MAYBE Problem: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Proof: DP Processor: DPs: a__U101#(tt(),V1,V2) -> a__isNatKind#(V1) a__U101#(tt(),V1,V2) -> a__U102#(a__isNatKind(V1),V1,V2) a__U102#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) -> a__isNat#(V1) a__U104#(tt(),V1,V2) -> a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__U105#(tt(),V2) -> a__U106#(a__isNatIList(V2)) a__U11#(tt(),V1) -> a__isNatIListKind#(V1) a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__U111#(tt(),L,N) -> a__isNatIListKind#(L) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__isNat#(N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__isNatKind#(N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> mark#(L) a__U114#(tt(),L) -> a__length#(mark(L)) a__U12#(tt(),V1) -> a__isNatList#(V1) a__U12#(tt(),V1) -> a__U13#(a__isNatList(V1)) a__U121#(tt(),IL) -> a__isNatIListKind#(IL) a__U121#(tt(),IL) -> a__U122#(a__isNatIListKind(IL)) a__U131#(tt(),IL,M,N) -> a__isNatIListKind#(IL) a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__isNat#(M) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__isNatKind#(M) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__isNat#(N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__isNatKind#(N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) a__U21#(tt(),V1) -> a__isNatKind#(V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U22#(tt(),V1) -> a__U23#(a__isNat(V1)) a__U31#(tt(),V) -> a__isNatIListKind#(V) a__U31#(tt(),V) -> a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) -> a__isNatList#(V) a__U32#(tt(),V) -> a__U33#(a__isNatList(V)) a__U41#(tt(),V1,V2) -> a__isNatKind#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isNat#(V1) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) a__U45#(tt(),V2) -> a__U46#(a__isNatIList(V2)) a__U51#(tt(),V2) -> a__isNatIListKind#(V2) a__U51#(tt(),V2) -> a__U52#(a__isNatIListKind(V2)) a__U61#(tt(),V2) -> a__isNatIListKind#(V2) a__U61#(tt(),V2) -> a__U62#(a__isNatIListKind(V2)) a__U91#(tt(),V1,V2) -> a__isNatKind#(V1) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__U94#(tt(),V1,V2) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U95#(tt(),V2) -> a__U96#(a__isNatList(V2)) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__isNatIList#(V) -> a__isNatIListKind#(V) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__U51#(a__isNatKind(V1),V2) a__isNatIListKind#(take(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(take(V1,V2)) -> a__U61#(a__isNatKind(V1),V2) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatKind#(length(V1)) -> a__U71#(a__isNatIListKind(V1)) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__U81#(a__isNatKind(V1)) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__isNatList#(take(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(take(V1,V2)) -> a__U101#(a__isNatKind(V1),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) a__take#(0(),IL) -> a__isNatIList#(IL) a__take#(0(),IL) -> a__U121#(a__isNatIList(IL),IL) a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) a__take#(s(M),cons(N,IL)) -> a__U131#(a__isNatIList(IL),IL,M,N) mark#(zeros()) -> a__zeros#() mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U101(X1,X2,X3)) -> a__U101#(mark(X1),X2,X3) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> a__U102#(mark(X1),X2,X3) mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> a__U103#(mark(X1),X2,X3) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> a__U104#(mark(X1),X2,X3) mark#(U105(X1,X2)) -> mark#(X1) mark#(U105(X1,X2)) -> a__U105#(mark(X1),X2) mark#(isNat(X)) -> a__isNat#(X) mark#(U106(X)) -> mark#(X) mark#(U106(X)) -> a__U106#(mark(X)) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(U111(X1,X2,X3)) -> mark#(X1) mark#(U111(X1,X2,X3)) -> a__U111#(mark(X1),X2,X3) mark#(U112(X1,X2,X3)) -> mark#(X1) mark#(U112(X1,X2,X3)) -> a__U112#(mark(X1),X2,X3) mark#(U113(X1,X2,X3)) -> mark#(X1) mark#(U113(X1,X2,X3)) -> a__U113#(mark(X1),X2,X3) mark#(U114(X1,X2)) -> mark#(X1) mark#(U114(X1,X2)) -> a__U114#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> a__U13#(mark(X)) mark#(isNatList(X)) -> a__isNatList#(X) mark#(U121(X1,X2)) -> mark#(X1) mark#(U121(X1,X2)) -> a__U121#(mark(X1),X2) mark#(U122(X)) -> mark#(X) mark#(U122(X)) -> a__U122#(mark(X)) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> a__U23#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> a__U32#(mark(X1),X2) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> a__U33#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> a__U42#(mark(X1),X2,X3) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> a__U43#(mark(X1),X2,X3) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> a__U44#(mark(X1),X2,X3) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> a__U45#(mark(X1),X2) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> a__U46#(mark(X)) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> a__U51#(mark(X1),X2) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> a__U52#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> a__U62#(mark(X)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> a__U71#(mark(X)) mark#(U81(X)) -> mark#(X) mark#(U81(X)) -> a__U81#(mark(X)) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> a__U91#(mark(X1),X2,X3) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> a__U92#(mark(X1),X2,X3) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> a__U93#(mark(X1),X2,X3) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> a__U94#(mark(X1),X2,X3) mark#(U95(X1,X2)) -> mark#(X1) mark#(U95(X1,X2)) -> a__U95#(mark(X1),X2) mark#(U96(X)) -> mark#(X) mark#(U96(X)) -> a__U96#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) TDG Processor: DPs: a__U101#(tt(),V1,V2) -> a__isNatKind#(V1) a__U101#(tt(),V1,V2) -> a__U102#(a__isNatKind(V1),V1,V2) a__U102#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) -> a__isNat#(V1) a__U104#(tt(),V1,V2) -> a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__U105#(tt(),V2) -> a__U106#(a__isNatIList(V2)) a__U11#(tt(),V1) -> a__isNatIListKind#(V1) a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__U111#(tt(),L,N) -> a__isNatIListKind#(L) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__isNat#(N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__isNatKind#(N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> mark#(L) a__U114#(tt(),L) -> a__length#(mark(L)) a__U12#(tt(),V1) -> a__isNatList#(V1) a__U12#(tt(),V1) -> a__U13#(a__isNatList(V1)) a__U121#(tt(),IL) -> a__isNatIListKind#(IL) a__U121#(tt(),IL) -> a__U122#(a__isNatIListKind(IL)) a__U131#(tt(),IL,M,N) -> a__isNatIListKind#(IL) a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__isNat#(M) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__isNatKind#(M) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__isNat#(N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__isNatKind#(N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) a__U21#(tt(),V1) -> a__isNatKind#(V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U22#(tt(),V1) -> a__U23#(a__isNat(V1)) a__U31#(tt(),V) -> a__isNatIListKind#(V) a__U31#(tt(),V) -> a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) -> a__isNatList#(V) a__U32#(tt(),V) -> a__U33#(a__isNatList(V)) a__U41#(tt(),V1,V2) -> a__isNatKind#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isNat#(V1) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) a__U45#(tt(),V2) -> a__U46#(a__isNatIList(V2)) a__U51#(tt(),V2) -> a__isNatIListKind#(V2) a__U51#(tt(),V2) -> a__U52#(a__isNatIListKind(V2)) a__U61#(tt(),V2) -> a__isNatIListKind#(V2) a__U61#(tt(),V2) -> a__U62#(a__isNatIListKind(V2)) a__U91#(tt(),V1,V2) -> a__isNatKind#(V1) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__U94#(tt(),V1,V2) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U95#(tt(),V2) -> a__U96#(a__isNatList(V2)) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__isNatIList#(V) -> a__isNatIListKind#(V) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__U51#(a__isNatKind(V1),V2) a__isNatIListKind#(take(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(take(V1,V2)) -> a__U61#(a__isNatKind(V1),V2) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatKind#(length(V1)) -> a__U71#(a__isNatIListKind(V1)) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__U81#(a__isNatKind(V1)) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__isNatList#(take(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(take(V1,V2)) -> a__U101#(a__isNatKind(V1),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) a__take#(0(),IL) -> a__isNatIList#(IL) a__take#(0(),IL) -> a__U121#(a__isNatIList(IL),IL) a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) a__take#(s(M),cons(N,IL)) -> a__U131#(a__isNatIList(IL),IL,M,N) mark#(zeros()) -> a__zeros#() mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U101(X1,X2,X3)) -> a__U101#(mark(X1),X2,X3) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> a__U102#(mark(X1),X2,X3) mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> a__U103#(mark(X1),X2,X3) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> a__U104#(mark(X1),X2,X3) mark#(U105(X1,X2)) -> mark#(X1) mark#(U105(X1,X2)) -> a__U105#(mark(X1),X2) mark#(isNat(X)) -> a__isNat#(X) mark#(U106(X)) -> mark#(X) mark#(U106(X)) -> a__U106#(mark(X)) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(U111(X1,X2,X3)) -> mark#(X1) mark#(U111(X1,X2,X3)) -> a__U111#(mark(X1),X2,X3) mark#(U112(X1,X2,X3)) -> mark#(X1) mark#(U112(X1,X2,X3)) -> a__U112#(mark(X1),X2,X3) mark#(U113(X1,X2,X3)) -> mark#(X1) mark#(U113(X1,X2,X3)) -> a__U113#(mark(X1),X2,X3) mark#(U114(X1,X2)) -> mark#(X1) mark#(U114(X1,X2)) -> a__U114#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> a__U13#(mark(X)) mark#(isNatList(X)) -> a__isNatList#(X) mark#(U121(X1,X2)) -> mark#(X1) mark#(U121(X1,X2)) -> a__U121#(mark(X1),X2) mark#(U122(X)) -> mark#(X) mark#(U122(X)) -> a__U122#(mark(X)) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> a__U23#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> a__U32#(mark(X1),X2) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> a__U33#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> a__U42#(mark(X1),X2,X3) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> a__U43#(mark(X1),X2,X3) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> a__U44#(mark(X1),X2,X3) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> a__U45#(mark(X1),X2) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> a__U46#(mark(X)) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> a__U51#(mark(X1),X2) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> a__U52#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> a__U62#(mark(X)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> a__U71#(mark(X)) mark#(U81(X)) -> mark#(X) mark#(U81(X)) -> a__U81#(mark(X)) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> a__U91#(mark(X1),X2,X3) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> a__U92#(mark(X1),X2,X3) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> a__U93#(mark(X1),X2,X3) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> a__U94#(mark(X1),X2,X3) mark#(U95(X1,X2)) -> mark#(X1) mark#(U95(X1,X2)) -> a__U95#(mark(X1),X2) mark#(U96(X)) -> mark#(X) mark#(U96(X)) -> a__U96#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) graph: ... SCC Processor: #sccs: 3 #rules: 113 #arcs: 5698/38416 DPs: a__take#(s(M),cons(N,IL)) -> a__U131#(a__isNatIList(IL),IL,M,N) a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) mark#(U111(X1,X2,X3)) -> mark#(X1) mark#(U111(X1,X2,X3)) -> a__U111#(mark(X1),X2,X3) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> mark#(L) mark#(U112(X1,X2,X3)) -> mark#(X1) mark#(U112(X1,X2,X3)) -> a__U112#(mark(X1),X2,X3) mark#(U113(X1,X2,X3)) -> mark#(X1) mark#(U113(X1,X2,X3)) -> a__U113#(mark(X1),X2,X3) mark#(U114(X1,X2)) -> mark#(X1) mark#(U114(X1,X2)) -> a__U114#(mark(X1),X2) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(U13(X)) -> mark#(X) mark#(U121(X1,X2)) -> mark#(X1) mark#(U122(X)) -> mark#(X) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__take#](x0, x1) = x1, [a__U136#](x0, x1, x2, x3) = x3, [a__U135#](x0, x1, x2, x3) = x3, [a__U134#](x0, x1, x2, x3) = x0 + x3, [a__U133#](x0, x1, x2, x3) = x1 + x3, [a__U132#](x0, x1, x2, x3) = x1 + x3, [a__U131#](x0, x1, x2, x3) = x1 + x3, [a__length#](x0) = x0, [mark#](x0) = x0, [a__U114#](x0, x1) = x1, [a__U113#](x0, x1, x2) = x1, [a__U112#](x0, x1, x2) = x1, [a__U111#](x0, x1, x2) = x1, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [U135](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [U134](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [U133](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [U132](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [U131](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [U122](x0) = x0, [U121](x0, x1) = x0, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = x0 + x1 + 1, [U113](x0, x1, x2) = x0 + x1 + 1, [U112](x0, x1, x2) = x0 + x1 + x2 + 1, [U111](x0, x1, x2) = x0 + x1 + x2 + 1, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = x0 + x1, [length](x0) = x0 + 1, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = x0 + x1, [a__U136](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [a__U135](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [a__U134](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [a__U133](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [a__U132](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [a__U131](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = x0, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = x0 + 1, [mark](x0) = x0, [a__U114](x0, x1) = x0 + x1 + 1, [a__U113](x0, x1, x2) = x0 + x1 + 1, [a__U112](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U111](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x0 + x1, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__take#(s(M),cons(N,IL)) = IL + N >= IL + N = a__U131#(a__isNatIList(IL),IL,M,N) a__U131#(tt(),IL,M,N) = IL + N >= IL + N = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) = IL + N >= IL + N = a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) = IL + N >= N = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = N >= N = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = N >= N = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = N >= N = mark#(N) mark#(U101(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U102(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U103(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U104(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U105(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U106(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U111(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U111(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X2 = a__U111#(mark(X1),X2,X3) a__U111#(tt(),L,N) = L >= L = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = L >= L = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = L >= L = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = L >= L = mark#(L) mark#(U112(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 = mark#(X1) mark#(U112(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X2 = a__U112#(mark(X1),X2,X3) mark#(U113(X1,X2,X3)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U113(X1,X2,X3)) = X1 + X2 + 1 >= X2 = a__U113#(mark(X1),X2,X3) mark#(U114(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U114(X1,X2)) = X1 + X2 + 1 >= X2 = a__U114#(mark(X1),X2) a__U114#(tt(),L) = L >= L = a__length#(mark(L)) a__length#(cons(N,L)) = L + N >= L = a__U111#(a__isNatList(L),L,N) mark#(length(X)) = X + 1 >= X = mark#(X) mark#(length(X)) = X + 1 >= X = a__length#(mark(X)) mark#(U13(X)) = X >= X = mark#(X) mark#(U121(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U122(X)) = X >= X = mark#(X) mark#(U131(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 = mark#(X1) mark#(U131(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X2 + X4 = a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 = mark#(X1) mark#(U132(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X2 + X4 = a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X2 + X4 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 + X4 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X4 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X4 = a__U136#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) = X1 + X2 >= X2 = mark#(X2) mark#(take(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(take(X1,X2)) = X1 + X2 >= X2 = a__take#(mark(X1),mark(X2)) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U23(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U91(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U95(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U96(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = L + N + 1 >= L + N + 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = L + N + 1 >= L + 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = L + 1 >= L + 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = L + 1 >= L + 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = IL + M + N >= IL + M + N = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL + M + N >= IL + M + N = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL + M + N >= IL + M + N = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL + M + N >= IL + M + N = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL + M + N >= IL + M + N = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL + M + N >= IL + M + N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = L + N + 1 >= L + N + 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL + M + N >= IL + M + N = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = X1 >= X1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 >= X1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 >= X1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 >= X1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 >= X1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = X1 >= X1 = a__U121(mark(X1),X2) mark(U122(X)) = X >= X = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 >= X1 + X2 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 >= X1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 >= X1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 >= X1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 >= X1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 >= X1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 >= X1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X1 + X2 + 1 >= X1 + X2 + 1 = U113(X1,X2,X3) a__U114(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U114(X1,X2) a__length(X) = X + 1 >= X + 1 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = X1 >= X1 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 + X2 + X3 + X4 >= X1 + X2 + X3 + X4 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 >= X1 + X2 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__take#(s(M),cons(N,IL)) -> a__U131#(a__isNatIList(IL),IL,M,N) a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> mark#(L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U121(X1,X2)) -> mark#(X1) mark#(U122(X)) -> mark#(X) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__take#](x0, x1) = 0, [a__U136#](x0, x1, x2, x3) = 0, [a__U135#](x0, x1, x2, x3) = 0, [a__U134#](x0, x1, x2, x3) = 0, [a__U133#](x0, x1, x2, x3) = 0, [a__U132#](x0, x1, x2, x3) = 0, [a__U131#](x0, x1, x2, x3) = 0, [a__length#](x0) = 1, [mark#](x0) = 0, [a__U114#](x0, x1) = 1, [a__U113#](x0, x1, x2) = 1, [a__U112#](x0, x1, x2) = 1, [a__U111#](x0, x1, x2) = 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__take#(s(M),cons(N,IL)) = 0 >= 0 = a__U131#(a__isNatIList(IL),IL,M,N) a__U131#(tt(),IL,M,N) = 0 >= 0 = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) = 0 >= 0 = a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) = 0 >= 0 = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = 0 >= 0 = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = 0 >= 0 = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = 0 >= 0 = mark#(N) mark#(U101(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U102(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U103(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U104(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U105(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U106(X)) = 0 >= 0 = mark#(X) mark#(U11(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U12(X1,X2)) = 0 >= 0 = mark#(X1) a__U111#(tt(),L,N) = 1 >= 1 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 1 >= 1 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 1 >= 1 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 1 >= 0 = mark#(L) a__U114#(tt(),L) = 1 >= 1 = a__length#(mark(L)) a__length#(cons(N,L)) = 1 >= 1 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = 0 >= 0 = mark#(X) mark#(U121(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U122(X)) = 0 >= 0 = mark#(X) mark#(U131(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) = 0 >= 0 = mark#(X2) mark#(take(X1,X2)) = 0 >= 0 = mark#(X1) mark#(take(X1,X2)) = 0 >= 0 = a__take#(mark(X1),mark(X2)) mark#(U21(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U22(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U23(X)) = 0 >= 0 = mark#(X) mark#(U31(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U32(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U33(X)) = 0 >= 0 = mark#(X) mark#(U41(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U42(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U43(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U44(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U45(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U46(X)) = 0 >= 0 = mark#(X) mark#(U51(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U52(X)) = 0 >= 0 = mark#(X) mark#(U61(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U62(X)) = 0 >= 0 = mark#(X) mark#(U71(X)) = 0 >= 0 = mark#(X) mark#(U81(X)) = 0 >= 0 = mark#(X) mark#(U91(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U92(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U93(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U94(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U95(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U96(X)) = 0 >= 0 = mark#(X) mark#(cons(X1,X2)) = 0 >= 0 = mark#(X1) mark#(s(X)) = 0 >= 0 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__take#(s(M),cons(N,IL)) -> a__U131#(a__isNatIList(IL),IL,M,N) a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U121(X1,X2)) -> mark#(X1) mark#(U122(X)) -> mark#(X) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__take#](x0, x1) = x1, [a__U136#](x0, x1, x2, x3) = x3, [a__U135#](x0, x1, x2, x3) = x3, [a__U134#](x0, x1, x2, x3) = x3, [a__U133#](x0, x1, x2, x3) = x3, [a__U132#](x0, x1, x2, x3) = x3, [a__U131#](x0, x1, x2, x3) = x3, [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x0 + x3, [U135](x0, x1, x2, x3) = x0 + x3, [U134](x0, x1, x2, x3) = x0 + x3, [U133](x0, x1, x2, x3) = x0 + x3, [U132](x0, x1, x2, x3) = x0 + x3, [U131](x0, x1, x2, x3) = x0 + x3, [U122](x0) = x0, [U121](x0, x1) = x0, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = 0, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x0 + x3, [a__U135](x0, x1, x2, x3) = x0 + x3, [a__U134](x0, x1, x2, x3) = x0 + x3, [a__U133](x0, x1, x2, x3) = x0 + x3, [a__U132](x0, x1, x2, x3) = x0 + x3, [a__U131](x0, x1, x2, x3) = x0 + x3, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = x0, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__take#(s(M),cons(N,IL)) = N >= N = a__U131#(a__isNatIList(IL),IL,M,N) a__U131#(tt(),IL,M,N) = N >= N = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) = N >= N = a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) = N >= N = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = N >= N = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = N >= N = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = N >= N = mark#(N) mark#(U101(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U102(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U103(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U104(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U105(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U106(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = X >= X = mark#(X) mark#(U121(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U122(X)) = X >= X = mark#(X) mark#(U131(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U131(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U132(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U136#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) = X1 + X2 + 1 >= X2 = mark#(X2) mark#(take(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(take(X1,X2)) = X1 + X2 + 1 >= X2 = a__take#(mark(X1),mark(X2)) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U23(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U91(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U95(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U96(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = X1 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = N >= N = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = N >= N = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = N >= N = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = N >= N = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = N >= N = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = N >= N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = M + N + 1 >= N = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X1 >= X1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 >= X1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 >= X1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 >= X1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 >= X1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = X1 >= X1 = a__U121(mark(X1),X2) mark(U122(X)) = X >= X = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 >= X1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 >= X1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 >= X1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 >= X1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 >= X1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 >= X1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 >= X1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = X1 >= X1 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__take#(s(M),cons(N,IL)) -> a__U131#(a__isNatIList(IL),IL,M,N) a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U121(X1,X2)) -> mark#(X1) mark#(U122(X)) -> mark#(X) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__take#](x0, x1) = x1 + 1, [a__U136#](x0, x1, x2, x3) = x3, [a__U135#](x0, x1, x2, x3) = x3, [a__U134#](x0, x1, x2, x3) = x0 + x3, [a__U133#](x0, x1, x2, x3) = x3, [a__U132#](x0, x1, x2, x3) = x3, [a__U131#](x0, x1, x2, x3) = x3, [a__length#](x0) = 1, [mark#](x0) = x0, [a__U114#](x0, x1) = 1, [a__U113#](x0, x1, x2) = 1, [a__U112#](x0, x1, x2) = 1, [a__U111#](x0, x1, x2) = 1, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x0 + x3, [U135](x0, x1, x2, x3) = x0 + x3, [U134](x0, x1, x2, x3) = x0 + x3, [U133](x0, x1, x2, x3) = x0 + x3, [U132](x0, x1, x2, x3) = x0 + x3, [U131](x0, x1, x2, x3) = x0 + x3, [U122](x0) = x0, [U121](x0, x1) = x0 + 1, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = x1 + 1, [length](x0) = 0, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = x1 + 1, [a__U136](x0, x1, x2, x3) = x0 + x3, [a__U135](x0, x1, x2, x3) = x0 + x3, [a__U134](x0, x1, x2, x3) = x0 + x3, [a__U133](x0, x1, x2, x3) = x0 + x3, [a__U132](x0, x1, x2, x3) = x0 + x3, [a__U131](x0, x1, x2, x3) = x0 + x3, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = x0 + 1, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__take#(s(M),cons(N,IL)) = N + 1 >= N = a__U131#(a__isNatIList(IL),IL,M,N) a__U131#(tt(),IL,M,N) = N >= N = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) = N >= N = a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) = N >= N = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = N >= N = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = N >= N = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = N >= N = mark#(N) mark#(U101(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U102(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U103(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U104(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U105(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U106(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) a__U111#(tt(),L,N) = 1 >= 1 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 1 >= 1 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 1 >= 1 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 1 >= 1 = a__length#(mark(L)) a__length#(cons(N,L)) = 1 >= 1 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = X >= X = mark#(X) mark#(U121(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U122(X)) = X >= X = mark#(X) mark#(U131(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U131(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U132(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U23(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U91(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U95(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U96(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = X1 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 1 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = N >= N = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = N >= N = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = N >= N = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = N >= N = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = N >= N = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = N >= N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = N + 1 >= N = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = X1 >= X1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 >= X1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 >= X1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 >= X1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 >= X1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = X1 + 1 >= X1 + 1 = a__U121(mark(X1),X2) mark(U122(X)) = X >= X = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X2 + 1 >= X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 >= X1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 >= X1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 >= X1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 >= X1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 >= X1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 >= X1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 >= X1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = X1 + 1 >= X1 + 1 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U136(X1,X2,X3,X4) a__take(X1,X2) = X2 + 1 >= X2 + 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U122(X)) -> mark#(X) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U136#](x0, x1, x2, x3) = x3, [a__U135#](x0, x1, x2, x3) = x3, [a__U134#](x0, x1, x2, x3) = x3, [a__U133#](x0, x1, x2, x3) = x2 + x3, [a__U132#](x0, x1, x2, x3) = x2 + x3, [a__U131#](x0, x1, x2, x3) = x2 + x3, [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x0 + x3, [U135](x0, x1, x2, x3) = x0 + x3, [U134](x0, x1, x2, x3) = x0 + x3, [U133](x0, x1, x2, x3) = x0 + x2 + x3, [U132](x0, x1, x2, x3) = x0 + x2 + x3, [U131](x0, x1, x2, x3) = x0 + x2 + x3, [U122](x0) = x0 + 1, [U121](x0, x1) = 1, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = 1, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x0 + x3, [a__U135](x0, x1, x2, x3) = x0 + x3, [a__U134](x0, x1, x2, x3) = x0 + x3, [a__U133](x0, x1, x2, x3) = x0 + x2 + x3, [a__U132](x0, x1, x2, x3) = x0 + x2 + x3, [a__U131](x0, x1, x2, x3) = x0 + x2 + x3, [nil] = 0, [a__U122](x0) = x0 + 1, [a__U121](x0, x1) = 1, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = 1, [mark](x0) = x0, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U131#(tt(),IL,M,N) = M + N >= M + N = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) = M + N >= M + N = a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) = M + N >= N = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = N >= N = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = N >= N = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = N >= N = mark#(N) mark#(U101(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U102(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U103(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U104(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U105(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U106(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = X >= X = mark#(X) mark#(U122(X)) = X + 1 >= X = mark#(X) mark#(U131(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 = mark#(X1) mark#(U131(X1,X2,X3,X4)) = X1 + X3 + X4 >= X3 + X4 = a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 = mark#(X1) mark#(U132(X1,X2,X3,X4)) = X1 + X3 + X4 >= X3 + X4 = a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = X1 + X3 + X4 >= X3 + X4 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U23(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U91(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U95(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U96(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = X1 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = M + N >= M + N = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = M + N >= M + N = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = M + N >= N = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = N >= N = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = N >= N = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = N >= N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = M + N + 1 >= M + N = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X1 >= X1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 >= X1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 >= X1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 >= X1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 >= X1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = X + 1 >= X + 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 + X3 + X4 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 + X3 + X4 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 + X3 + X4 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 >= X1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 >= X1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 >= X1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 >= X1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 >= X1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 >= X1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 >= X1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = X + 1 >= X + 1 = U122(X) a__U131(X1,X2,X3,X4) = X1 + X3 + X4 >= X1 + X3 + X4 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 + X3 + X4 >= X1 + X3 + X4 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 + X3 + X4 >= X1 + X3 + X4 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U136#](x0, x1, x2, x3) = x3, [a__U135#](x0, x1, x2, x3) = x3, [a__U134#](x0, x1, x2, x3) = x3, [a__U133#](x0, x1, x2, x3) = x2 + x3, [a__U132#](x0, x1, x2, x3) = x2 + x3, [a__U131#](x0, x1, x2, x3) = x2 + x3, [a__length#](x0) = 1, [mark#](x0) = x0, [a__U114#](x0, x1) = 1, [a__U113#](x0, x1, x2) = 1, [a__U112#](x0, x1, x2) = 1, [a__U111#](x0, x1, x2) = 1, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x0 + x3, [U135](x0, x1, x2, x3) = x0 + x3, [U134](x0, x1, x2, x3) = x0 + x3, [U133](x0, x1, x2, x3) = x0 + x2 + x3, [U132](x0, x1, x2, x3) = x0 + x2 + x3, [U131](x0, x1, x2, x3) = x0 + x2 + x3 + 1, [U122](x0) = 0, [U121](x0, x1) = x1 + 1, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = 1, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x0 + x3, [a__U135](x0, x1, x2, x3) = x0 + x3, [a__U134](x0, x1, x2, x3) = x0 + x3, [a__U133](x0, x1, x2, x3) = x0 + x2 + x3, [a__U132](x0, x1, x2, x3) = x0 + x2 + x3, [a__U131](x0, x1, x2, x3) = x0 + x2 + x3 + 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = x1 + 1, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = 1, [mark](x0) = x0, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U131#(tt(),IL,M,N) = M + N >= M + N = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) = M + N >= M + N = a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) = M + N >= N = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = N >= N = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = N >= N = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = N >= N = mark#(N) mark#(U101(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U102(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U103(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U104(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U105(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U106(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) a__U111#(tt(),L,N) = 1 >= 1 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 1 >= 1 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 1 >= 1 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 1 >= 1 = a__length#(mark(L)) a__length#(cons(N,L)) = 1 >= 1 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = X >= X = mark#(X) mark#(U131(X1,X2,X3,X4)) = X1 + X3 + X4 + 1 >= X1 = mark#(X1) mark#(U131(X1,X2,X3,X4)) = X1 + X3 + X4 + 1 >= X3 + X4 = a__U131#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 = mark#(X1) mark#(U132(X1,X2,X3,X4)) = X1 + X3 + X4 >= X3 + X4 = a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = X1 + X3 + X4 >= X3 + X4 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = X1 + X4 >= X4 = a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U23(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U91(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U95(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U96(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = X1 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = IL + 1 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = M + N + 1 >= M + N = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = M + N >= M + N = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = M + N >= N = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = N >= N = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = N >= N = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = N >= N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= IL + 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = M + N + 1 >= M + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X1 >= X1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 >= X1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 >= X1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 >= X1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 >= X1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = X2 + 1 >= X2 + 1 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X1 + X3 + X4 + 1 >= X1 + X3 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 + X3 + X4 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X1 + X3 + X4 >= X1 + X3 + X4 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 >= X1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 >= X1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 >= X1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 >= X1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 >= X1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 >= X1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 >= X1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = X2 + 1 >= X2 + 1 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X1 + X3 + X4 + 1 >= X1 + X3 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 + X3 + X4 >= X1 + X3 + X4 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 + X3 + X4 >= X1 + X3 + X4 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U136#](x0, x1, x2, x3) = x3 + 1, [a__U135#](x0, x1, x2, x3) = x3 + 1, [a__U134#](x0, x1, x2, x3) = x3 + 1, [a__U133#](x0, x1, x2, x3) = x3 + 1, [a__U132#](x0, x1, x2, x3) = x0 + x3, [a__U131#](x0, x1, x2, x3) = x1 + x3 + 1, [a__length#](x0) = 0, [mark#](x0) = x0 + 1, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x0 + x3, [U135](x0, x1, x2, x3) = x0 + x3, [U134](x0, x1, x2, x3) = x0 + x3, [U133](x0, x1, x2, x3) = x0 + x3, [U132](x0, x1, x2, x3) = x0 + x3, [U131](x0, x1, x2, x3) = x3 + 1, [U122](x0) = 0, [U121](x0, x1) = 1, [isNatList](x0) = 1, [U13](x0) = x0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 1, [U106](x0) = x0, [isNat](x0) = 1, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 1, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 1, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = x1 + 1, [length](x0) = 0, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = x1 + 1, [a__U136](x0, x1, x2, x3) = x0 + x3, [a__U135](x0, x1, x2, x3) = x0 + x3, [a__U134](x0, x1, x2, x3) = x0 + x3, [a__U133](x0, x1, x2, x3) = x0 + x3, [a__U132](x0, x1, x2, x3) = x0 + x3, [a__U131](x0, x1, x2, x3) = x3 + 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 1, [a__U13](x0) = x0, [a__isNatList](x0) = 1, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = x0, [a__isNat](x0) = 1, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 1, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 1, [a__U101](x0, x1, x2) = x0, [tt] = 1, [cons](x0, x1) = x0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U131#(tt(),IL,M,N) = IL + N + 1 >= N + 1 = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) = N + 1 >= N + 1 = a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) = N + 1 >= N + 1 = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = N + 1 >= N + 1 = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = N + 1 >= N + 1 = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = N + 1 >= N + 1 = mark#(N) mark#(U101(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U102(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U103(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U104(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U105(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U106(X)) = X + 1 >= X + 1 = mark#(X) mark#(U11(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U12(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = X + 1 >= X + 1 = mark#(X) mark#(U132(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + 1 = mark#(X1) mark#(U132(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + X4 = a__U132#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + 1 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = X1 + X4 + 1 >= X4 + 1 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + 1 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = X1 + X4 + 1 >= X4 + 1 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + 1 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = X1 + X4 + 1 >= X4 + 1 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + 1 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = X1 + X4 + 1 >= X4 + 1 = a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U22(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U23(X)) = X + 1 >= X + 1 = mark#(X) mark#(U31(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U32(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U33(X)) = X + 1 >= X + 1 = mark#(X) mark#(U41(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U45(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U46(X)) = X + 1 >= X + 1 = mark#(X) mark#(U51(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U52(X)) = X + 1 >= X + 1 = mark#(X) mark#(U61(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U62(X)) = X + 1 >= X + 1 = mark#(X) mark#(U71(X)) = X + 1 >= X + 1 = mark#(X) mark#(U81(X)) = X + 1 >= X + 1 = mark#(X) mark#(U91(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U95(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U96(X)) = X + 1 >= X + 1 = mark#(X) mark#(cons(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(s(X)) = X + 1 >= X + 1 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 1 >= 1 = tt() a__U11(tt(),V1) = 1 >= 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 1 >= 1 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 1 >= 1 = tt() a__U131(tt(),IL,M,N) = N + 1 >= N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = N + 1 >= N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = N + 1 >= N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = N + 1 >= N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = N + 1 >= N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = N + 1 >= N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 1 >= 1 = a__U23(a__isNat(V1)) a__U23(tt()) = 1 >= 1 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 1 >= 1 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 1 >= 1 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 1 >= 1 = tt() a__U51(tt(),V2) = 1 >= 1 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 1 >= 1 = tt() a__U61(tt(),V2) = 1 >= 1 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 1 >= 1 = tt() a__U71(tt()) = 1 >= 1 = tt() a__U81(tt()) = 1 >= 1 = tt() a__U91(tt(),V1,V2) = 1 >= 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 1 >= 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 1 >= 1 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 1 >= 1 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 1 >= 1 = a__U96(a__isNatList(V2)) a__U96(tt()) = 1 >= 1 = tt() a__isNat(0()) = 1 >= 1 = tt() a__isNat(length(V1)) = 1 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 1 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 1 >= 1 = tt() a__isNatIListKind(zeros()) = 1 >= 1 = tt() a__isNatIListKind(cons(V1,V2)) = 1 >= 1 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 1 >= 1 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 1 >= 1 = tt() a__isNatKind(length(V1)) = 1 >= 1 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 1 >= 1 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 1 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = N + 1 >= N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X1 >= X1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 >= X1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 1 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 >= X1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 1 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 >= X1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 >= X1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 1 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X4 + 1 >= X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X1 + X4 >= X1 + X4 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X2 + 1 >= X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 >= X1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 >= X1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 >= X1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 >= X1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 >= X1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 >= X1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 >= X1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 1 >= 1 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 1 >= 1 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 1 >= 1 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 1 >= 1 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X4 + 1 >= X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 + X4 >= X1 + X4 = U136(X1,X2,X3,X4) a__take(X1,X2) = X2 + 1 >= X2 + 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) -> a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U136#](x0, x1, x2, x3) = 0, [a__U135#](x0, x1, x2, x3) = 0, [a__U134#](x0, x1, x2, x3) = 0, [a__U133#](x0, x1, x2, x3) = 0, [a__U132#](x0, x1, x2, x3) = 1, [a__U131#](x0, x1, x2, x3) = x1 + x2 + 1, [a__length#](x0) = 0, [mark#](x0) = 0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = 0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = 0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x0, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 1, [U21](x0, x1) = 1, [U136](x0, x1, x2, x3) = x0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = x0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = x0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 1, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 1, [U11](x0, x1) = 1, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = 1, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = 1, [length](x0) = 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = 0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U23](x0) = 0, [a__U22](x0, x1) = 1, [a__U21](x0, x1) = 1, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = x0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = x0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = x0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = 0, [a__length](x0) = 1, [mark](x0) = 1, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = 1, [a__U11](x0, x1) = 1, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = x0, [a__isNat](x0) = 1, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U131#(tt(),IL,M,N) = IL + M + 1 >= 1 = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U132#(tt(),IL,M,N) = 1 >= 0 = a__U133#(a__isNat(M),IL,M,N) a__U133#(tt(),IL,M,N) = 0 >= 0 = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = 0 >= 0 = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = 0 >= 0 = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = 0 >= 0 = mark#(N) mark#(U101(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U102(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U103(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U104(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U105(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U106(X)) = 0 >= 0 = mark#(X) mark#(U11(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U12(X1,X2)) = 0 >= 0 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = 0 >= 0 = mark#(X) mark#(U132(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U22(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U23(X)) = 0 >= 0 = mark#(X) mark#(U31(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U32(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U33(X)) = 0 >= 0 = mark#(X) mark#(U41(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U42(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U43(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U44(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U45(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U46(X)) = 0 >= 0 = mark#(X) mark#(U51(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U52(X)) = 0 >= 0 = mark#(X) mark#(U61(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U62(X)) = 0 >= 0 = mark#(X) mark#(U71(X)) = 0 >= 0 = mark#(X) mark#(U81(X)) = 0 >= 0 = mark#(X) mark#(U91(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U92(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U93(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U94(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U95(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U96(X)) = 0 >= 0 = mark#(X) mark#(cons(X1,X2)) = 0 >= 0 = mark#(X1) mark#(s(X)) = 0 >= 0 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 1 >= 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 1 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 1 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 1 >= 0 = tt() a__isNat(length(V1)) = 1 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 1 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 1 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 1 = a__U62(mark(X)) mark(U71(X)) = 1 >= 1 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 0 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 0 = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 1 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 0 = isNatIList(X) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 0 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 >= X1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 >= X1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 >= X1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = 1 >= 1 = U21(X1,X2) a__U22(X1,X2) = 1 >= 1 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= 0 = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U131#(tt(),IL,M,N) -> a__U132#(a__isNatIListKind(IL),IL,M,N) a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U136#](x0, x1, x2, x3) = 0, [a__U135#](x0, x1, x2, x3) = 0, [a__U134#](x0, x1, x2, x3) = 0, [a__U133#](x0, x1, x2, x3) = 0, [a__U132#](x0, x1, x2, x3) = 0, [a__U131#](x0, x1, x2, x3) = 1, [a__length#](x0) = 0, [mark#](x0) = 0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = x0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = x0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 1, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = x0, [U133](x0, x1, x2, x3) = 1, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 1, [U122](x0) = x0, [U121](x0, x1) = 1, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = x0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 1, [U106](x0) = 0, [isNat](x0) = 1, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 1, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 1, [length](x0) = 1, [a__U96](x0) = x0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 1, [a__U71](x0) = x0, [a__U62](x0) = 0, [a__U61](x0, x1) = x0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = x0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 1, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = x0, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = 1, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 1, [mark](x0) = 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = x0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 0, [a__isNat](x0) = 1, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 1, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 1, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U131#(tt(),IL,M,N) = 1 >= 0 = a__U132#(a__isNatIListKind(IL),IL,M,N) a__U133#(tt(),IL,M,N) = 0 >= 0 = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = 0 >= 0 = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = 0 >= 0 = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = 0 >= 0 = mark#(N) mark#(U101(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U102(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U103(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U104(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U105(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U106(X)) = 0 >= 0 = mark#(X) mark#(U11(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U12(X1,X2)) = 0 >= 0 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = 0 >= 0 = mark#(X) mark#(U132(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = 0 >= 0 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U22(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U23(X)) = 0 >= 0 = mark#(X) mark#(U31(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U32(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U33(X)) = 0 >= 0 = mark#(X) mark#(U41(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U42(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U43(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U44(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U45(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U46(X)) = 