) -> mark#(U21(isNat(V1))) active#(isNatIList(V)) -> isNatList#(V) active#(isNatIList(V)) -> U31#(isNatList(V)) active#(isNatIList(V)) -> mark#(U31(isNatList(V))) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(V1,V2))) -> isNat#(V1) active#(isNatIList(cons(V1,V2))) -> U41#(isNat(V1),V2) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNat(V1),V2)) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> isNat#(V1) active#(isNatList(cons(V1,V2))) -> U51#(isNat(V1),V2) active#(isNatList(cons(V1,V2))) -> mark#(U51(isNat(V1),V2)) active#(isNatList(take(V1,V2))) -> isNat#(V1) active#(isNatList(take(V1,V2))) -> U61#(isNat(V1),V2) active#(isNatList(take(V1,V2))) -> mark#(U61(isNat(V1),V2)) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> U71#(isNatList(L),L,N) active#(length(cons(N,L))) -> mark#(U71(isNatList(L),L,N)) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> U81#(isNatIList(IL)) active#(take(0(),IL)) -> mark#(U81(isNatIList(IL))) active#(take(s(M),cons(N,IL))) -> isNatIList#(IL) active#(take(s(M),cons(N,IL))) -> U91#(isNatIList(IL),IL,M,N) active#(take(s(M),cons(N,IL))) -> mark#(U91(isNatIList(IL),IL,M,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(X)) -> mark#(X) mark#(U11(X)) -> U11#(mark(X)) mark#(U11(X)) -> active#(U11(mark(X))) mark#(tt()) -> active#(tt()) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> U21#(mark(X)) mark#(U21(X)) -> active#(U21(mark(X))) mark#(U31(X)) -> mark#(X) mark#(U31(X)) -> U31#(mark(X)) mark#(U31(X)) -> active#(U31(mark(X))) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> U41#(mark(X1),X2) mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2)) mark#(U42(X)) -> mark#(X) mark#(U42(X)) -> U42#(mark(X)) mark#(U42(X)) -> active#(U42(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#(isNatList(X)) -> active#(isNatList(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> U71#(mark(X1),X2,X3) mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3)) mark#(U72(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> U72#(mark(X1),X2) mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) 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#(U81(X)) -> mark#(X) mark#(U81(X)) -> U81#(mark(X)) mark#(U81(X)) -> active#(U81(mark(X))) mark#(nil()) -> active#(nil()) mark#(U91(X1,X2,X3,X4)) -> mark#(X1) mark#(U91(X1,X2,X3,X4)) -> U91#(mark(X1),X2,X3,X4) mark#(U91(X1,X2,X3,X4)) -> active#(U91(mark(X1),X2,X3,X4)) mark#(U92(X1,X2,X3,X4)) -> mark#(X1) mark#(U92(X1,X2,X3,X4)) -> U92#(mark(X1),X2,X3,X4) mark#(U92(X1,X2,X3,X4)) -> active#(U92(mark(X1),X2,X3,X4)) mark#(U93(X1,X2,X3,X4)) -> mark#(X1) mark#(U93(X1,X2,X3,X4)) -> U93#(mark(X1),X2,X3,X4) mark#(U93(X1,X2,X3,X4)) -> active#(U93(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) 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(X)) -> U11#(X) U11#(active(X)) -> U11#(X) U21#(mark(X)) -> U21#(X) U21#(active(X)) -> U21#(X) U31#(mark(X)) -> U31#(X) U31#(active(X)) -> U31#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U41#(X1,mark(X2)) -> U41#(X1,X2) U41#(active(X1),X2) -> U41#(X1,X2) U41#(X1,active(X2)) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U42#(active(X)) -> U42#(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) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) U72#(active(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) U81#(mark(X)) -> U81#(X) U81#(active(X)) -> U81#(X) U91#(mark(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,mark(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,mark(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,mark(X4)) -> U91#(X1,X2,X3,X4) U91#(active(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,active(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,active(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,active(X4)) -> U91#(X1,X2,X3,X4) U92#(mark(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,mark(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,mark(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,mark(X4)) -> U92#(X1,X2,X3,