0 >= 0 = mark#(X) mark#(U51(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U52(X)) = 0 >= 0 = mark#(X) mark#(U61(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U62(X)) = 0 >= 0 = mark#(X) mark#(U71(X)) = 0 >= 0 = mark#(X) mark#(U81(X)) = 0 >= 0 = mark#(X) mark#(U91(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U92(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U93(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U94(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U95(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U96(X)) = 0 >= 0 = mark#(X) mark#(cons(X1,X2)) = 0 >= 0 = mark#(X1) mark#(s(X)) = 0 >= 0 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 1 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 1 >= 0 = tt() a__isNat(length(V1)) = 1 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 1 >= 0 = tt() a__isNatIListKind(zeros()) = 1 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 1 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 1 >= 1 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 1 >= 0 = tt() a__isNatKind(length(V1)) = 1 >= 1 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 1 >= 1 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 1 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 1 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 1 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 0 = a__U62(mark(X)) mark(U71(X)) = 1 >= 1 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 1 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 0 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 0 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 1 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 1 >= 1 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 1 >= 1 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = X1 >= X1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 >= X1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = 1 >= 1 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = X >= 0 = U71(X) a__U81(X) = 1 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) -> a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U136#](x0, x1, x2, x3) = x3, [a__U135#](x0, x1, x2, x3) = x3, [a__U134#](x0, x1, x2, x3) = x3 + 1, [a__U133#](x0, x1, x2, x3) = x3 + 1, [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x0 + x3 + 1, [U135](x0, x1, x2, x3) = x0 + x3 + 1, [U134](x0, x1, x2, x3) = x0 + x3 + 1, [U133](x0, x1, x2, x3) = x0 + x2 + x3 + 1, [U132](x0, x1, x2, x3) = x0 + x2 + x3 + 1, [U131](x0, x1, x2, x3) = x2 + x3 + 1, [U122](x0) = 0, [U121](x0, x1) = x1 + 1, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = 0, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x0 + x3 + 1, [a__U135](x0, x1, x2, x3) = x0 + x3 + 1, [a__U134](x0, x1, x2, x3) = x0 + x3 + 1, [a__U133](x0, x1, x2, x3) = x0 + x2 + x3 + 1, [a__U132](x0, x1, x2, x3) = x0 + x2 + x3 + 1, [a__U131](x0, x1, x2, x3) = x2 + x3 + 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = x1 + 1, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x0 + 1, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__U133#(tt(),IL,M,N) = N + 1 >= N + 1 = a__U134#(a__isNatKind(M),IL,M,N) a__U134#(tt(),IL,M,N) = N + 1 >= N = a__U135#(a__isNat(N),IL,M,N) a__U135#(tt(),IL,M,N) = N >= N = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = N >= N = mark#(N) mark#(U101(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U102(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U103(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U104(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U105(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U106(X)) = X >= X = mark#(X) mark#(U11(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 >= X1 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = X >= X = mark#(X) mark#(U132(X1,X2,X3,X4)) = X1 + X3 + X4 + 1 >= X1 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = X1 + X3 + X4 + 1 >= X1 = mark#(X1) mark#(U133(X1,X2,X3,X4)) = X1 + X3 + X4 + 1 >= X4 + 1 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 = mark#(X1) mark#(U134(X1,X2,X3,X4)) = X1 + X4 + 1 >= X4 + 1 = a__U134#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 = mark#(X1) mark#(U135(X1,X2,X3,X4)) = X1 + X4 + 1 >= X4 = a__U135#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 = mark#(X1) mark#(U136(X1,X2,X3,X4)) = X1 + X4 + 1 >= X4 = a__U136#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U23(X)) = X >= X = mark#(X) mark#(U31(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U32(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U33(X)) = X >= X = mark#(X) mark#(U41(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U45(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U91(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U95(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U96(X)) = X >= X = mark#(X) mark#(cons(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = IL + 1 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = M + N + 1 >= M + N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = M + N + 1 >= M + N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = M + N + 1 >= N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = N + 1 >= N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = N + 1 >= N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = N + 1 >= N + 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= IL + 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = M + N + 2 >= M + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = X1 >= X1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 >= X1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 >= X1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 >= X1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 >= X1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = X1 >= X1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = X2 + 1 >= X2 + 1 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X3 + X4 + 1 >= X3 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X1 + X3 + X4 + 1 >= X1 + X3 + X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X1 + X3 + X4 + 1 >= X1 + X3 + X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + X4 + 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + X4 + 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X1 + X4 + 1 >= X1 + X4 + 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 >= X1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X1 >= X1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 >= X1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X1 >= X1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 >= X1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 >= X1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 >= X1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 >= X1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 >= X1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 >= X1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 >= X1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 >= X1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 >= X1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = X2 + 1 >= X2 + 1 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X3 + X4 + 1 >= X3 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 + X3 + X4 + 1 >= X1 + X3 + X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 + X3 + X4 + 1 >= X1 + X3 + X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 + X4 + 1 >= X1 + X4 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 + X4 + 1 >= X1 + X4 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 + X4 + 1 >= X1 + X4 + 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) -> mark#(N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U136#](x0, x1, x2, x3) = 1, [a__U135#](x0, x1, x2, x3) = x2 + 1, [a__U134#](x0, x1, x2, x3) = 0, [a__U133#](x0, x1, x2, x3) = 0, [a__length#](x0) = 0, [mark#](x0) = 0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = x0, [U21](x0, x1) = 1, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = x0, [U11](x0, x1) = 1, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = x0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 1, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 1, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = 1, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 1, [a__length](x0) = 1, [mark](x0) = x0, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = 1, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = x0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 1, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 1, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U133#(tt(),IL,M,N) = 0 >= 0 = a__U134#(a__isNatKind(M),IL,M,N) a__U135#(tt(),IL,M,N) = M + 1 >= 1 = a__U136#(a__isNatKind(N),IL,M,N) a__U136#(tt(),IL,M,N) = 1 >= 0 = mark#(N) mark#(U101(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U102(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U103(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U104(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U105(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U106(X)) = 0 >= 0 = mark#(X) mark#(U11(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U12(X1,X2)) = 0 >= 0 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = 0 >= 0 = mark#(X) mark#(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U22(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U23(X)) = 0 >= 0 = mark#(X) mark#(U31(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U32(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U33(X)) = 0 >= 0 = mark#(X) mark#(U41(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U42(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U43(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U44(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U45(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U46(X)) = 0 >= 0 = mark#(X) mark#(U51(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U52(X)) = 0 >= 0 = mark#(X) mark#(U61(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U62(X)) = 0 >= 0 = mark#(X) mark#(U71(X)) = 0 >= 0 = mark#(X) mark#(U81(X)) = 0 >= 0 = mark#(X) mark#(U91(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U92(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U93(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U94(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U95(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U96(X)) = 0 >= 0 = mark#(X) mark#(s(X)) = 0 >= 0 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 1 >= 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 1 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 1 >= 0 = tt() a__isNatIListKind(zeros()) = 1 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 1 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 1 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 1 >= 0 = tt() a__isNatKind(length(V1)) = 1 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 1 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 1 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 1 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = X >= X = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 1 >= 1 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 1 >= 1 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 1 >= 1 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = X >= X = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 1 >= 1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) a__U135#(tt(),IL,M,N) -> a__U136#(a__isNatKind(N),IL,M,N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U136#](x0, x1, x2, x3) = 0, [a__U135#](x0, x1, x2, x3) = x3 + 1, [a__U134#](x0, x1, x2, x3) = 1, [a__U133#](x0, x1, x2, x3) = 1, [a__length#](x0) = 0, [mark#](x0) = 1, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = x1, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x1, [U33](x0) = 0, [U32](x0, x1) = x1, [U31](x0, x1) = x1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x3, [U135](x0, x1, x2, x3) = x3, [U134](x0, x1, x2, x3) = x3, [U133](x0, x1, x2, x3) = x2 + x3 + 1, [U132](x0, x1, x2, x3) = x2 + x3 + 1, [U131](x0, x1, x2, x3) = x2 + x3 + 1, [U122](x0) = 0, [U121](x0, x1) = x1, [isNatList](x0) = x0, [U13](x0) = 1, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = 1, [U11](x0, x1) = 1, [isNatIList](x0) = x0, [U106](x0) = 0, [isNat](x0) = 1, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = x1 + 1, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = x1, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = x1, [a__U33](x0) = 0, [a__U32](x0, x1) = x1, [a__U31](x0, x1) = x1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x3, [a__U135](x0, x1, x2, x3) = x3, [a__U134](x0, x1, x2, x3) = x3, [a__U133](x0, x1, x2, x3) = x2 + x3 + 1, [a__U132](x0, x1, x2, x3) = x2 + x3 + 1, [a__U131](x0, x1, x2, x3) = x2 + x3 + 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = x1, [a__U13](x0) = 1, [a__isNatList](x0) = x0, [s](x0) = x0, [a__length](x0) = 1, [mark](x0) = x0, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = 1, [a__U11](x0, x1) = 1, [a__U106](x0) = 0, [a__isNatIList](x0) = x0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 1, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x1 + 1, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U133#(tt(),IL,M,N) = 1 >= 1 = a__U134#(a__isNatKind(M),IL,M,N) a__U135#(tt(),IL,M,N) = N + 1 >= 0 = a__U136#(a__isNatKind(N),IL,M,N) mark#(U101(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U102(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U103(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U104(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U105(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U106(X)) = 1 >= 1 = mark#(X) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U32(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U33(X)) = 1 >= 1 = mark#(X) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U43(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U44(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U45(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U61(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U81(X)) = 1 >= 1 = mark#(X) mark#(U91(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U92(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U93(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U94(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U95(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U96(X)) = 1 >= 1 = mark#(X) mark#(s(X)) = 1 >= 1 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = V1 + 1 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 1 >= 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 1 >= 1 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = IL >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 1 >= 0 = tt() a__U131(tt(),IL,M,N) = M + N + 1 >= M + N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = M + N + 1 >= M + N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = M + N + 1 >= N = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = N >= N = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = N >= N = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = N >= N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= V = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = V >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = V1 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 1 >= 0 = tt() a__isNat(length(V1)) = 1 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V >= V = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = V1 >= V1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = V1 >= V1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = V1 + V2 + 1 >= V1 + 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= IL = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = M + N + 1 >= M + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 1 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = X >= X = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U121(X1,X2)) = X2 >= X2 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X3 + X4 + 1 >= X3 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X3 + X4 + 1 >= X3 + X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X3 + X4 + 1 >= X3 + X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X4 >= X4 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X4 >= X4 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X4 >= X4 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = X2 >= X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X2 >= X2 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X2 >= X2 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X2 >= X2 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X1 >= X1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X2 + 1 >= X2 + 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 1 >= 1 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = X >= X = isNatIList(X) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 1 >= 1 = U13(X) a__isNatList(X) = X >= X = isNatList(X) a__U121(X1,X2) = X2 >= X2 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X3 + X4 + 1 >= X3 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X3 + X4 + 1 >= X3 + X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X3 + X4 + 1 >= X3 + X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X4 >= X4 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X4 >= X4 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X4 >= X4 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = X2 >= X2 = U31(X1,X2) a__U32(X1,X2) = X2 >= X2 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = X2 >= X2 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = X2 >= X2 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U133(X1,X2,X3,X4)) -> a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U134#](x0, x1, x2, x3) = x0, [a__U133#](x0, x1, x2, x3) = 0, [a__length#](x0) = 0, [mark#](x0) = 1, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = 0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 1, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = x0, [U133](x0, x1, x2, x3) = x0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = x0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = x0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 1, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 1, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = x0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = x0, [a__U133](x0, x1, x2, x3) = x0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = x0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = x0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U133#(tt(),IL,M,N) = 0 >= 0 = a__U134#(a__isNatKind(M),IL,M,N) mark#(U101(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U102(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U103(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U104(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U105(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U106(X)) = 1 >= 1 = mark#(X) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U133(X1,X2,X3,X4)) = 1 >= 0 = a__U133#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U32(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U33(X)) = 1 >= 1 = mark#(X) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U43(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U44(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U45(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U61(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U81(X)) = 1 >= 1 = mark#(X) mark#(U91(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U92(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U93(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U94(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U95(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U96(X)) = 1 >= 1 = mark#(X) mark#(s(X)) = 1 >= 1 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 0 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 1 = a__U62(mark(X)) mark(U71(X)) = 1 >= 1 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 0 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 0 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X1 >= X1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X1 >= X1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 >= X1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 >= X1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 >= X1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 0 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U133#(tt(),IL,M,N) -> a__U134#(a__isNatKind(M),IL,M,N) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U134#](x0, x1, x2, x3) = 0, [a__U133#](x0, x1, x2, x3) = x2 + 1, [a__length#](x0) = 0, [mark#](x0) = 0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = 1, [U94](x0, x1, x2) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = 0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x0, [U135](x0, x1, x2, x3) = x0, [U134](x0, x1, x2, x3) = x0, [U133](x0, x1, x2, x3) = x0, [U132](x0, x1, x2, x3) = x0, [U131](x0, x1, x2, x3) = x0, [U122](x0) = x0, [U121](x0, x1) = x0, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = 1, [isNat](x0) = 0, [U105](x0, x1) = 1, [U104](x0, x1, x2) = 1, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = 0, [length](x0) = 1, [a__U96](x0) = x0, [a__U95](x0, x1) = 1, [a__U94](x0, x1, x2) = 1, [a__U93](x0, x1, x2) = 1, [a__U92](x0, x1, x2) = 1, [a__U91](x0, x1, x2) = 1, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = 0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = 0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = x0, [a__U135](x0, x1, x2, x3) = x0, [a__U134](x0, x1, x2, x3) = x0, [a__U133](x0, x1, x2, x3) = x0, [a__U132](x0, x1, x2, x3) = x0, [a__U131](x0, x1, x2, x3) = x0, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = x0, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = 1, [a__length](x0) = 1, [mark](x0) = 1, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = 1, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 1, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 1, [a__zeros] = 0 orientation: a__U133#(tt(),IL,M,N) = M + 1 >= 0 = a__U134#(a__isNatKind(M),IL,M,N) mark#(U101(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U102(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U103(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U104(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U105(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U106(X)) = 0 >= 0 = mark#(X) mark#(U11(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U12(X1,X2)) = 0 >= 0 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = 0 >= 0 = mark#(X) mark#(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U22(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U23(X)) = 0 >= 0 = mark#(X) mark#(U31(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U32(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U33(X)) = 0 >= 0 = mark#(X) mark#(U41(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U42(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U43(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U44(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U45(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U46(X)) = 0 >= 0 = mark#(X) mark#(U51(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U52(X)) = 0 >= 0 = mark#(X) mark#(U61(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U62(X)) = 0 >= 0 = mark#(X) mark#(U71(X)) = 0 >= 0 = mark#(X) mark#(U81(X)) = 0 >= 0 = mark#(X) mark#(U91(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U92(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U93(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U94(X1,X2,X3)) = 0 >= 0 = mark#(X1) mark#(U95(X1,X2)) = 0 >= 0 = mark#(X1) mark#(U96(X)) = 0 >= 0 = mark#(X) mark#(s(X)) = 0 >= 0 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 1 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 1 >= 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 1 >= 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 1 >= 1 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 1 >= 1 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 1 >= 1 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 1 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 1 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 1 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 1 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 1 = a__U62(mark(X)) mark(U71(X)) = 1 >= 1 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 1 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 1 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 0 = cons(mark(X1),X2) mark(0()) = 1 >= 1 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 1 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 1 = U104(X1,X2,X3) a__U105(X1,X2) = 1 >= 1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 1 >= 1 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = X1 >= X1 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = X1 >= X1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 >= X1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 >= X1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 >= X1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 >= X1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 >= X1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 1 >= 1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 1 >= 1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 1 >= 1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 1 >= 1 = U94(X1,X2,X3) a__U95(X1,X2) = 1 >= 1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U134(X1,X2,X3,X4)) -> a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U134#](x0, x1, x2, x3) = 0, [a__length#](x0) = 0, [mark#](x0) = 1, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = x1, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x1, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = x0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = x0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: mark#(U101(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U102(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U103(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U104(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U105(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U106(X)) = 1 >= 1 = mark#(X) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U12(X1,X2)) = 1 >= 1 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = 1 >= 1 = mark#(X) mark#(U134(X1,X2,X3,X4)) = 1 >= 0 = a__U134#(mark(X1),X2,X3,X4) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U22(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U23(X)) = 1 >= 1 = mark#(X) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U32(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U33(X)) = 1 >= 1 = mark#(X) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U43(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U44(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U45(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U46(X)) = 1 >= 1 = mark#(X) mark#(U51(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X)) = 1 >= 1 = mark#(X) mark#(U61(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U62(X)) = 1 >= 1 = mark#(X) mark#(U71(X)) = 1 >= 1 = mark#(X) mark#(U81(X)) = 1 >= 1 = mark#(X) mark#(U91(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U92(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U93(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U94(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U95(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U96(X)) = 