X4) U92#(active(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,active(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,active(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,active(X4)) -> U92#(X1,X2,X3,X4) U93#(mark(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,mark(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,mark(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,mark(X4)) -> U93#(X1,X2,X3,X4) U93#(active(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,active(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,active(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,active(X4)) -> U93#(X1,X2,X3,X4) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) SCC Processor: #sccs: 23 #rules: 139 #arcs: 4263/42849 DPs: mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(take(s(M),cons(N,IL))) -> mark#(U91(isNatIList(IL),IL,M,N)) mark#(take(X1,X2)) -> mark#(X1) mark#(U93(X1,X2,X3,X4)) -> active#(U93(mark(X1),X2,X3,X4)) active#(take(0(),IL)) -> mark#(U81(isNatIList(IL))) mark#(U93(X1,X2,X3,X4)) -> mark#(X1) mark#(U92(X1,X2,X3,X4)) -> active#(U92(mark(X1),X2,X3,X4)) active#(length(cons(N,L))) -> mark#(U71(isNatList(L),L,N)) mark#(U92(X1,X2,X3,X4)) -> mark#(X1) mark#(U91(X1,X2,X3,X4)) -> active#(U91(mark(X1),X2,X3,X4)) active#(isNatList(take(V1,V2))) -> mark#(U61(isNat(V1),V2)) mark#(U91(X1,X2,X3,X4)) -> mark#(X1) mark#(U81(X)) -> active#(U81(mark(X))) active#(isNatList(cons(V1,V2))) -> mark#(U51(isNat(V1),V2)) mark#(U81(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNat(V1),V2)) mark#(length(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNatIList(V)) -> mark#(U31(isNatList(V))) mark#(s(X)) -> mark#(X) mark#(isNat(X)) -> active#(isNat(X)) active#(isNat(s(V1))) -> mark#(U21(isNat(V1))) mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2)) active#(isNat(length(V1))) -> mark#(U11(isNatList(V1))) mark#(U72(X1,X2)) -> mark#(X1) mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3)) active#(U93(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) mark#(U71(X1,X2,X3)) -> mark#(X1) mark#(U62(X)) -> active#(U62(mark(X))) active#(U92(tt(),IL,M,N)) -> mark#(U93(isNat(N),IL,M,N)) mark#(U62(X)) -> mark#(X) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(U91(tt(),IL,M,N)) -> mark#(U92(isNat(M),IL,M,N)) mark#(U61(X1,X2)) -> mark#(X1) mark#(isNatList(X)) -> active#(isNatList(X)) active#(U72(tt(),L)) -> mark#(s(length(L))) mark#(U52(X)) -> active#(U52(mark(X))) active#(U71(tt(),L,N)) -> mark#(U72(isNat(N),L)) mark#(U52(X)) -> mark#(X) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U61(tt(),V2)) -> mark#(U62(isNatIList(V2))) mark#(U51(X1,X2)) -> mark#(X1) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U51(tt(),V2)) -> mark#(U52(isNatList(V2))) mark#(U42(X)) -> active#(U42(mark(X))) active#(U41(tt(),V2)) -> mark#(U42(isNatIList(V2))) mark#(U42(X)) -> mark#(X) mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2)) mark#(U41(X1,X2)) -> mark#(X1) mark#(U31(X)) -> active#(U31(mark(X))) mark#(U31(X)) -> mark#(X) mark#(U21(X)) -> active#(U21(mark(X))) mark#(U21(X)) -> mark#(X) mark#(U11(X)) -> active#(U11(mark(X))) mark#(U11(X)) -> mark#(X) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(zeros()) -> active#(zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U42#(mark(X)) -> U42#(X) U42#(active(X)) -> U42#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) U72#(active(X1),X2) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U92#(mark(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,active(X4)) -> U92#(X1,X2,X3,X4) U92#(X1,X2,active(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,active(X2),X3,X4) -> U92#(X1,X2,X3,X4) U92#(active(X1),X2,X3,X4) -> U92#(X1,X2,X3,X4) U92#(X1,X2,X3,mark(X4)) -> U92#(X1,X2,X3,X4) U92#(X1,X2,mark(X3),X4) -> U92#(X1,X2,X3,X4) U92#(X1,mark(X2),X3,X4) -> U92#(X1,X2,X3,X4) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U93#(mark(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,active(X4)) -> U93#(X1,X2,X3,X4) U93#(X1,X2,active(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,active(X2),X3,X4) -> U93#(X1,X2,X3,X4) U93#(active(X1),X2,X3,X4) -> U93#(X1,X2,X3,X4) U93#(X1,X2,X3,mark(X4)) -> U93#(X1,X2,X3,X4) U93#(X1,X2,mark(X3),X4) -> U93#(X1,X2,X3,X4) U93#(X1,mark(X2),X3,X4) -> U93#(X1,X2,X3,X4) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: take#(mark(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U11#(mark(X)) -> U11#(X) U11#(active(X)) -> U11#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U21#(mark(X)) -> U21#(X) U21#(active(X)) -> U21#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U31#(mark(X)) -> U31#(X) U31#(active(X)) -> U31#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U41#(mark(X1),X2) -> U41#(X1,X2) U41#(X1,active(X2)) -> U41#(X1,X2) U41#(active(X1),X2) -> U41#(X1,X2) U41#(X1,mark(X2)) -> U41#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3) U71#(X1,active(X2),X3) -> U71#(X1,X2,X3) U71#(active(X1),X2,X3) -> U71#(X1,X2,X3) U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3) U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U81#(mark(X)) -> U81#(X) U81#(active(X)) -> U81#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U91#(mark(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,active(X4)) -> U91#(X1,X2,X3,X4) U91#(X1,X2,active(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,active(X2),X3,X4) -> U91#(X1,X2,X3,X4) U91#(active(X1),X2,X3,X4) -> U91#(X1,X2,X3,X4) U91#(X1,X2,X3,mark(X4)) -> U91#(X1,X2,X3,X4) U91#(X1,X2,mark(X3),X4) -> U91#(X1,X2,X3,X4) U91#(X1,mark(X2),X3,X4) -> U91#(X1,X2,X3,X4) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatIList(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),L,N)) -> mark(U72(isNat(N),L)) active(U72(tt(),L)) -> mark(s(length(L))) active(U81(tt())) -> mark(nil()) active(U91(tt(),IL,M,N)) -> mark(U92(isNat(M),IL,M,N)) active(U92(tt(),IL,M,N)) -> mark(U93(isNat(N),IL,M,N)) active(U93(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N)) active(take(0(),IL)) -> mark(U81(isNatIList(IL))) active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(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(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(nil()) -> active(nil()) mark(U91(X1,X2,X3,X4)) -> active(U91(mark(X1),X2,X3,X4)) mark(U92(X1,X2,X3,X4)) -> active(U92(mark(X1),X2,X3,X4)) mark(U93(X1,X2,X3,X4)) -> active(U93(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 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(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(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) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,mark(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,mark(X3)) -> U71(X1,X2,X3) U71(active(X1),X2,X3) -> U71(X1,X2,X3) U71(X1,active(X2),X3) -> U71(X1,X2,X3) U71(X1,X2,active(X3)) -> U71(X1,X2,X3) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,mark(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,mark(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,mark(X4)) -> U91(X1,X2,X3,X4) U91(active(X1),X2,X3,X4) -> U91(X1,X2,X3,X4) U91(X1,active(X2),X3,X4) -> U91(X1,X2,X3,X4) U91(X1,X2,active(X3),X4) -> U91(X1,X2,X3,X4) U91(X1,X2,X3,active(X4)) -> U91(X1,X2,X3,X4) U92(mark(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,mark(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,mark(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,mark(X4)) -> U92(X1,X2,X3,X4) U92(active(X1),X2,X3,X4) -> U92(X1,X2,X3,X4) U92(X1,active(X2),X3,X4) -> U92(X1,X2,X3,X4) U92(X1,X2,active(X3),X4) -> U92(X1,X2,X3,X4) U92(X1,X2,X3,active(X4)) -> U92(X1,X2,X3,X4) U93(mark(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,mark(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,mark(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,mark(X4)) -> U93(X1,X2,X3,X4) U93(active(X1),X2,X3,X4) -> U93(X1,X2,X3,X4) U93(X1,active(X2),X3,X4) -> U93(X1,X2,X3,X4) U93(X1,X2,active(X3),X4) -> U93(X1,X2,X3,X4) U93(X1,X2,X3,active(X4)) -> U93(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open