1 >= 1 = mark#(X) mark#(s(X)) = 1 >= 1 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = N >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X1 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = X2 >= X2 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= 0 = U45(X1,X2) a__U46(X) = X >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U105(X1,X2)) -> mark#(X1) mark#(U106(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U13(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> mark#(X1) mark#(U33(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U45(X1,X2)) -> mark#(X1) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0 + 1, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0 + x1, [U94](x0, x1, x2) = x0 + x1 + x2, [U93](x0, x1, x2) = x0 + x1 + x2, [U92](x0, x1, x2) = x0 + x1 + x2, [U91](x0, x1, x2) = x0 + x1 + x2, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0 + x1 + 1, [U44](x0, x1, x2) = x0 + x1 + x2 + 1, [U43](x0, x1, x2) = x0 + x1 + x2 + 1, [U42](x0, x1, x2) = x0 + x1 + x2 + 1, [U41](x0, x1, x2) = x0 + x1 + x2 + 1, [U33](x0) = x0 + 1, [U32](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + x1 + 1, [U23](x0) = x0, [U22](x0, x1) = x0 + x1, [U21](x0, x1) = x0 + x1, [U136](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U135](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U134](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U133](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U132](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U131](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U122](x0) = 0, [U121](x0, x1) = x0, [isNatList](x0) = x0, [U13](x0) = x0 + 1, [U114](x0, x1) = x1 + 1, [U113](x0, x1, x2) = x1 + 1, [U112](x0, x1, x2) = x1 + 1, [U111](x0, x1, x2) = x1 + 1, [U12](x0, x1) = x0 + x1 + 1, [U11](x0, x1) = x0 + x1 + 1, [isNatIList](x0) = x0 + 1, [U106](x0) = x0, [isNat](x0) = x0, [U105](x0, x1) = x0 + x1 + 1, [U104](x0, x1, x2) = x0 + x1 + x2 + 1, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0 + x1 + x2 + 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0 + x1 + x2 + 1, [U101](x0, x1, x2) = x0 + x1 + x2 + 1, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = x0 + 1, [a__U96](x0) = x0, [a__U95](x0, x1) = x0 + x1, [a__U94](x0, x1, x2) = x0 + x1 + x2, [a__U93](x0, x1, x2) = x0 + x1 + x2, [a__U92](x0, x1, x2) = x0 + x1 + x2, [a__U91](x0, x1, x2) = x0 + x1 + x2, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0 + x1 + 1, [a__U44](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U43](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U42](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U41](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U33](x0) = x0 + 1, [a__U32](x0, x1) = x0 + x1 + 1, [a__U31](x0, x1) = x0 + x1 + 1, [a__U23](x0) = x0, [a__U22](x0, x1) = x0 + x1, [a__U21](x0, x1) = x0 + x1, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U135](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U134](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U133](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U132](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U131](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = x0, [a__U13](x0) = x0 + 1, [a__isNatList](x0) = x0, [s](x0) = x0, [a__length](x0) = x0 + 1, [mark](x0) = x0, [a__U114](x0, x1) = x1 + 1, [a__U113](x0, x1, x2) = x1 + 1, [a__U112](x0, x1, x2) = x1 + 1, [a__U111](x0, x1, x2) = x1 + 1, [a__U12](x0, x1) = x0 + x1 + 1, [a__U11](x0, x1) = x0 + x1 + 1, [a__U106](x0) = x0, [a__isNatIList](x0) = x0 + 1, [a__U105](x0, x1) = x0 + x1 + 1, [a__isNat](x0) = x0, [a__U104](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U103](x0, x1, x2) = x0 + x1 + x2 + 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0 + x1 + x2 + 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0 + x1 + x2 + 1, [tt] = 0, [cons](x0, x1) = x0 + x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: mark#(U101(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U102(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U103(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U104(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U105(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(U106(X)) = X + 1 >= X + 1 = mark#(X) mark#(U11(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U13(X)) = X + 2 >= X + 1 = mark#(X) mark#(U21(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(U22(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(U23(X)) = X + 1 >= X + 1 = mark#(X) mark#(U31(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(U32(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(U33(X)) = X + 2 >= X + 1 = mark#(X) mark#(U41(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U42(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U43(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U44(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = mark#(X1) mark#(U45(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = mark#(X1) mark#(U46(X)) = X + 1 >= X + 1 = mark#(X) mark#(U51(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U52(X)) = X + 1 >= X + 1 = mark#(X) mark#(U61(X1,X2)) = X1 + 1 >= X1 + 1 = mark#(X1) mark#(U62(X)) = X + 1 >= X + 1 = mark#(X) mark#(U71(X)) = X + 1 >= X + 1 = mark#(X) mark#(U81(X)) = X + 1 >= X + 1 = mark#(X) mark#(U91(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1) mark#(U95(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1) mark#(U96(X)) = X + 1 >= X + 1 = mark#(X) mark#(s(X)) = X + 1 >= X + 1 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = V2 + 1 >= V2 + 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = V1 + 1 >= V1 + 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = L + 1 >= L + 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = L + 1 >= L + 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = L + 1 >= L + 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = L + 1 >= L + 1 = s(a__length(mark(L))) a__U12(tt(),V1) = V1 + 1 >= V1 + 1 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 1 >= 0 = tt() a__U131(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = V1 >= V1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = V1 >= V1 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V + 1 >= V + 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = V + 1 >= V + 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = V2 + 1 >= V2 + 1 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = V2 >= V2 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = V1 + 1 >= V1 + 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = V1 >= V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V + 1 >= V + 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = V1 + V2 >= V1 + V2 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = L + N + 1 >= L + 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= IL + 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL + M + N + 1 >= IL + M + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U105(mark(X1),X2) mark(isNat(X)) = X >= X = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = X + 1 >= X + 1 = a__isNatIList(X) mark(U11(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = X2 + 1 >= X2 + 1 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = X + 1 >= X + 1 = a__U13(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U121(X1,X2)) = X1 >= X1 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 + X2 >= X1 + X2 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U32(mark(X1),X2) mark(U33(X)) = X + 1 >= X + 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 + X2 >= X1 + X2 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U105(X1,X2) a__isNat(X) = X >= X = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = X + 1 >= X + 1 = isNatIList(X) a__U11(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U12(X1,X2) a__U111(X1,X2,X3) = X2 + 1 >= X2 + 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X2 + 1 >= X2 + 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X2 + 1 >= X2 + 1 = U113(X1,X2,X3) a__U114(X1,X2) = X2 + 1 >= X2 + 1 = U114(X1,X2) a__length(X) = X + 1 >= X + 1 = length(X) a__U13(X) = X + 1 >= X + 1 = U13(X) a__isNatList(X) = X >= X = isNatList(X) a__U121(X1,X2) = X1 >= X1 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) a__U22(X1,X2) = X1 + X2 >= X1 + X2 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(X1,X2) a__U32(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U32(X1,X2) a__U33(X) = X + 1 >= X + 1 = U33(X) a__U41(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U94(X1,X2,X3) a__U95(X1,X2) = X1 + X2 >= X1 + X2 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: mark#(U106(X)) -> mark#(X) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U95(X1,X2)) -> mark#(X1) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0 + 1, [U94](x0, x1, x2) = x0 + 1, [U93](x0, x1, x2) = x0 + 1, [U92](x0, x1, x2) = x0 + 1, [U91](x0, x1, x2) = x0 + 1, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 1, [U133](x0, x1, x2, x3) = 1, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 1, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = 1, [U104](x0, x1, x2) = 1, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = 1, [length](x0) = 0, [a__U96](x0) = x0, [a__U95](x0, x1) = x0 + 1, [a__U94](x0, x1, x2) = x0 + 1, [a__U93](x0, x1, x2) = x0 + 1, [a__U92](x0, x1, x2) = x0 + 1, [a__U91](x0, x1, x2) = x0 + 1, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 1, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: mark#(U106(X)) = X >= X = mark#(X) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U21(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U91(X1,X2,X3)) = X1 + 1 >= X1 = mark#(X1) mark#(U92(X1,X2,X3)) = X1 + 1 >= X1 = mark#(X1) mark#(U93(X1,X2,X3)) = X1 + 1 >= X1 = mark#(X1) mark#(U94(X1,X2,X3)) = X1 + 1 >= X1 = mark#(X1) mark#(U95(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U96(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 1 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 1 >= 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 1 >= 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 1 >= 1 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 1 >= 1 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 1 >= 1 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 >= X1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 >= X1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 + 1 >= X1 + 1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 1 = U104(X1,X2,X3) a__U105(X1,X2) = 1 >= 1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 + 1 >= X1 + 1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 + 1 >= X1 + 1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 + 1 >= X1 + 1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 + 1 >= X1 + 1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 + 1 >= X1 + 1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: mark#(U106(X)) -> mark#(X) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> mark#(X1) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = x0 + 1, [U21](x0, x1) = x0 + 1, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 1, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = x0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0 + 1, [a__U21](x0, x1) = x0 + 1, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 1, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: mark#(U106(X)) = X >= X = mark#(X) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U21(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U22(X1,X2)) = X1 + 1 >= X1 = mark#(X1) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U96(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 1 >= 1 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 1 >= 0 = tt() a__isNat(length(V1)) = 1 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 1 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 + 1 >= X1 + 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 + 1 >= X1 + 1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 >= X1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 1 >= 1 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = X1 + 1 >= X1 + 1 = U21(X1,X2) a__U22(X1,X2) = X1 + 1 >= X1 + 1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: mark#(U106(X)) -> mark#(X) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0 + x1 + 1, [U52](x0) = x0, [U51](x0, x1) = x0 + x1, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U135](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U134](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U133](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U132](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U131](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U122](x0) = 1, [U121](x0, x1) = x1 + 1, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = x1 + 1, [U113](x0, x1, x2) = x1 + 1, [U112](x0, x1, x2) = x1 + 1, [U111](x0, x1, x2) = x1 + 1, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = x0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = x0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = x0 + 1, [a__U96](x0) = x0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0 + x1 + 1, [a__U52](x0) = x0, [a__U51](x0, x1) = x0 + x1, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = x0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U135](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U134](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U133](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U132](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U131](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = x1 + 1, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = x0 + 1, [mark](x0) = x0, [a__U114](x0, x1) = x1 + 1, [a__U113](x0, x1, x2) = x1 + 1, [a__U112](x0, x1, x2) = x1 + 1, [a__U111](x0, x1, x2) = x1 + 1, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = x0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = x0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = x0 + x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: mark#(U106(X)) = X >= X = mark#(X) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U61(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U96(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = L + 1 >= L + 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = L + 1 >= L + 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = L + 1 >= L + 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = L + 1 >= L + 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = IL + 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = V2 >= V2 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = V2 + 1 >= V2 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 1 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = V1 + V2 >= V1 + V2 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = V1 + 1 >= V1 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = V1 >= V1 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 2 >= 0 = 0() a__length(cons(N,L)) = L + N + 1 >= L + 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= IL + 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL + M + N + 1 >= IL + M + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = X >= X = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = X >= X = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = X2 + 1 >= X2 + 1 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = X2 + 1 >= X2 + 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 + X2 >= X1 + X2 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = X >= X = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = X2 + 1 >= X2 + 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X2 + 1 >= X2 + 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X2 + 1 >= X2 + 1 = U113(X1,X2,X3) a__U114(X1,X2) = X2 + 1 >= X2 + 1 = U114(X1,X2) a__length(X) = X + 1 >= X + 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = X2 + 1 >= X2 + 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: mark#(U106(X)) -> mark#(X) a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = 1, [U94](x0, x1, x2) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = 0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 1, [U135](x0, x1, x2, x3) = 1, [U134](x0, x1, x2, x3) = 1, [U133](x0, x1, x2, x3) = 1, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 1, [U122](x0) = 1, [U121](x0, x1) = 1, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = x0 + 1, [isNat](x0) = 0, [U105](x0, x1) = 1, [U104](x0, x1, x2) = 1, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = x1 + 1, [length](x0) = 0, [a__U96](x0) = x0, [a__U95](x0, x1) = 1, [a__U94](x0, x1, x2) = 1, [a__U93](x0, x1, x2) = 1, [a__U92](x0, x1, x2) = 1, [a__U91](x0, x1, x2) = 1, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = 0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = x0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x1 + 1, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = x0 + 1, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 1, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = 1, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: mark#(U106(X)) = X + 1 >= X = mark#(X) a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U62(X)) = X >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U96(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 1 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 1 >= 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 1 >= 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 1 >= 1 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 1 >= 1 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 1 >= 1 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 2 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X + 1 >= X + 1 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X2 + 1 >= X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 >= X1 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 1 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 1 = U104(X1,X2,X3) a__U105(X1,X2) = 1 >= 1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X + 1 >= X + 1 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X2 + 1 >= X2 + 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 1 >= 1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 1 >= 1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 1 >= 1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 1 >= 1 = U94(X1,X2,X3) a__U95(X1,X2) = 1 >= 1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U62(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x1, [U94](x0, x1, x2) = x2, [U93](x0, x1, x2) = x1 + x2, [U92](x0, x1, x2) = x1 + x2, [U91](x0, x1, x2) = x1 + x2, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0 + 1, [U61](x0, x1) = x1 + 1, [U52](x0) = x0, [U51](x0, x1) = x0 + x1, [U46](x0) = x0, [U45](x0, x1) = x1, [U44](x0, x1, x2) = x1 + x2, [U43](x0, x1, x2) = x1 + x2, [U42](x0, x1, x2) = x1 + x2, [U41](x0, x1, x2) = x1 + x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = x1, [U23](x0) = x0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x1 + x3 + 1, [U135](x0, x1, x2, x3) = x1 + x3 + 1, [U134](x0, x1, x2, x3) = x1 + x3 + 1, [U133](x0, x1, x2, x3) = x1 + x3 + 1, [U132](x0, x1, x2, x3) = x1 + x3 + 1, [U131](x0, x1, x2, x3) = x1 + x3 + 1, [U122](x0) = 1, [U121](x0, x1) = x1 + 1, [isNatList](x0) = x0, [U13](x0) = 0, [U114](x0, x1) = x1, [U113](x0, x1, x2) = x1 + x2, [U112](x0, x1, x2) = x1 + x2, [U111](x0, x1, x2) = x1 + x2, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = x0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = x0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = x0, [U102](x0, x1, x2) = x2, [U101](x0, x1, x2) = x2, [a__take](x0, x1) = x1 + 1, [length](x0) = x0, [a__U96](x0) = x0, [a__U95](x0, x1) = x1, [a__U94](x0, x1, x2) = x2, [a__U93](x0, x1, x2) = x1 + x2, [a__U92](x0, x1, x2) = x1 + x2, [a__U91](x0, x1, x2) = x1 + x2, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0 + 1, [a__U61](x0, x1) = x1 + 1, [a__U52](x0) = x0, [a__U51](x0, x1) = x0 + x1, [a__U46](x0) = x0, [a__U45](x0, x1) = x1, [a__U44](x0, x1, x2) = x1 + x2, [a__U43](x0, x1, x2) = x1 + x2, [a__U42](x0, x1, x2) = x1 + x2, [a__U41](x0, x1, x2) = x1 + x2, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = x1, [a__U23](x0) = x0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x1 + 1, [a__U136](x0, x1, x2, x3) = x1 + x3 + 1, [a__U135](x0, x1, x2, x3) = x1 + x3 + 1, [a__U134](x0, x1, x2, x3) = x1 + x3 + 1, [a__U133](x0, x1, x2, x3) = x1 + x3 + 1, [a__U132](x0, x1, x2, x3) = x1 + x3 + 1, [a__U131](x0, x1, x2, x3) = x1 + x3 + 1, [nil] = 0, [a__U122](x0) = 1, [a__U121](x0, x1) = x1 + 1, [a__U13](x0) = 0, [a__isNatList](x0) = x0, [s](x0) = x0, [a__length](x0) = x0, [mark](x0) = x0, [a__U114](x0, x1) = x1, [a__U113](x0, x1, x2) = x1 + x2, [a__U112](x0, x1, x2) = x1 + x2, [a__U111](x0, x1, x2) = x1 + x2, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = x0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = x0, [a__U102](x0, x1, x2) = x2, [a__isNatKind](x0) = x0, [a__U101](x0, x1, x2) = x2, [tt] = 0, [cons](x0, x1) = x0 + x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U62(X)) = X + 1 >= X = mark#(X) mark#(U71(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U96(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = V2 >= V2 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = V2 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = L + N >= L + N = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = L + N >= L + N = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = L + N >= L = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = L >= L = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = IL + 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V1 + V2 >= V2 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = V2 >= V2 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = V2 >= V2 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = V2 + 1 >= V2 + 1 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 1 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = V1 + V2 >= V2 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = V2 >= V2 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = V2 >= V2 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V >= V = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = V1 + V2 >= V1 + V2 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = V1 + V2 >= V1 + V2 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = V2 + 1 >= V2 + 1 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = V1 >= V1 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = V1 >= V1 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = V1 + V2 >= V1 + V2 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = V2 + 1 >= V2 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = L + N >= L + N = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= IL + 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL + N + 1 >= IL + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X3 >= X3 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X3 >= X3 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = X >= X = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = X >= X = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = X >= X = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = X2 >= X2 = a__U114(mark(X1),X2) mark(length(X)) = X >= X = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U121(X1,X2)) = X2 + 1 >= X2 + 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X2 + 1 >= X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = X2 >= X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X2 >= X2 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 + X2 >= X1 + X2 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = X2 + 1 >= X2 + 1 = a__U61(mark(X1),X2) mark(U62(X)) = X + 1 >= X + 1 = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X2 + X3 >= X2 + X3 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X3 >= X3 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X2 >= X2 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X3 >= X3 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X3 >= X3 = U102(X1,X2,X3) a__isNatKind(X) = X >= X = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = X >= X = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = X2 + X3 >= X2 + X3 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X2 + X3 >= X2 + X3 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X2 + X3 >= X2 + X3 = U113(X1,X2,X3) a__U114(X1,X2) = X2 >= X2 = U114(X1,X2) a__length(X) = X >= X = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = X >= X = isNatList(X) a__U121(X1,X2) = X2 + 1 >= X2 + 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X2 + 1 >= X2 + 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X2 >= X2 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = X2 + X3 >= X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X2 + X3 >= X2 + X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X2 + X3 >= X2 + X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X2 + X3 >= X2 + X3 = U44(X1,X2,X3) a__U45(X1,X2) = X2 >= X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X2 + 1 >= X2 + 1 = U61(X1,X2) a__U62(X) = X + 1 >= X + 1 = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X2 + X3 >= X2 + X3 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X2 + X3 >= X2 + X3 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X2 + X3 >= X2 + X3 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X3 >= X3 = U94(X1,X2,X3) a__U95(X1,X2) = X2 >= X2 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = x0, [U71](x0) = x0 + 1, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = x0, [U51](x0, x1) = x0 + x1, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = x1, [U21](x0, x1) = x1, [U136](x0, x1, x2, x3) = x1 + x3, [U135](x0, x1, x2, x3) = x1 + x3, [U134](x0, x1, x2, x3) = x1 + x3, [U133](x0, x1, x2, x3) = x1 + x3, [U132](x0, x1, x2, x3) = x1 + x3, [U131](x0, x1, x2, x3) = x1 + x3, [U122](x0) = x0, [U121](x0, x1) = x1, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = x1 + 1, [U113](x0, x1, x2) = x1 + 1, [U112](x0, x1, x2) = x1 + 1, [U111](x0, x1, x2) = x1 + 1, [U12](x0, x1) = x1 + 1, [U11](x0, x1) = x1 + 1, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = x0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = x0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = x0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = x1, [length](x0) = x0 + 1, [a__U96](x0) = x0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = x0, [a__U71](x0) = x0 + 1, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0 + x1, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = x0, [a__U22](x0, x1) = x1, [a__U21](x0, x1) = x1, [take](x0, x1) = x1, [a__U136](x0, x1, x2, x3) = x1 + x3, [a__U135](x0, x1, x2, x3) = x1 + x3, [a__U134](x0, x1, x2, x3) = x1 + x3, [a__U133](x0, x1, x2, x3) = x1 + x3, [a__U132](x0, x1, x2, x3) = x1 + x3, [a__U131](x0, x1, x2, x3) = x1 + x3, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = x1, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = x0 + 1, [mark](x0) = x0, [a__U114](x0, x1) = x1 + 1, [a__U113](x0, x1, x2) = x1 + 1, [a__U112](x0, x1, x2) = x1 + 1, [a__U111](x0, x1, x2) = x1 + 1, [a__U12](x0, x1) = x1 + 1, [a__U11](x0, x1) = x1 + 1, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = x0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = x0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = x0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = x0 + x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 + X2 >= X1 = mark#(X1) mark#(U52(X)) = X >= X = mark#(X) mark#(U71(X)) = X + 1 >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U96(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = V1 + 1 >= V1 + 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = L + 1 >= L + 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = L + 1 >= L + 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = L + 1 >= L + 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = L + 1 >= L + 1 = s(a__length(mark(L))) a__U12(tt(),V1) = V1 + 1 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = IL >= IL = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = IL + N >= IL + N = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL + N >= IL + N = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL + N >= IL + N = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL + N >= IL + N = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL + N >= IL + N = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL + N >= IL + N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = V1 >= V1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = V1 >= V1 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = V2 >= V2 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 1 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = V1 + 1 >= V1 + 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = V1 >= V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = V1 + V2 >= V1 + V2 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = V2 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = V1 + 1 >= V1 + 1 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = V1 >= V1 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = L + N + 1 >= L + 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL >= IL = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL + N >= IL + N = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = X >= X = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = X >= X = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = X >= X = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = X2 + 1 >= X2 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X2 + 1 >= X2 + 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = X2 + 1 >= X2 + 1 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = X2 >= X2 = a__U121(mark(X1),X2) mark(U122(X)) = X >= X = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X2 + X4 >= X2 + X4 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X2 + X4 >= X2 + X4 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X2 + X4 >= X2 + X4 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X2 + X4 >= X2 + X4 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X2 + X4 >= X2 + X4 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X2 + X4 >= X2 + X4 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X2 >= X2 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X2 >= X2 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X2 >= X2 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = X1 + X2 >= X1 + X2 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = X + 1 >= X + 1 = a__U71(mark(X)) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = X >= X = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = X >= X = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = X >= X = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X2 + 1 >= X2 + 1 = U11(X1,X2) a__U12(X1,X2) = X2 + 1 >= X2 + 1 = U12(X1,X2) a__U111(X1,X2,X3) = X2 + 1 >= X2 + 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X2 + 1 >= X2 + 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X2 + 1 >= X2 + 1 = U113(X1,X2,X3) a__U114(X1,X2) = X2 + 1 >= X2 + 1 = U114(X1,X2) a__length(X) = X + 1 >= X + 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = X2 >= X2 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = X2 + X4 >= X2 + X4 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X2 + X4 >= X2 + X4 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X2 + X4 >= X2 + X4 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X2 + X4 >= X2 + X4 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X2 + X4 >= X2 + X4 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X2 + X4 >= X2 + X4 = U136(X1,X2,X3,X4) a__take(X1,X2) = X2 >= X2 = take(X1,X2) a__U21(X1,X2) = X2 >= X2 = U21(X1,X2) a__U22(X1,X2) = X2 >= X2 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = X + 1 >= X + 1 = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U51(X1,X2)) -> mark#(X1) mark#(U52(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = x0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = x0 + 1, [U51](x0, x1) = x0 + x1 + 1, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 1, [U135](x0, x1, x2, x3) = 1, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 1, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 1, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = x0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 1, [length](x0) = 1, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = x0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = x0 + 1, [a__U51](x0, x1) = x0 + x1 + 1, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = x0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = 1, [mark](x0) = x0 + 1, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = x0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = x1 + 1, [zeros] = 0, [0] = 0, [a__zeros] = 1 orientation: a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U51(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(U52(X)) = X + 1 >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U96(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = V2 + 1 >= V2 + 1 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 1 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = X + 1 >= X = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 2 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 2 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 2 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 2 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 2 >= 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 2 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 2 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 2 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 2 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 2 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = X + 1 >= X + 1 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = X + 1 >= X + 1 = a__U46(mark(X)) mark(U51(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = a__U51(mark(X1),X2) mark(U52(X)) = X + 2 >= X + 2 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 0 = a__U62(mark(X)) mark(U71(X)) = 1 >= 0 = a__U71(mark(X)) mark(U81(X)) = X + 1 >= X + 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 + 1 >= X1 + 1 = a__U95(mark(X1),X2) mark(U96(X)) = X + 1 >= X + 1 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 + 2 >= X2 + 1 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = X + 1 >= X + 1 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 1 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U51(X1,X2) a__U52(X) = X + 1 >= X + 1 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(U96(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0 + 1, [U95](x0, x1) = x1, [U94](x0, x1, x2) = x2, [U93](x0, x1, x2) = x2, [U92](x0, x1, x2) = x2, [U91](x0, x1, x2) = x2, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 1, [U135](x0, x1, x2, x3) = 1, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 1, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 1, [U121](x0, x1) = 1, [isNatList](x0) = x0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 1, [length](x0) = 0, [a__U96](x0) = x0 + 1, [a__U95](x0, x1) = x1 + 1, [a__U94](x0, x1, x2) = x2 + 1, [a__U93](x0, x1, x2) = x2 + 1, [a__U92](x0, x1, x2) = x2 + 1, [a__U91](x0, x1, x2) = x2 + 1, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = x0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 0, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = 0, [a__isNatList](x0) = x0, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0 + 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = x1 + 1, [zeros] = 0, [0] = 0, [a__zeros] = 1 orientation: a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(U96(X)) = X + 1 >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = V2 + 1 >= V2 + 1 = a__U96(a__isNatList(V2)) a__U96(tt()) = 1 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 0 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = X + 1 >= X = a__isNatList(X) mark(U121(X1,X2)) = 2 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 2 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 2 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 2 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 2 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 2 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = X + 1 >= X + 1 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = X + 1 >= X + 1 = a__U46(mark(X)) mark(U51(X1,X2)) = X1 + 1 >= X1 + 1 = a__U51(mark(X1),X2) mark(U52(X)) = X + 1 >= X + 1 = a__U52(mark(X)) mark(U61(X1,X2)) = X1 + 1 >= X1 + 1 = a__U61(mark(X1),X2) mark(U62(X)) = X + 1 >= X + 1 = a__U62(mark(X)) mark(U71(X)) = X + 1 >= X + 1 = a__U71(mark(X)) mark(U81(X)) = X + 1 >= X + 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X2 + 1 >= X2 + 1 = a__U95(mark(X1),X2) mark(U96(X)) = X + 2 >= X + 2 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 + 2 >= X2 + 1 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = X + 1 >= X + 1 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 1 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = X >= X = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X3 + 1 >= X3 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X3 + 1 >= X3 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X3 + 1 >= X3 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X3 + 1 >= X3 = U94(X1,X2,X3) a__U95(X1,X2) = X2 + 1 >= X2 = U95(X1,X2) a__U96(X) = X + 1 >= X + 1 = U96(X) problem: DPs: a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U23(X)) -> mark#(X) mark#(U46(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = 0, [mark#](x0) = x0, [a__U114#](x0, x1) = 0, [a__U113#](x0, x1, x2) = 0, [a__U112#](x0, x1, x2) = 0, [a__U111#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = 0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0 + 1, [U45](x0, x1) = x1 + 1, [U44](x0, x1, x2) = x2 + 1, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2, [U41](x0, x1, x2) = x2, [U33](x0) = x0, [U32](x0, x1) = 0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 1, [U135](x0, x1, x2, x3) = x0 + 1, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = x0, [U112](x0, x1, x2) = x0, [U111](x0, x1, x2) = x0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = x0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = 1, [length](x0) = 0, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = 0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0 + 1, [a__U45](x0, x1) = x1 + 1, [a__U44](x0, x1, x2) = x2 + 1, [a__U43](x0, x1, x2) = x2 + 1, [a__U42](x0, x1, x2) = x2 + 1, [a__U41](x0, x1, x2) = x2 + 1, [a__U33](x0) = x0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = x0 + 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = x0 + 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = x0, [a__U112](x0, x1, x2) = x0, [a__U111](x0, x1, x2) = x0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = x0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x1 + 1, [zeros] = 0, [0] = 0, [a__zeros] = 1 orientation: a__U111#(tt(),L,N) = 0 >= 0 = a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) = 0 >= 0 = a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) = 0 >= 0 = a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) = 0 >= 0 = a__length#(mark(L)) a__length#(cons(N,L)) = 0 >= 0 = a__U111#(a__isNatList(L),L,N) mark#(U23(X)) = X >= X = mark#(X) mark#(U46(X)) = X + 1 >= X = mark#(X) mark#(U81(X)) = X >= X = mark#(X) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = V2 + 1 >= V2 + 1 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 1 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 + 1 >= X1 + 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = X + 1 >= X = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 0 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 2 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X1 + 2 >= X1 + 2 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 2 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = X + 1 >= X + 1 = a__U23(mark(X)) mark(U31(X1,X2)) = X1 + 1 >= X1 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = X + 1 >= X + 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X3 + 2 >= X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X3 + 2 >= X3 + 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X2 + 2 >= X2 + 1 = a__U45(mark(X1),X2) mark(U46(X)) = X + 2 >= X + 2 = a__U46(mark(X)) mark(U51(X1,X2)) = X1 + 1 >= X1 + 1 = a__U51(mark(X1),X2) mark(U52(X)) = X + 1 >= X + 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = X + 1 >= X + 1 = a__U62(mark(X)) mark(U71(X)) = X + 1 >= X + 1 = a__U71(mark(X)) mark(U81(X)) = X + 1 >= X + 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 + 1 >= X1 + 1 = a__U95(mark(X1),X2) mark(U96(X)) = X + 1 >= X + 1 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 + 2 >= X2 + 1 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = X + 1 >= X + 1 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 1 >= 0 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = X >= X = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = X1 >= X1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X1 >= X1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X1 >= X1 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 + 1 >= X1 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X3 + 1 >= X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X3 + 1 >= X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X3 + 1 >= X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X3 + 1 >= X3 + 1 = U44(X1,X2,X3) a__U45(X1,X2) = X2 + 1 >= X2 + 1 = U45(X1,X2) a__U46(X) = X + 1 >= X + 1 = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__U111#(tt(),L,N) -> a__U112#(a__isNatIListKind(L),L,N) a__U112#(tt(),L,N) -> a__U113#(a__isNat(N),L,N) a__U113#(tt(),L,N) -> a__U114#(a__isNatKind(N),L) a__U114#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U111#(a__isNatList(L),L,N) mark#(U23(X)) -> mark#(X) mark#(U81(X)) -> mark#(X) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Open DPs: a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__U12#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__U94#(tt(),V1,V2) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__isNatList#(take(V1,V2)) -> a__U101#(a__isNatKind(V1),V1,V2) a__U101#(tt(),V1,V2) -> a__U102#(a__isNatKind(V1),V1,V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) -> a__isNat#(V1) a__U104#(tt(),V1,V2) -> a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__U31#(tt(),V) -> a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) -> a__isNatList#(V) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isNat#(V1) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = x1, [a__U94#](x0, x1, x2) = x1 + x2, [a__U93#](x0, x1, x2) = x1 + x2, [a__U92#](x0, x1, x2) = x1 + x2, [a__U91#](x0, x1, x2) = x1 + x2, [a__U45#](x0, x1) = x1, [a__U44#](x0, x1, x2) = x1 + x2, [a__U43#](x0, x1, x2) = x1 + x2, [a__U42#](x0, x1, x2) = x1 + x2, [a__U41#](x0, x1, x2) = x1 + x2, [a__U32#](x0, x1) = x1, [a__U31#](x0, x1) = x1, [a__U22#](x0, x1) = x1, [a__U21#](x0, x1) = x1, [a__isNatList#](x0) = x0, [a__U12#](x0, x1) = x1, [a__U11#](x0, x1) = x1, [a__isNatIList#](x0) = x0, [a__U105#](x0, x1) = x1, [a__isNat#](x0) = x0, [a__U104#](x0, x1, x2) = x1 + x2, [a__U103#](x0, x1, x2) = x1 + x2, [a__U102#](x0, x1, x2) = x1 + x2, [a__U101#](x0, x1, x2) = x1 + x2, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = x2, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = x2, [U43](x0, x1, x2) = x2 + 1, [U42](x0, x1, x2) = x2 + 1, [U41](x0, x1, x2) = x1 + x2 + 1, [U33](x0) = 1, [U32](x0, x1) = 1, [U31](x0, x1) = x1 + 1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U135](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U134](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U133](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U132](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U131](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U122](x0) = 1, [U121](x0, x1) = x1 + 1, [isNatList](x0) = x0, [U13](x0) = 0, [U114](x0, x1) = x1 + 1, [U113](x0, x1, x2) = x1 + 1, [U112](x0, x1, x2) = x1 + 1, [U111](x0, x1, x2) = x1 + x2 + 1, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = x0 + 1, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = x1 + x2 + 1, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = x0 + 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = x2, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = x2, [a__U43](x0, x1, x2) = x2 + 1, [a__U42](x0, x1, x2) = x2 + 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = x1 + 1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U135](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U134](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U133](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U132](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U131](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = x1 + 1, [a__U13](x0) = 0, [a__isNatList](x0) = x0, [s](x0) = x0, [a__length](x0) = x0 + 1, [mark](x0) = x0, [a__U114](x0, x1) = x1 + 1, [a__U113](x0, x1, x2) = x1 + 1, [a__U112](x0, x1, x2) = x1 + 1, [a__U111](x0, x1, x2) = x1 + x2 + 1, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = x0 + 1, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x1 + x2 + 1, [tt] = 0, [cons](x0, x1) = x0 + x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNat#(length(V1)) = V1 + 1 >= V1 = a__U11#(a__isNatIListKind(V1),V1) a__U11#(tt(),V1) = V1 >= V1 = a__U12#(a__isNatIListKind(V1),V1) a__U12#(tt(),V1) = V1 >= V1 = a__isNatList#(V1) a__isNatList#(cons(V1,V2)) = V1 + V2 >= V1 + V2 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U94#(a__isNatIListKind(V2),V1,V2) a__U94#(tt(),V1,V2) = V1 + V2 >= V1 = a__isNat#(V1) a__isNat#(s(V1)) = V1 >= V1 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = V1 >= V1 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = V1 >= V1 = a__isNat#(V1) a__U94#(tt(),V1,V2) = V1 + V2 >= V2 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = V2 >= V2 = a__isNatList#(V2) a__isNatList#(take(V1,V2)) = V1 + V2 + 1 >= V1 + V2 = a__U101#(a__isNatKind(V1),V1,V2) a__U101#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U102#(a__isNatKind(V1),V1,V2) a__U102#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) = V1 + V2 >= V1 = a__isNat#(V1) a__U104#(tt(),V1,V2) = V1 + V2 >= V2 = a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) = V2 >= V2 = a__isNatIList#(V2) a__isNatIList#(V) = V >= V = a__U31#(a__isNatIListKind(V),V) a__U31#(tt(),V) = V >= V = a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) = V >= V = a__isNatList#(V) a__isNatIList#(cons(V1,V2)) = V1 + V2 >= V1 + V2 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = V1 + V2 >= V1 = a__isNat#(V1) a__U44#(tt(),V1,V2) = V1 + V2 >= V2 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = V2 >= V2 = a__isNatIList#(V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = V1 + V2 + 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = L + N + 1 >= L + 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = L + 1 >= L + 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = L + 1 >= L + 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = L + 1 >= L + 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = IL + 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V + 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= V2 + 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = V2 + 1 >= V2 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = V2 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = V2 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V + 1 >= V + 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = V1 + V2 >= V2 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 2 >= 0 = 0() a__length(cons(N,L)) = L + N + 1 >= L + N + 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= IL + 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL + M + N + 1 >= IL + M + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = X + 1 >= X + 1 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = X2 + 1 >= X2 + 1 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U121(X1,X2)) = X2 + 1 >= X2 + 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = X2 + 1 >= X2 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X3 >= X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X3 >= X3 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = X + 1 >= X + 1 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X2 + 1 >= X2 + 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X2 + 1 >= X2 + 1 = U113(X1,X2,X3) a__U114(X1,X2) = X2 + 1 >= X2 + 1 = U114(X1,X2) a__length(X) = X + 1 >= X + 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = X >= X = isNatList(X) a__U121(X1,X2) = X2 + 1 >= X2 + 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = X2 + 1 >= X2 + 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X3 + 1 >= X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X3 + 1 >= X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X3 >= X3 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = X3 >= X3 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__U12#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__U94#(tt(),V1,V2) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U101#(tt(),V1,V2) -> a__U102#(a__isNatKind(V1),V1,V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) -> a__isNat#(V1) a__U104#(tt(),V1,V2) -> a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__U31#(tt(),V) -> a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) -> a__isNatList#(V) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isNat#(V1) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U45#](x0, x1) = 0, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = 0, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U32#](x0, x1) = 0, [a__U31#](x0, x1) = 0, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__U12#](x0, x1) = x1 + 1, [a__U11#](x0, x1) = x1 + 1, [a__isNatIList#](x0) = 0, [a__U105#](x0, x1) = 0, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = x1, [a__U103#](x0, x1, x2) = x1, [a__U102#](x0, x1, x2) = x1, [a__U101#](x0, x1, x2) = x1 + 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U11#(tt(),V1) = V1 + 1 >= V1 + 1 = a__U12#(a__isNatIListKind(V1),V1) a__U12#(tt(),V1) = V1 + 1 >= 0 = a__isNatList#(V1) a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__U94#(tt(),V1,V2) = 0 >= 0 = a__isNat#(V1) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U101#(tt(),V1,V2) = V1 + 1 >= V1 = a__U102#(a__isNatKind(V1),V1,V2) a__U102#(tt(),V1,V2) = V1 >= V1 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = V1 >= V1 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) = V1 >= 0 = a__isNat#(V1) a__U104#(tt(),V1,V2) = V1 >= 0 = a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) = 0 >= 0 = a__isNatIList#(V2) a__isNatIList#(V) = 0 >= 0 = a__U31#(a__isNatIListKind(V),V) a__U31#(tt(),V) = 0 >= 0 = a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) = 0 >= 0 = a__isNatList#(V) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) = 0 >= 0 = a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = 0 >= 0 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = 0 >= 0 = a__isNat#(V1) a__U44#(tt(),V1,V2) = 0 >= 0 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = 0 >= 0 = a__isNatIList#(V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__U94#(tt(),V1,V2) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) -> a__isNat#(V1) a__U104#(tt(),V1,V2) -> a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__U31#(tt(),V) -> a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) -> a__isNatList#(V) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__isNat#(V1) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 1, [a__U94#](x0, x1, x2) = 1, [a__U93#](x0, x1, x2) = 1, [a__U92#](x0, x1, x2) = 1, [a__U91#](x0, x1, x2) = 1, [a__U45#](x0, x1) = 1, [a__U44#](x0, x1, x2) = 1, [a__U43#](x0, x1, x2) = 1, [a__U42#](x0, x1, x2) = 1, [a__U41#](x0, x1, x2) = 1, [a__U32#](x0, x1) = 1, [a__U31#](x0, x1) = 1, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 1, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = x1, [a__isNatIList#](x0) = 1, [a__U105#](x0, x1) = 1, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = x2 + 1, [a__U103#](x0, x1, x2) = x2 + 1, [a__U102#](x0, x1, x2) = x2 + 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U11#(tt(),V1) = V1 >= 0 = a__U12#(a__isNatIListKind(V1),V1) a__isNatList#(cons(V1,V2)) = 1 >= 1 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 1 >= 1 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 1 >= 1 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 1 >= 1 = a__U94#(a__isNatIListKind(V2),V1,V2) a__U94#(tt(),V1,V2) = 1 >= 0 = a__isNat#(V1) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 1 >= 1 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 1 >= 1 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) = V2 + 1 >= 0 = a__isNat#(V1) a__U104#(tt(),V1,V2) = V2 + 1 >= 1 = a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) = 1 >= 1 = a__isNatIList#(V2) a__isNatIList#(V) = 1 >= 1 = a__U31#(a__isNatIListKind(V),V) a__U31#(tt(),V) = 1 >= 1 = a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) = 1 >= 1 = a__isNatList#(V) a__isNatIList#(cons(V1,V2)) = 1 >= 1 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 1 >= 1 = a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) = 1 >= 1 = a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = 1 >= 1 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = 1 >= 0 = a__isNat#(V1) a__U44#(tt(),V1,V2) = 1 >= 1 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = 1 >= 1 = a__isNatIList#(V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) -> a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__U31#(tt(),V) -> a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) -> a__isNatList#(V) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U45#](x0, x1) = 1, [a__U44#](x0, x1, x2) = 1, [a__U43#](x0, x1, x2) = 1, [a__U42#](x0, x1, x2) = 1, [a__U41#](x0, x1, x2) = 1, [a__U32#](x0, x1) = 0, [a__U31#](x0, x1) = 0, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = 0, [a__isNatIList#](x0) = 1, [a__U105#](x0, x1) = 1, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = 1, [a__U103#](x0, x1, x2) = 1, [a__U102#](x0, x1, x2) = 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U11#(tt(),V1) = 0 >= 0 = a__U12#(a__isNatIListKind(V1),V1) a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = 1 >= 1 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = 1 >= 1 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) = 1 >= 1 = a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) = 1 >= 1 = a__isNatIList#(V2) a__isNatIList#(V) = 1 >= 0 = a__U31#(a__isNatIListKind(V),V) a__U31#(tt(),V) = 0 >= 0 = a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) = 0 >= 0 = a__isNatList#(V) a__isNatIList#(cons(V1,V2)) = 1 >= 1 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 1 >= 1 = a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) = 1 >= 1 = a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = 1 >= 1 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = 1 >= 1 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = 1 >= 1 = a__isNatIList#(V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) -> a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__U31#(tt(),V) -> a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) -> a__isNatList#(V) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U45#](x0, x1) = 0, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = 0, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U32#](x0, x1) = 1, [a__U31#](x0, x1) = 1, [a__U22#](x0, x1) = 1, [a__U21#](x0, x1) = 1, [a__isNatList#](x0) = 0, [a__U12#](x0, x1) = 0, [a__U11#](x0, x1) = 1, [a__isNatIList#](x0) = 0, [a__U105#](x0, x1) = 0, [a__isNat#](x0) = 1, [a__U104#](x0, x1, x2) = 1, [a__U103#](x0, x1, x2) = 1, [a__U102#](x0, x1, x2) = 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U11#(tt(),V1) = 1 >= 0 = a__U12#(a__isNatIListKind(V1),V1) a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 1 >= 1 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 1 >= 1 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 1 >= 1 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = 1 >= 1 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = 1 >= 1 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U104#(tt(),V1,V2) = 1 >= 0 = a__U105#(a__isNat(V1),V2) a__U105#(tt(),V2) = 0 >= 0 = a__isNatIList#(V2) a__U31#(tt(),V) = 1 >= 1 = a__U32#(a__isNatIListKind(V),V) a__U32#(tt(),V) = 1 >= 0 = a__isNatList#(V) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) = 0 >= 0 = a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = 0 >= 0 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = 0 >= 0 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = 0 >= 0 = a__isNatIList#(V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__U31#(tt(),V) -> a__U32#(a__isNatIListKind(V),V) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 1, [a__U94#](x0, x1, x2) = 1, [a__U93#](x0, x1, x2) = 1, [a__U92#](x0, x1, x2) = 1, [a__U91#](x0, x1, x2) = 1, [a__U45#](x0, x1) = 0, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = 0, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U32#](x0, x1) = 0, [a__U31#](x0, x1) = 1, [a__U22#](x0, x1) = 1, [a__U21#](x0, x1) = 1, [a__isNatList#](x0) = 1, [a__isNatIList#](x0) = 0, [a__U105#](x0, x1) = x1, [a__isNat#](x0) = 1, [a__U104#](x0, x1, x2) = x2, [a__U103#](x0, x1, x2) = x2, [a__U102#](x0, x1, x2) = x2, [U96](x0) = 0, [U95](x0, x1) = x0 + x1, [U94](x0, x1, x2) = x0 + x2 + 1, [U93](x0, x1, x2) = x2 + 1, [U92](x0, x1, x2) = x0 + x2 + 1, [U91](x0, x1, x2) = x2, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = 0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = x0 + 1, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = x1, [U135](x0, x1, x2, x3) = x1, [U134](x0, x1, x2, x3) = x1, [U133](x0, x1, x2, x3) = x1, [U132](x0, x1, x2, x3) = x1, [U131](x0, x1, x2, x3) = x1, [U122](x0) = x0, [U121](x0, x1) = 0, [isNatList](x0) = x0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = x0, [isNatIList](x0) = 1, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0 + 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x2, [U101](x0, x1, x2) = x2, [a__take](x0, x1) = x1, [length](x0) = x0, [a__U96](x0) = 0, [a__U95](x0, x1) = x0 + x1, [a__U94](x0, x1, x2) = x0 + x2 + 1, [a__U93](x0, x1, x2) = x2 + 1, [a__U92](x0, x1, x2) = x0 + x2 + 1, [a__U91](x0, x1, x2) = x2 + 1, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = 0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = x0 + 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = x0, [take](x0, x1) = x1, [a__U136](x0, x1, x2, x3) = x1, [a__U135](x0, x1, x2, x3) = x1, [a__U134](x0, x1, x2, x3) = x1, [a__U133](x0, x1, x2, x3) = x1, [a__U132](x0, x1, x2, x3) = x1, [a__U131](x0, x1, x2, x3) = x1, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = x0 + 1, [s](x0) = 0, [a__length](x0) = x0, [mark](x0) = x0 + 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = x0, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = x0 + 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x2 + 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x2 + 1, [tt] = 0, [cons](x0, x1) = x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNatList#(cons(V1,V2)) = 1 >= 1 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 1 >= 1 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 1 >= 1 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 1 >= 1 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 1 >= 1 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 1 >= 1 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 1 >= 1 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 1 >= 1 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 1 >= 1 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = V2 >= V2 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = V2 >= V2 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U105#(tt(),V2) = V2 >= 0 = a__isNatIList#(V2) a__U31#(tt(),V) = 1 >= 0 = a__U32#(a__isNatIListKind(V),V) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) = 0 >= 0 = a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = 0 >= 0 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = 0 >= 0 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = 0 >= 0 = a__isNatIList#(V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = V2 + 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = IL >= IL = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL >= IL = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL >= IL = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL >= IL = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL >= IL = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL >= IL = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = V2 + 1 >= V2 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = V2 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = V2 + 1 >= V2 + 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = L >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL >= IL = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 + 2 >= X1 + 2 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 2 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = X1 + 1 >= X1 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = X + 1 >= X + 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = X + 1 >= X + 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X2 + 1 >= X2 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X2 + 1 >= X2 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X2 + 1 >= X2 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X2 + 1 >= X2 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X2 + 1 >= X2 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X2 + 1 >= X2 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X2 + 1 >= X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 + 1 >= X1 + 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + 2 >= X1 + 2 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 2 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + 1 >= X1 + 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = X1 + 1 >= X1 + 1 = a__U51(mark(X1),X2) mark(U52(X)) = X + 1 >= X + 1 = a__U52(mark(X)) mark(U61(X1,X2)) = X1 + 1 >= X1 + 1 = a__U61(mark(X1),X2) mark(U62(X)) = X + 1 >= X + 1 = a__U62(mark(X)) mark(U71(X)) = X + 1 >= X + 1 = a__U71(mark(X)) mark(U81(X)) = X + 1 >= X + 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 + X3 + 2 >= X1 + X3 + 2 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X3 + 2 >= X3 + 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 + X3 + 2 >= X1 + X3 + 2 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 + 1 >= X2 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 0 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = X3 + 1 >= X3 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X3 + 1 >= X3 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 + 1 >= X1 + 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = X >= X = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = X + 1 >= X = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = X2 >= X2 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X2 >= X2 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X2 >= X2 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X2 >= X2 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X2 >= X2 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X2 >= X2 = U136(X1,X2,X3,X4) a__take(X1,X2) = X2 >= X2 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 1 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + 1 >= X1 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X3 + 1 >= X3 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 + X3 + 1 >= X1 + X3 + 1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X3 + 1 >= X3 + 1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 + X3 + 1 >= X1 + X3 + 1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 + X2 >= X1 + X2 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U105#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U45#](x0, x1) = 0, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = 0, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__isNatIList#](x0) = 0, [a__U105#](x0, x1) = 1, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = 0, [a__U103#](x0, x1, x2) = 0, [a__U102#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = 1, [U135](x0, x1, x2, x3) = 1, [U134](x0, x1, x2, x3) = 1, [U133](x0, x1, x2, x3) = 1, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 1, [U122](x0) = 1, [U121](x0, x1) = 1, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = 1, [length](x0) = 1, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = 1, [a__length](x0) = 1, [mark](x0) = 1, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 1, [0] = 1, [a__zeros] = 1 orientation: a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = 0 >= 0 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = 0 >= 0 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U105#(tt(),V2) = 1 >= 0 = a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) = 0 >= 0 = a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = 0 >= 0 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = 0 >= 0 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = 0 >= 0 = a__isNatIList#(V2) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 1 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 1 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 1 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 1 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 1 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 1 = a__U62(mark(X)) mark(U71(X)) = 1 >= 1 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 1 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 1 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 1 = cons(mark(X1),X2) mark(0()) = 1 >= 1 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 1 = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) -> a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U45#](x0, x1) = x1, [a__U44#](x0, x1, x2) = x2, [a__U43#](x0, x1, x2) = x2, [a__U42#](x0, x1, x2) = x2 + 1, [a__U41#](x0, x1, x2) = x2 + 1, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__isNatIList#](x0) = x0, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = x2 + 1, [a__U103#](x0, x1, x2) = x2 + 1, [a__U102#](x0, x1, x2) = x2 + 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = 0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = 0, [U52](x0) = x0, [U51](x0, x1) = 0, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = x0, [U32](x0, x1) = 0, [U31](x0, x1) = x0 + 1, [U23](x0) = 0, [U22](x0, x1) = x0, [U21](x0, x1) = x0 + 1, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = x0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = x0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 1, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 1, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = 1, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = 0, [a__U52](x0) = x0, [a__U51](x0, x1) = 0, [a__U46](x0) = x0, [a__U45](x0, x1) = 1, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = x0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = x0 + 1, [a__U23](x0) = 0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0 + 1, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = 0, [a__U13](x0) = x0, [a__isNatList](x0) = 1, [s](x0) = 1, [a__length](x0) = 1, [mark](x0) = x0 + 1, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = 1, [a__U11](x0, x1) = 1, [a__U106](x0) = x0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 1, [a__isNat](x0) = x0 + 1, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 1, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = x1 + 1, [zeros] = 0, [0] = 1, [a__zeros] = 1 orientation: a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U104#(a__isNatIListKind(V2),V1,V2) a__isNatIList#(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U42#(a__isNatKind(V1),V1,V2) a__U42#(tt(),V1,V2) = V2 + 1 >= V2 = a__U43#(a__isNatIListKind(V2),V1,V2) a__U43#(tt(),V1,V2) = V2 >= V2 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = V2 >= V2 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = V2 >= V2 = a__isNatIList#(V2) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 1 >= 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 1 >= 1 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 1 >= 1 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 1 >= 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 2 >= 0 = tt() a__isNat(length(V1)) = 1 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 2 >= 2 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 1 >= 0 = tt() a__isNatKind(length(V1)) = 1 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 1 >= 1 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 1 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 2 >= 1 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = X + 1 >= X + 1 = a__isNat(X) mark(U106(X)) = X + 1 >= X + 1 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = X + 1 >= X + 1 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = X + 1 >= X + 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 + 2 >= X1 + 2 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 + 1 >= X1 + 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = X1 + 2 >= X1 + 2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = X + 1 >= X + 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = X + 1 >= X + 1 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = X + 1 >= X + 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = X + 1 >= X + 1 = a__U62(mark(X)) mark(U71(X)) = X + 1 >= X + 1 = a__U71(mark(X)) mark(U81(X)) = X + 1 >= X + 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 + 2 >= X2 + 1 = cons(mark(X1),X2) mark(0()) = 2 >= 1 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 2 >= 1 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 1 >= 0 = zeros() a__U101(X1,X2,X3) = 1 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 1 >= 1 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 1 >= 0 = U105(X1,X2) a__isNat(X) = X + 1 >= X = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 1 >= 0 = isNatIList(X) a__U11(X1,X2) = 1 >= 0 = U11(X1,X2) a__U12(X1,X2) = 1 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 0 = U114(X1,X2) a__length(X) = 1 >= 0 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 1 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 0 = take(X1,X2) a__U21(X1,X2) = X1 + 1 >= X1 + 1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = X1 + 1 >= X1 + 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 0 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = 1 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 1 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 1 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) -> a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = x1 + 1, [a__U94#](x0, x1, x2) = x2 + 1, [a__U93#](x0, x1, x2) = x2 + 1, [a__U92#](x0, x1, x2) = x2 + 1, [a__U91#](x0, x1, x2) = x2 + 1, [a__U45#](x0, x1) = 0, [a__U44#](x0, x1, x2) = 1, [a__U43#](x0, x1, x2) = 1, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = x0 + 1, [a__isNatIList#](x0) = 0, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = 0, [a__U103#](x0, x1, x2) = 0, [a__U102#](x0, x1, x2) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = x0, [U22](x0, x1) = 1, [U21](x0, x1) = 1, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 1, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 1, [U106](x0) = 0, [isNat](x0) = 1, [U105](x0, x1) = x0, [U104](x0, x1, x2) = 1, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = 0, [length](x0) = 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U23](x0) = x0, [a__U22](x0, x1) = 1, [a__U21](x0, x1) = 1, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = 0, [a__length](x0) = 1, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = x0, [a__isNat](x0) = 1, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNatList#(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = V2 + 1 >= V2 + 1 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = 0 >= 0 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = 0 >= 0 = a__U104#(a__isNatIListKind(V2),V1,V2) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isNatKind(V1),V1,V2) a__U43#(tt(),V1,V2) = 1 >= 1 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U44#(tt(),V1,V2) = 1 >= 0 = a__U45#(a__isNat(V1),V2) a__U45#(tt(),V2) = 0 >= 0 = a__isNatIList#(V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 1 >= 1 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 1 >= 0 = tt() a__isNat(length(V1)) = 1 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 >= X1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 1 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 1 = a__U22(mark(X1),X2) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 >= X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 1 >= 1 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 1 >= 1 = U21(X1,X2) a__U22(X1,X2) = 1 >= 1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) a__U45#(tt(),V2) -> a__isNatIList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U45#](x0, x1) = 1, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = x2, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__isNatIList#](x0) = 0, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = 0, [a__U103#](x0, x1, x2) = 0, [a__U102#](x0, x1, x2) = x2, [U96](x0) = x0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = 0, [U51](x0, x1) = x0, [U46](x0) = 0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = x0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x0, [U135](x0, x1, x2, x3) = x0, [U134](x0, x1, x2, x3) = x0, [U133](x0, x1, x2, x3) = x0, [U132](x0, x1, x2, x3) = x0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = x0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 1, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = 0, [length](x0) = 1, [a__U96](x0) = x0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = 0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = x0, [a__U135](x0, x1, x2, x3) = x0, [a__U134](x0, x1, x2, x3) = x0, [a__U133](x0, x1, x2, x3) = x0, [a__U132](x0, x1, x2, x3) = x0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = 0, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = 1, [a__length](x0) = 1, [mark](x0) = 1, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 1, [0] = 1, [a__zeros] = 1 orientation: a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = V2 >= 0 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = 0 >= 0 = a__U104#(a__isNatIListKind(V2),V1,V2) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isNatKind(V1),V1,V2) a__U43#(tt(),V1,V2) = V2 >= 0 = a__U44#(a__isNatIListKind(V2),V1,V2) a__U45#(tt(),V2) = 1 >= 0 = a__isNatIList#(V2) a__zeros() = 1 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 1 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 1 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 1 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 1 = a__U62(mark(X)) mark(U71(X)) = 1 >= 1 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 1 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 0 = cons(mark(X1),X2) mark(0()) = 1 >= 1 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 1 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 0 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = X >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 >= X1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 >= X1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 >= X1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 >= X1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X1 >= X1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = X1 >= 0 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= 0 = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= 0 = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = x1 + 1, [a__U94#](x0, x1, x2) = x2 + 1, [a__U93#](x0, x1, x2) = x2 + 1, [a__U92#](x0, x1, x2) = x2 + 1, [a__U91#](x0, x1, x2) = x2 + 1, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = 0, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = 0, [a__U22#](x0, x1) = x1, [a__U21#](x0, x1) = x1, [a__isNatList#](x0) = x0 + 1, [a__isNatIList#](x0) = 1, [a__isNat#](x0) = x0, [a__U104#](x0, x1, x2) = 0, [a__U103#](x0, x1, x2) = 0, [a__U102#](x0, x1, x2) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U81](x0) = 0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = 1, [U52](x0) = 1, [U51](x0, x1) = 1, [U46](x0) = x0, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 1, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = x0, [U11](x0, x1) = 1, [isNatIList](x0) = 1, [U106](x0) = 0, [isNat](x0) = 1, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 1, [U103](x0, x1, x2) = x0, [isNatKind](x0) = x0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = 0, [length](x0) = 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = 1, [a__U91](x0, x1, x2) = 1, [a__U81](x0) = 0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = 1, [a__U52](x0) = 1, [a__U51](x0, x1) = 1, [a__U46](x0) = x0, [a__U45](x0, x1) = 1, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 1, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = x0, [a__length](x0) = 1, [mark](x0) = x0, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = 1, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 0, [a__isNat](x0) = 1, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 1, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = x0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = x1, [zeros] = 0, [0] = 1, [a__zeros] = 0 orientation: a__isNatList#(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = V1 >= V1 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = V1 >= V1 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = V1 >= V1 = a__isNat#(V1) a__U94#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = V2 + 1 >= V2 + 1 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = 0 >= 0 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = 0 >= 0 = a__U104#(a__isNatIListKind(V2),V1,V2) a__isNatIList#(cons(V1,V2)) = 1 >= 0 = a__U41#(a__isNatKind(V1),V1,V2) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isNatKind(V1),V1,V2) a__U43#(tt(),V1,V2) = 0 >= 0 = a__U44#(a__isNatIListKind(V2),V1,V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 1 >= 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 1 >= 1 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 1 >= 1 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 1 >= 0 = tt() a__U61(tt(),V2) = 1 >= 1 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 1 >= 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 1 >= 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 1 >= 0 = tt() a__isNat(length(V1)) = 1 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 1 >= 0 = tt() a__isNatIListKind(zeros()) = 1 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 1 >= 1 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 1 >= 1 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 1 >= 0 = tt() a__isNatKind(length(V1)) = 1 >= 1 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = V1 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 1 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = X >= X = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 >= X1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 1 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 1 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 >= X1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 1 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = X >= X = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 >= X1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 >= X2 = cons(mark(X1),X2) mark(0()) = 1 >= 1 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = X >= X = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 1 >= 1 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 1 >= 1 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 1 >= 1 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 1 >= 1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = 1 >= 1 = U51(X1,X2) a__U52(X) = 1 >= 1 = U52(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 1 >= 1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 1 >= 1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) a__U43#(tt(),V1,V2) -> a__U44#(a__isNatIListKind(V2),V1,V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U44#](x0, x1, x2) = 0, [a__U43#](x0, x1, x2) = 1, [a__U42#](x0, x1, x2) = x1, [a__U41#](x0, x1, x2) = x1 + x2, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = 0, [a__U103#](x0, x1, x2) = x1 + x2, [a__U102#](x0, x1, x2) = x1 + x2, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = x0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 1, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 1, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = 1, [length](x0) = 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 1, [a__U93](x0, x1, x2) = 1, [a__U92](x0, x1, x2) = 1, [a__U91](x0, x1, x2) = 1, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = x0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = 0, [a__length](x0) = 1, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = V1 + V2 >= 0 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U41#(tt(),V1,V2) = V1 + V2 >= V1 = a__U42#(a__isNatKind(V1),V1,V2) a__U43#(tt(),V1,V2) = 1 >= 0 = a__U44#(a__isNatIListKind(V2),V1,V2) a__zeros() = 1 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 1 >= 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 1 >= 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 1 >= 1 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 1 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X1 >= X1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X1 >= X1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 1 >= 1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 1 >= 1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 1 >= 1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 1 >= 1 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) a__U41#(tt(),V1,V2) -> a__U42#(a__isNatKind(V1),V1,V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U42#](x0, x1, x2) = 0, [a__U41#](x0, x1, x2) = x1 + 1, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = 0, [a__U103#](x0, x1, x2) = 0, [a__U102#](x0, x1, x2) = 0, [U96](x0) = x0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = x0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = x0, [U42](x0, x1, x2) = x0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = 1, [U135](x0, x1, x2, x3) = 1, [U134](x0, x1, x2, x3) = 1, [U133](x0, x1, x2, x3) = 1, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 1, [U122](x0) = 1, [U121](x0, x1) = 1, [isNatList](x0) = 0, [U13](x0) = x0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = 1, [length](x0) = 1, [a__U96](x0) = x0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = x0, [a__U42](x0, x1, x2) = x0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = 1, [a__length](x0) = 1, [mark](x0) = 1, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 1, [0] = 1, [a__zeros] = 1 orientation: a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = 0 >= 0 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = 0 >= 0 = a__U104#(a__isNatIListKind(V2),V1,V2) a__U41#(tt(),V1,V2) = V1 + 1 >= 0 = a__U42#(a__isNatKind(V1),V1,V2) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 1 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 1 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 1 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 1 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 1 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 1 = a__U62(mark(X)) mark(U71(X)) = 1 >= 1 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 1 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 1 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 1 = cons(mark(X1),X2) mark(0()) = 1 >= 1 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 1 = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = X1 >= X1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 >= X1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= X1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = X >= X = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U102#(tt(),V1,V2) -> a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 0, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = 0, [a__U103#](x0, x1, x2) = x2, [a__U102#](x0, x1, x2) = x1 + x2 + 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 1, [U122](x0) = 1, [U121](x0, x1) = 1, [isNatList](x0) = x0 + 1, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 1, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = 1, [U104](x0, x1, x2) = 1, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = x0 + 1, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 1, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x0 + 1, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = 0, [a__isNatList](x0) = x0 + 1, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = x0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 1, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 0 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 0 >= 0 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) a__U102#(tt(),V1,V2) = V1 + V2 + 1 >= V2 = a__U103#(a__isNatIListKind(V2),V1,V2) a__U103#(tt(),V1,V2) = V2 >= 0 = a__U104#(a__isNatIListKind(V2),V1,V2) a__zeros() = 1 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 1 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 2 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = V1 + 2 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = X + 1 >= X + 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + 1 >= X1 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 1 = U104(X1,X2,X3) a__U105(X1,X2) = 1 >= 1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = X + 1 >= X + 1 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + 1 >= X1 + 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 1 >= 1 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) a__U103#(tt(),V1,V2) -> a__U104#(a__isNatIListKind(V2),V1,V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = 1, [a__U94#](x0, x1, x2) = 1, [a__U93#](x0, x1, x2) = 1, [a__U92#](x0, x1, x2) = 1, [a__U91#](x0, x1, x2) = 1, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 1, [a__isNat#](x0) = 0, [a__U104#](x0, x1, x2) = 0, [a__U103#](x0, x1, x2) = x1 + x2 + 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = x0, [U61](x0, x1) = 1, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = x1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = x0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 1, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = x0, [a__U61](x0, x1) = 1, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = x1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = x0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 1, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNatList#(cons(V1,V2)) = 1 >= 1 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 1 >= 1 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 1 >= 1 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 1 >= 1 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = 1 >= 1 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = 1 >= 1 = a__isNatList#(V2) a__U103#(tt(),V1,V2) = V1 + V2 + 1 >= 0 = a__U104#(a__isNatIListKind(V2),V1,V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 1 >= 1 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V >= V = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 1 >= 0 = tt() a__isNatIListKind(zeros()) = 1 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 1 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 1 >= 1 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 1 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = X >= X = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = X2 >= X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = X >= X = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 1 >= 1 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = X >= X = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = X2 >= X2 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 1 >= 1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U94#(tt(),V1,V2) -> a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) -> a__isNatList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = x1, [a__U94#](x0, x1, x2) = x2 + 1, [a__U93#](x0, x1, x2) = x2 + 1, [a__U92#](x0, x1, x2) = x2 + 1, [a__U91#](x0, x1, x2) = x2 + 1, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = x0, [a__isNat#](x0) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = x0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = x0, [U61](x0, x1) = x0, [U52](x0) = x0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = x2, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = x0 + x1, [U23](x0) = 0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = x0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = x0, [isNatIList](x0) = x0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = x0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = x0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = x0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = 1, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = x0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = x2 + 1, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = x0 + x1, [a__U23](x0) = 0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = x0 + 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = x0, [a__U11](x0, x1) = x0, [a__U106](x0) = 0, [a__isNatIList](x0) = x0, [a__U105](x0, x1) = x0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = x0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = x1 + 1, [zeros] = 0, [0] = 0, [a__zeros] = 1 orientation: a__isNatList#(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = V2 + 1 >= V2 + 1 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U94#(tt(),V1,V2) = V2 + 1 >= V2 = a__U95#(a__isNat(V1),V2) a__U95#(tt(),V2) = V2 >= V2 = a__isNatList#(V2) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V2 + 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V >= V = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = X1 + 1 >= X1 + 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = X + 1 >= X = a__isNatIList(X) mark(U11(X1,X2)) = X1 + 1 >= X1 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + 1 >= X1 + 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 0 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = X + 1 >= X + 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 + 1 >= X1 + 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 + 1 >= X1 + 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 2 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 2 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 2 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = X + 1 >= X + 1 = a__U52(mark(X)) mark(U61(X1,X2)) = X1 + 1 >= X1 + 1 = a__U61(mark(X1),X2) mark(U62(X)) = X + 1 >= X + 1 = a__U62(mark(X)) mark(U71(X)) = 1 >= 0 = a__U71(mark(X)) mark(U81(X)) = 1 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 + 2 >= X2 + 1 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 0 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 1 >= 0 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= X1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = X1 >= X1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = X1 >= X1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = X >= X = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 0 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = X3 + 1 >= X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 >= X1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) -> a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U95#(tt(),V2) -> a__isNatList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = x1 + 1, [a__U94#](x0, x1, x2) = 0, [a__U93#](x0, x1, x2) = 1, [a__U92#](x0, x1, x2) = 1, [a__U91#](x0, x1, x2) = 1, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = x0 + 1, [a__isNat#](x0) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNatList#(cons(V1,V2)) = V1 + 1 >= 1 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 1 >= 1 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 1 >= 1 = a__U93#(a__isNatIListKind(V2),V1,V2) a__U93#(tt(),V1,V2) = 1 >= 0 = a__U94#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U95#(tt(),V2) = V2 + 1 >= V2 + 1 = a__isNatList#(V2) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = X >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatList#(cons(V1,V2)) -> a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U95#(tt(),V2) -> a__isNatList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = x1 + 1, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 0, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = x0 + 1, [a__isNat#](x0) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 1, [U135](x0, x1, x2, x3) = 1, [U134](x0, x1, x2, x3) = 1, [U133](x0, x1, x2, x3) = 1, [U132](x0, x1, x2, x3) = 1, [U131](x0, x1, x2, x3) = 1, [U122](x0) = 1, [U121](x0, x1) = 1, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 1, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = x0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 1, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__isNatList#(cons(V1,V2)) = 2 >= 0 = a__U91#(a__isNatKind(V1),V1,V2) a__U91#(tt(),V1,V2) = 0 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 0 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U95#(tt(),V2) = V2 + 1 >= V2 + 1 = a__isNatList#(V2) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) a__U95#(tt(),V2) -> a__isNatList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U95#](x0, x1) = x1 + 1, [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = x2, [a__U91#](x0, x1, x2) = x2, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__isNat#](x0) = 0, [U96](x0) = 0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = x0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = x0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = 1, [U33](x0) = 1, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = 1, [U135](x0, x1, x2, x3) = 1, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 1, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = x0, [isNatIList](x0) = 1, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = x0, [a__take](x0, x1) = 1, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = x0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = 0, [a__U62](x0) = x0, [a__U61](x0, x1) = x0, [a__U52](x0) = 0, [a__U51](x0, x1) = x0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = 1, [a__U33](x0) = 1, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U23](x0) = x0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = 1, [a__U133](x0, x1, x2, x3) = 1, [a__U132](x0, x1, x2, x3) = 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = x0, [a__U106](x0) = 0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = x0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = x0, [tt] = 0, [cons](x0, x1) = 1, [zeros] = 0, [0] = 0, [a__zeros] = 1 orientation: a__U91#(tt(),V1,V2) = V2 >= V2 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = V2 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U95#(tt(),V2) = V2 + 1 >= 0 = a__isNatList#(V2) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 1 >= 0 = tt() a__U41(tt(),V1,V2) = 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 0 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 1 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 1 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 1 = a__U62(mark(X)) mark(U71(X)) = 1 >= 0 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 1 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 1 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 0 = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 1 >= 0 = zeros() a__U101(X1,X2,X3) = X1 >= X1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = X1 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 1 >= 0 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 1 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 1 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 1 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 1 >= 0 = U31(X1,X2) a__U32(X1,X2) = 1 >= 0 = U32(X1,X2) a__U33(X) = 1 >= 1 = U33(X) a__U41(X1,X2,X3) = 1 >= 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = X1 >= 0 = U61(X1,X2) a__U62(X) = X >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = X1 >= X1 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) -> a__U93#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U93#](x0, x1, x2) = 0, [a__U92#](x0, x1, x2) = 1, [a__U91#](x0, x1, x2) = 1, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNat#](x0) = 0, [U96](x0) = 1, [U95](x0, x1) = 1, [U94](x0, x1, x2) = 1, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 1, [U91](x0, x1, x2) = 1, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x3 + 1, [U135](x0, x1, x2, x3) = x3 + 1, [U134](x0, x1, x2, x3) = x3 + 1, [U133](x0, x1, x2, x3) = x3 + 1, [U132](x0, x1, x2, x3) = x3 + 1, [U131](x0, x1, x2, x3) = x3 + 1, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = x2 + 1, [U111](x0, x1, x2) = x2 + 1, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 1, [isNat](x0) = 0, [U105](x0, x1) = 1, [U104](x0, x1, x2) = 1, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = x0 + x1, [length](x0) = x0 + 1, [a__U96](x0) = 1, [a__U95](x0, x1) = 1, [a__U94](x0, x1, x2) = 1, [a__U93](x0, x1, x2) = 1, [a__U92](x0, x1, x2) = 1, [a__U91](x0, x1, x2) = 1, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x0 + x1, [a__U136](x0, x1, x2, x3) = x3 + 1, [a__U135](x0, x1, x2, x3) = x3 + 1, [a__U134](x0, x1, x2, x3) = x3 + 1, [a__U133](x0, x1, x2, x3) = x3 + 1, [a__U132](x0, x1, x2, x3) = x3 + 1, [a__U131](x0, x1, x2, x3) = x3 + 1, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = 1, [a__length](x0) = x0 + 1, [mark](x0) = x0, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = x2 + 1, [a__U111](x0, x1, x2) = x2 + 1, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 1, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 1, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__U91#(tt(),V1,V2) = 1 >= 1 = a__U92#(a__isNatKind(V1),V1,V2) a__U92#(tt(),V1,V2) = 1 >= 0 = a__U93#(a__isNatIListKind(V2),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__zeros() = 1 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 1 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = N + 1 >= N + 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = N + 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = N + 1 >= N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = N + 1 >= N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = N + 1 >= N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = N + 1 >= N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = N + 1 >= N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = N + 1 >= N = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 1 >= 1 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 1 >= 1 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 1 >= 1 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 1 >= 1 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 1 >= 1 = a__U96(a__isNatList(V2)) a__U96(tt()) = 1 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = N + 1 >= N + 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = N + 1 >= N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 1 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X3 + 1 >= X3 + 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X4 + 1 >= X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X4 + 1 >= X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X4 + 1 >= X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X4 + 1 >= X4 + 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X4 + 1 >= X4 + 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X4 + 1 >= X4 + 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 >= X1 + X2 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 1 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 1 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 1 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 1 = a__U96(mark(X)) mark(cons(X1,X2)) = X1 >= X1 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 1 >= 1 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 1 = U104(X1,X2,X3) a__U105(X1,X2) = 1 >= 1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 1 >= 1 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = X3 + 1 >= X3 + 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X3 + 1 >= X3 + 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = X + 1 >= X + 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = X4 + 1 >= X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X4 + 1 >= X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X4 + 1 >= X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X4 + 1 >= X4 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X4 + 1 >= X4 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X4 + 1 >= X4 + 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 >= X1 + X2 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 1 >= 1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 1 >= 1 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 1 >= 1 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 1 >= 1 = U94(X1,X2,X3) a__U95(X1,X2) = 1 >= 1 = U95(X1,X2) a__U96(X) = 1 >= 1 = U96(X) problem: DPs: a__U91#(tt(),V1,V2) -> a__U92#(a__isNatKind(V1),V1,V2) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U92#](x0, x1, x2) = 0, [a__U91#](x0, x1, x2) = 1, [a__U22#](x0, x1) = 0, [a__U21#](x0, x1) = 0, [a__isNat#](x0) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = x1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 1, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = x0, [U13](x0) = 0, [U114](x0, x1) = 1, [U113](x0, x1, x2) = 1, [U112](x0, x1, x2) = 1, [U111](x0, x1, x2) = 1, [U12](x0, x1) = 1, [U11](x0, x1) = 1, [isNatIList](x0) = x0, [U106](x0) = 0, [isNat](x0) = x0 + 1, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = x0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = 1, [length](x0) = 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = x1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 1, [take](x0, x1) = 1, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = x0, [s](x0) = 0, [a__length](x0) = 1, [mark](x0) = x0, [a__U114](x0, x1) = 1, [a__U113](x0, x1, x2) = 1, [a__U112](x0, x1, x2) = 1, [a__U111](x0, x1, x2) = 1, [a__U12](x0, x1) = 1, [a__U11](x0, x1) = 1, [a__U106](x0) = 0, [a__isNatIList](x0) = x0, [a__U105](x0, x1) = 0, [a__isNat](x0) = x0 + 1, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = x0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__U91#(tt(),V1,V2) = 1 >= 0 = a__U92#(a__isNatKind(V1),V1,V2) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 1 >= 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 1 >= 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 1 >= 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 1 >= 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 1 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 1 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 1 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 1 >= 0 = tt() a__isNat(length(V1)) = 2 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V >= V = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 1 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = 1 >= 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = X >= X = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = X + 1 >= X + 1 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = X >= X = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 1 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 1 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = X2 >= X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = X + 1 >= X + 1 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = X >= X = isNatIList(X) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 1 = U12(X1,X2) a__U111(X1,X2,X3) = 1 >= 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 1 >= 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 1 >= 1 = U113(X1,X2,X3) a__U114(X1,X2) = 1 >= 1 = U114(X1,X2) a__length(X) = 1 >= 1 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = X >= X = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 1 = take(X1,X2) a__U21(X1,X2) = 1 >= 1 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = X2 >= X2 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) a__U22#(tt(),V1) -> a__isNat#(V1) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Open DPs: a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) -> a__isNatIListKind#(V2) a__isNatIListKind#(take(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(take(V1,V2)) -> a__U61#(a__isNatKind(V1),V2) a__U61#(tt(),V2) -> a__isNatIListKind#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U61#](x0, x1) = x1 + 1, [a__U51#](x0, x1) = x1, [a__isNatIListKind#](x0) = x0, [a__isNatKind#](x0) = x0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = x0, [U32](x0, x1) = 1, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U135](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U134](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U133](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U132](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U131](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [U122](x0) = 1, [U121](x0, x1) = 1, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = x1, [U113](x0, x1, x2) = x1, [U112](x0, x1, x2) = x1, [U111](x0, x1, x2) = x1, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 1, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = 1, [U104](x0, x1, x2) = 1, [isNatIListKind](x0) = x0, [U103](x0, x1, x2) = 1, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 1, [U101](x0, x1, x2) = 1, [a__take](x0, x1) = x0 + x1 + 1, [length](x0) = x0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x0 + x1 + 1, [a__U136](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U135](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U134](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U133](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U132](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [a__U131](x0, x1, x2, x3) = x1 + x2 + x3 + 1, [nil] = 1, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = x0, [a__length](x0) = x0, [mark](x0) = x0, [a__U114](x0, x1) = x1, [a__U113](x0, x1, x2) = x1, [a__U112](x0, x1, x2) = x1, [a__U111](x0, x1, x2) = x1, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = x0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 1, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = x0, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = x0 + x1, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__isNatIListKind#(cons(V1,V2)) = V1 + V2 >= V1 = a__isNatKind#(V1) a__isNatKind#(length(V1)) = V1 >= V1 = a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) = V1 + V2 >= V2 = a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) = V2 >= V2 = a__isNatIListKind#(V2) a__isNatIListKind#(take(V1,V2)) = V1 + V2 + 1 >= V1 = a__isNatKind#(V1) a__isNatKind#(s(V1)) = V1 >= V1 = a__isNatKind#(V1) a__isNatIListKind#(take(V1,V2)) = V1 + V2 + 1 >= V2 + 1 = a__U61#(a__isNatKind(V1),V2) a__U61#(tt(),V2) = V2 + 1 >= V2 = a__isNatIListKind#(V2) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = L >= L = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = L >= L = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = L >= L = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = L >= L = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 1 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 1 >= 0 = tt() a__isNatIListKind(zeros()) = 1 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = V1 + V2 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = V1 + V2 + 1 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = L + N >= L = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL + M + N + 1 >= IL + M + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = X >= X = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = X >= X = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X2 >= X2 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X2 >= X2 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X2 >= X2 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = X2 >= X2 = a__U114(mark(X1),X2) mark(length(X)) = X >= X = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = X >= X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = 1 >= 1 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 1 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 1 = U103(X1,X2,X3) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 1 = U104(X1,X2,X3) a__U105(X1,X2) = 1 >= 1 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 1 >= 1 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = X2 >= X2 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X2 >= X2 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X2 >= X2 = U113(X1,X2,X3) a__U114(X1,X2) = X2 >= X2 = U114(X1,X2) a__length(X) = X >= X = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X2 + X3 + X4 + 1 >= X2 + X3 + X4 + 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 1 >= 1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) -> a__isNatIListKind#(V2) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(take(V1,V2)) -> a__U61#(a__isNatKind(V1),V2) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U61#](x0, x1) = 0, [a__U51#](x0, x1) = 1, [a__isNatIListKind#](x0) = 1, [a__isNatKind#](x0) = 1, [U96](x0) = 0, [U95](x0, x1) = x0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = x0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = 0, [U61](x0, x1) = x0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = x0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = x0, [U33](x0) = x0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = x0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = x0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = x0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 1, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = x0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 1, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = x0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = x0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = x0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = 0, [a__U61](x0, x1) = x0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = x0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = x0, [a__U32](x0, x1) = 1, [a__U31](x0, x1) = 1, [a__U23](x0) = x0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = x0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = x0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 1, [s](x0) = x0, [a__length](x0) = 0, [mark](x0) = 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = x0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = x0, [a__isNatIList](x0) = 1, [a__U105](x0, x1) = 1, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 1, [a__U103](x0, x1, x2) = 1, [a__isNatIListKind](x0) = 1, [a__U102](x0, x1, x2) = 1, [a__isNatKind](x0) = 1, [a__U101](x0, x1, x2) = 1, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 1, [0] = 0, [a__zeros] = 1 orientation: a__isNatIListKind#(cons(V1,V2)) = 1 >= 1 = a__isNatKind#(V1) a__isNatKind#(length(V1)) = 1 >= 1 = a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) = 1 >= 1 = a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) = 1 >= 1 = a__isNatIListKind#(V2) a__isNatKind#(s(V1)) = 1 >= 1 = a__isNatKind#(V1) a__isNatIListKind#(take(V1,V2)) = 1 >= 0 = a__U61#(a__isNatKind(V1),V2) a__zeros() = 1 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 1 >= 1 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 1 >= 1 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 1 >= 1 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 1 >= 1 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 1 >= 1 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 1 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 1 >= 1 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 1 >= 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 1 >= 0 = tt() a__isNatIListKind(zeros()) = 1 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 1 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 1 >= 1 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 1 >= 0 = tt() a__isNatKind(length(V1)) = 1 >= 1 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 1 >= 1 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 1 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 1 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = M >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 1 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 1 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 1 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 1 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 1 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 1 >= 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 1 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = 1 >= 1 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 1 >= 0 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 1 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 1 >= 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 1 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 1 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 1 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 1 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 1 >= 1 = a__U32(mark(X1),X2) mark(U33(X)) = 1 >= 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 1 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 1 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 1 = a__U61(mark(X1),X2) mark(U62(X)) = 1 >= 0 = a__U62(mark(X)) mark(U71(X)) = 1 >= 1 = a__U71(mark(X)) mark(U81(X)) = 1 >= 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 1 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 1 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 1 >= 0 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 1 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 1 >= 1 = zeros() a__U101(X1,X2,X3) = 1 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 1 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 1 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 1 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 1 >= 1 = isNatIListKind(X) a__U104(X1,X2,X3) = 1 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 1 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 1 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X1 >= X1 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 >= X1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X1 >= X1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = X1 >= X1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = X >= X = U23(X) a__U31(X1,X2) = 1 >= 0 = U31(X1,X2) a__U32(X1,X2) = 1 >= 0 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 >= X1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = X1 >= X1 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = X1 >= X1 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = X1 >= X1 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = X1 >= X1 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) -> a__isNatIListKind#(V2) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U51#](x0, x1) = x1, [a__isNatIListKind#](x0) = x0, [a__isNatKind#](x0) = x0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 1, [U45](x0, x1) = 1, [U44](x0, x1, x2) = 1, [U43](x0, x1, x2) = 1, [U42](x0, x1, x2) = 1, [U41](x0, x1, x2) = x1 + x2 + 1, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 1, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = x1 + x3 + 1, [U135](x0, x1, x2, x3) = x1 + x3 + 1, [U134](x0, x1, x2, x3) = x1 + x3 + 1, [U133](x0, x1, x2, x3) = x1 + x3 + 1, [U132](x0, x1, x2, x3) = x1 + x3 + 1, [U131](x0, x1, x2, x3) = x1 + x3 + 1, [U122](x0) = 1, [U121](x0, x1) = 1, [isNatList](x0) = 1, [U13](x0) = 1, [U114](x0, x1) = x1 + 1, [U113](x0, x1, x2) = x1 + 1, [U112](x0, x1, x2) = x1 + 1, [U111](x0, x1, x2) = x1 + 1, [U12](x0, x1) = 1, [U11](x0, x1) = 1, [isNatIList](x0) = x0 + 1, [U106](x0) = 0, [isNat](x0) = x0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = x1 + 1, [length](x0) = x0 + 1, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 1, [a__U45](x0, x1) = 1, [a__U44](x0, x1, x2) = 1, [a__U43](x0, x1, x2) = 1, [a__U42](x0, x1, x2) = 1, [a__U41](x0, x1, x2) = x1 + x2 + 1, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 1, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = x1 + 1, [a__U136](x0, x1, x2, x3) = x1 + x3 + 1, [a__U135](x0, x1, x2, x3) = x1 + x3 + 1, [a__U134](x0, x1, x2, x3) = x1 + x3 + 1, [a__U133](x0, x1, x2, x3) = x1 + x3 + 1, [a__U132](x0, x1, x2, x3) = x1 + x3 + 1, [a__U131](x0, x1, x2, x3) = x1 + x3 + 1, [nil] = 0, [a__U122](x0) = 1, [a__U121](x0, x1) = 1, [a__U13](x0) = 1, [a__isNatList](x0) = 1, [s](x0) = x0, [a__length](x0) = x0 + 1, [mark](x0) = x0, [a__U114](x0, x1) = x1 + 1, [a__U113](x0, x1, x2) = x1 + 1, [a__U112](x0, x1, x2) = x1 + 1, [a__U111](x0, x1, x2) = x1 + 1, [a__U12](x0, x1) = 1, [a__U11](x0, x1) = 1, [a__U106](x0) = 0, [a__isNatIList](x0) = x0 + 1, [a__U105](x0, x1) = 0, [a__isNat](x0) = x0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = x0 + x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNatIListKind#(cons(V1,V2)) = V1 + V2 >= V1 = a__isNatKind#(V1) a__isNatKind#(length(V1)) = V1 + 1 >= V1 = a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) = V1 + V2 >= V2 = a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) = V2 >= V2 = a__isNatIListKind#(V2) a__isNatKind#(s(V1)) = V1 >= V1 = a__isNatKind#(V1) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 1 >= 1 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = L + 1 >= L + 1 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = L + 1 >= L + 1 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = L + 1 >= L + 1 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = L + 1 >= L + 1 = s(a__length(mark(L))) a__U12(tt(),V1) = 1 >= 1 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 1 >= 1 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 1 >= 0 = nil() a__U13(tt()) = 1 >= 0 = tt() a__U131(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = IL + N + 1 >= IL + N + 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 1 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + V2 + 1 >= 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 1 >= 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 1 >= 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 1 >= 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 1 >= 1 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 1 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = V1 + 1 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = V1 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = V + 1 >= 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = V1 + V2 + 1 >= V1 + V2 + 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 1 >= 0 = tt() a__isNatList(cons(V1,V2)) = 1 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 1 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 1 >= 0 = 0() a__length(cons(N,L)) = L + N + 1 >= L + 1 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = IL + 1 >= 1 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = IL + N + 1 >= IL + N + 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = X >= X = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = X + 1 >= X + 1 = a__isNatIList(X) mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 1 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = X2 + 1 >= X2 + 1 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = X2 + 1 >= X2 + 1 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 1 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 1 = a__isNatList(X) mark(U121(X1,X2)) = 1 >= 1 = a__U121(mark(X1),X2) mark(U122(X)) = 1 >= 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = X2 + X4 + 1 >= X2 + X4 + 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = X2 + 1 >= X2 + 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = X2 + X3 + 1 >= X2 + X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 1 >= 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 1 = a__U45(mark(X1),X2) mark(U46(X)) = 1 >= 1 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = X >= X = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = X + 1 >= X + 1 = isNatIList(X) a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X1,X2) = 1 >= 1 = U12(X1,X2) a__U111(X1,X2,X3) = X2 + 1 >= X2 + 1 = U111(X1,X2,X3) a__U112(X1,X2,X3) = X2 + 1 >= X2 + 1 = U112(X1,X2,X3) a__U113(X1,X2,X3) = X2 + 1 >= X2 + 1 = U113(X1,X2,X3) a__U114(X1,X2) = X2 + 1 >= X2 + 1 = U114(X1,X2) a__length(X) = X + 1 >= X + 1 = length(X) a__U13(X) = 1 >= 1 = U13(X) a__isNatList(X) = 1 >= 1 = isNatList(X) a__U121(X1,X2) = 1 >= 1 = U121(X1,X2) a__U122(X) = 1 >= 1 = U122(X) a__U131(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = X2 + X4 + 1 >= X2 + X4 + 1 = U136(X1,X2,X3,X4) a__take(X1,X2) = X2 + 1 >= X2 + 1 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 1 >= 1 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = X2 + X3 + 1 >= X2 + X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 1 >= 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 1 >= 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 1 >= 1 = U44(X1,X2,X3) a__U45(X1,X2) = 1 >= 1 = U45(X1,X2) a__U46(X) = 1 >= 1 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) -> a__isNatIListKind#(V2) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U51#](x0, x1) = 1, [a__isNatIListKind#](x0) = 1, [a__isNatKind#](x0) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = x0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNatIListKind#(cons(V1,V2)) = 1 >= 0 = a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) = 1 >= 1 = a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) = 1 >= 1 = a__isNatIListKind#(V2) a__isNatKind#(s(V1)) = 0 >= 0 = a__isNatKind#(V1) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = X1 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatIListKind#(cons(V1,V2)) -> a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) -> a__isNatIListKind#(V2) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U51#](x0, x1) = x1 + 1, [a__isNatIListKind#](x0) = x0, [a__isNatKind#](x0) = 0, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = x0, [U71](x0) = x0, [U62](x0) = x0, [U61](x0, x1) = 0, [U52](x0) = x0, [U51](x0, x1) = x0, [U46](x0) = x0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = x0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = x0, [U32](x0, x1) = x0, [U31](x0, x1) = x0, [U23](x0) = 0, [U22](x0, x1) = x0, [U21](x0, x1) = x0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = x0 + 1, [U133](x0, x1, x2, x3) = x0 + 1, [U132](x0, x1, x2, x3) = x0 + 1, [U131](x0, x1, x2, x3) = 0, [U122](x0) = x0, [U121](x0, x1) = x0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = x0, [isNatIList](x0) = 0, [U106](x0) = x0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = x0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 1, [length](x0) = x0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = x0, [a__U71](x0) = x0, [a__U62](x0) = x0, [a__U61](x0, x1) = 0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0, [a__U46](x0) = x0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = x0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = x0, [a__U32](x0, x1) = x0, [a__U31](x0, x1) = x0, [a__U23](x0) = 0, [a__U22](x0, x1) = x0, [a__U21](x0, x1) = x0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 1, [a__U135](x0, x1, x2, x3) = 1, [a__U134](x0, x1, x2, x3) = x0 + 1, [a__U133](x0, x1, x2, x3) = x0 + 1, [a__U132](x0, x1, x2, x3) = x0 + 1, [a__U131](x0, x1, x2, x3) = 1, [nil] = 0, [a__U122](x0) = x0, [a__U121](x0, x1) = x0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = x0, [mark](x0) = x0 + 1, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = x0, [a__U106](x0) = x0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = x0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = x1 + 1, [zeros] = 0, [0] = 0, [a__zeros] = 1 orientation: a__isNatIListKind#(cons(V1,V2)) = V2 + 1 >= V2 + 1 = a__U51#(a__isNatKind(V1),V2) a__U51#(tt(),V2) = V2 + 1 >= V2 = a__isNatIListKind#(V2) a__isNatKind#(s(V1)) = 0 >= 0 = a__isNatKind#(V1) a__zeros() = 1 >= 1 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 1 >= 1 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 1 >= 1 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 1 >= 1 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 1 >= 1 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 1 >= 1 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 1 >= 1 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = L + 1 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 1 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 1 >= 1 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 1 >= 1 = a__zeros() mark(U101(X1,X2,X3)) = 1 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 1 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 1 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 1 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 1 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 1 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 1 >= 0 = a__isNat(X) mark(U106(X)) = X + 1 >= X + 1 = a__U106(mark(X)) mark(isNatIList(X)) = 1 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = X1 + 1 >= X1 + 1 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 1 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 1 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 1 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 1 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 1 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = X + 1 >= X + 1 = a__length(mark(X)) mark(U13(X)) = 1 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = X1 + 1 >= X1 + 1 = a__U121(mark(X1),X2) mark(U122(X)) = X + 1 >= X + 1 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 1 >= 1 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = X1 + 2 >= X1 + 2 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = X1 + 2 >= X1 + 2 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = X1 + 2 >= X1 + 2 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 1 >= 1 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 1 >= 1 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 1 >= 1 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = X1 + 1 >= X1 + 1 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 + 1 >= X1 + 1 = a__U22(mark(X1),X2) mark(U23(X)) = 1 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = X1 + 1 >= X1 + 1 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = X1 + 1 >= X1 + 1 = a__U32(mark(X1),X2) mark(U33(X)) = X + 1 >= X + 1 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 1 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 1 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 1 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + 1 >= X1 + 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 1 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = X + 1 >= X + 1 = a__U46(mark(X)) mark(U51(X1,X2)) = X1 + 1 >= X1 + 1 = a__U51(mark(X1),X2) mark(U52(X)) = X + 1 >= X + 1 = a__U52(mark(X)) mark(U61(X1,X2)) = 1 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = X + 1 >= X + 1 = a__U62(mark(X)) mark(U71(X)) = X + 1 >= X + 1 = a__U71(mark(X)) mark(U81(X)) = X + 1 >= X + 1 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 1 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 1 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 1 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 1 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 1 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 1 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = X2 + 2 >= X2 + 1 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 0 = tt() mark(s(X)) = 1 >= 0 = s(mark(X)) mark(nil()) = 1 >= 0 = nil() a__zeros() = 1 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = X1 >= X1 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = X >= X = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = X1 >= X1 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = X >= X = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = X1 >= X1 = U121(X1,X2) a__U122(X) = X >= X = U122(X) a__U131(X1,X2,X3,X4) = 1 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = X1 + 1 >= X1 + 1 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = X1 + 1 >= X1 + 1 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = X1 + 1 >= X1 + 1 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 1 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 1 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 1 >= 0 = take(X1,X2) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = X1 >= X1 = U31(X1,X2) a__U32(X1,X2) = X1 >= X1 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 >= X1 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__U51(X1,X2) = X1 >= X1 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = X >= X = U62(X) a__U71(X) = X >= X = U71(X) a__U81(X) = X >= X = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatIListKind#(cons(V1,V2)) -> a__U51#(a__isNatKind(V1),V2) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Matrix Interpretation Processor: dimension: 1 interpretation: [a__U51#](x0, x1) = 0, [a__isNatIListKind#](x0) = 1, [a__isNatKind#](x0) = 1, [U96](x0) = 0, [U95](x0, x1) = 0, [U94](x0, x1, x2) = 0, [U93](x0, x1, x2) = 0, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U81](x0) = 0, [U71](x0) = 0, [U62](x0) = 0, [U61](x0, x1) = 0, [U52](x0) = 0, [U51](x0, x1) = 0, [U46](x0) = 0, [U45](x0, x1) = 0, [U44](x0, x1, x2) = 0, [U43](x0, x1, x2) = 0, [U42](x0, x1, x2) = 0, [U41](x0, x1, x2) = 0, [U33](x0) = 0, [U32](x0, x1) = 0, [U31](x0, x1) = 0, [U23](x0) = 0, [U22](x0, x1) = 0, [U21](x0, x1) = 0, [U136](x0, x1, x2, x3) = 0, [U135](x0, x1, x2, x3) = 0, [U134](x0, x1, x2, x3) = 0, [U133](x0, x1, x2, x3) = 0, [U132](x0, x1, x2, x3) = 0, [U131](x0, x1, x2, x3) = 0, [U122](x0) = 0, [U121](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [U114](x0, x1) = 0, [U113](x0, x1, x2) = 0, [U112](x0, x1, x2) = 0, [U111](x0, x1, x2) = 0, [U12](x0, x1) = 0, [U11](x0, x1) = 0, [isNatIList](x0) = 0, [U106](x0) = 0, [isNat](x0) = 0, [U105](x0, x1) = 0, [U104](x0, x1, x2) = 0, [isNatIListKind](x0) = 0, [U103](x0, x1, x2) = 0, [isNatKind](x0) = 0, [U102](x0, x1, x2) = 0, [U101](x0, x1, x2) = 0, [a__take](x0, x1) = 0, [length](x0) = 0, [a__U96](x0) = 0, [a__U95](x0, x1) = 0, [a__U94](x0, x1, x2) = 0, [a__U93](x0, x1, x2) = 0, [a__U92](x0, x1, x2) = 0, [a__U91](x0, x1, x2) = 0, [a__U81](x0) = 0, [a__U71](x0) = 0, [a__U62](x0) = 0, [a__U61](x0, x1) = 0, [a__U52](x0) = 0, [a__U51](x0, x1) = 0, [a__U46](x0) = 0, [a__U45](x0, x1) = 0, [a__U44](x0, x1, x2) = 0, [a__U43](x0, x1, x2) = 0, [a__U42](x0, x1, x2) = 0, [a__U41](x0, x1, x2) = 0, [a__U33](x0) = 0, [a__U32](x0, x1) = 0, [a__U31](x0, x1) = 0, [a__U23](x0) = 0, [a__U22](x0, x1) = 0, [a__U21](x0, x1) = 0, [take](x0, x1) = 0, [a__U136](x0, x1, x2, x3) = 0, [a__U135](x0, x1, x2, x3) = 0, [a__U134](x0, x1, x2, x3) = 0, [a__U133](x0, x1, x2, x3) = 0, [a__U132](x0, x1, x2, x3) = 0, [a__U131](x0, x1, x2, x3) = 0, [nil] = 0, [a__U122](x0) = 0, [a__U121](x0, x1) = 0, [a__U13](x0) = 0, [a__isNatList](x0) = 0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 0, [a__U114](x0, x1) = 0, [a__U113](x0, x1, x2) = 0, [a__U112](x0, x1, x2) = 0, [a__U111](x0, x1, x2) = 0, [a__U12](x0, x1) = 0, [a__U11](x0, x1) = 0, [a__U106](x0) = 0, [a__isNatIList](x0) = 0, [a__U105](x0, x1) = 0, [a__isNat](x0) = 0, [a__U104](x0, x1, x2) = 0, [a__U103](x0, x1, x2) = 0, [a__isNatIListKind](x0) = 0, [a__U102](x0, x1, x2) = 0, [a__isNatKind](x0) = 0, [a__U101](x0, x1, x2) = 0, [tt] = 0, [cons](x0, x1) = 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNatIListKind#(cons(V1,V2)) = 1 >= 0 = a__U51#(a__isNatKind(V1),V2) a__isNatKind#(s(V1)) = 1 >= 1 = a__isNatKind#(V1) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U101(tt(),V1,V2) = 0 >= 0 = a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) = 0 >= 0 = a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) = 0 >= 0 = a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) = 0 >= 0 = a__U105(a__isNat(V1),V2) a__U105(tt(),V2) = 0 >= 0 = a__U106(a__isNatIList(V2)) a__U106(tt()) = 0 >= 0 = tt() a__U11(tt(),V1) = 0 >= 0 = a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) = 0 >= 0 = a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) = 0 >= 0 = a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) = 0 >= 0 = a__U114(a__isNatKind(N),L) a__U114(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__U12(tt(),V1) = 0 >= 0 = a__U13(a__isNatList(V1)) a__U121(tt(),IL) = 0 >= 0 = a__U122(a__isNatIListKind(IL)) a__U122(tt()) = 0 >= 0 = nil() a__U13(tt()) = 0 >= 0 = tt() a__U131(tt(),IL,M,N) = 0 >= 0 = a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) = 0 >= 0 = a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) = 0 >= 0 = a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) = 0 >= 0 = a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) = 0 >= 0 = a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) = 0 >= 0 = cons(mark(N),take(M,IL)) a__U21(tt(),V1) = 0 >= 0 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 0 >= 0 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 0 >= 0 = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = 0 >= 0 = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 0 >= 0 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 0 >= 0 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 0 >= 0 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 0 >= 0 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 0 >= 0 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt(),V2) = 0 >= 0 = a__U62(a__isNatIListKind(V2)) a__U62(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__U91(tt(),V1,V2) = 0 >= 0 = a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) = 0 >= 0 = a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) = 0 >= 0 = a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) = 0 >= 0 = a__U95(a__isNat(V1),V2) a__U95(tt(),V2) = 0 >= 0 = a__U96(a__isNatList(V2)) a__U96(tt()) = 0 >= 0 = tt() a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 0 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 0 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 0 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 0 >= 0 = a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) = 0 >= 0 = a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 0 >= 0 = a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 0 >= 0 = a__U81(a__isNatKind(V1)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) = 0 >= 0 = a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) = 0 >= 0 = 0() a__length(cons(N,L)) = 0 >= 0 = a__U111(a__isNatList(L),L,N) a__take(0(),IL) = 0 >= 0 = a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) = 0 >= 0 = a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U101(X1,X2,X3)) = 0 >= 0 = a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) = 0 >= 0 = a__U102(mark(X1),X2,X3) mark(isNatKind(X)) = 0 >= 0 = a__isNatKind(X) mark(U103(X1,X2,X3)) = 0 >= 0 = a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind(X) mark(U104(X1,X2,X3)) = 0 >= 0 = a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) = 0 >= 0 = a__U105(mark(X1),X2) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U106(X)) = 0 >= 0 = a__U106(mark(X)) mark(isNatIList(X)) = 0 >= 0 = a__isNatIList(X) mark(U11(X1,X2)) = 0 >= 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 0 >= 0 = a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) = 0 >= 0 = a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) = 0 >= 0 = a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) = 0 >= 0 = a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) = 0 >= 0 = a__U114(mark(X1),X2) mark(length(X)) = 0 >= 0 = a__length(mark(X)) mark(U13(X)) = 0 >= 0 = a__U13(mark(X)) mark(isNatList(X)) = 0 >= 0 = a__isNatList(X) mark(U121(X1,X2)) = 0 >= 0 = a__U121(mark(X1),X2) mark(U122(X)) = 0 >= 0 = a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) = 0 >= 0 = a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) = 0 >= 0 = a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) = 0 >= 0 = a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) = 0 >= 0 = a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) = 0 >= 0 = a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) = 0 >= 0 = a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) = 0 >= 0 = a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) = 0 >= 0 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 0 >= 0 = a__U22(mark(X1),X2) mark(U23(X)) = 0 >= 0 = a__U23(mark(X)) mark(U31(X1,X2)) = 0 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 0 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 0 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 0 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 0 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 0 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 0 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 0 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 0 >= 0 = a__U46(mark(X)) mark(U51(X1,X2)) = 0 >= 0 = a__U51(mark(X1),X2) mark(U52(X)) = 0 >= 0 = a__U52(mark(X)) mark(U61(X1,X2)) = 0 >= 0 = a__U61(mark(X1),X2) mark(U62(X)) = 0 >= 0 = a__U62(mark(X)) mark(U71(X)) = 0 >= 0 = a__U71(mark(X)) mark(U81(X)) = 0 >= 0 = a__U81(mark(X)) mark(U91(X1,X2,X3)) = 0 >= 0 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 0 >= 0 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 0 >= 0 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) = 0 >= 0 = a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) = 0 >= 0 = a__U95(mark(X1),X2) mark(U96(X)) = 0 >= 0 = a__U96(mark(X)) mark(cons(X1,X2)) = 0 >= 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 0 >= 0 = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U101(X1,X2,X3) = 0 >= 0 = U101(X1,X2,X3) a__U102(X1,X2,X3) = 0 >= 0 = U102(X1,X2,X3) a__isNatKind(X) = 0 >= 0 = isNatKind(X) a__U103(X1,X2,X3) = 0 >= 0 = U103(X1,X2,X3) a__isNatIListKind(X) = 0 >= 0 = isNatIListKind(X) a__U104(X1,X2,X3) = 0 >= 0 = U104(X1,X2,X3) a__U105(X1,X2) = 0 >= 0 = U105(X1,X2) a__isNat(X) = 0 >= 0 = isNat(X) a__U106(X) = 0 >= 0 = U106(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U11(X1,X2) = 0 >= 0 = U11(X1,X2) a__U12(X1,X2) = 0 >= 0 = U12(X1,X2) a__U111(X1,X2,X3) = 0 >= 0 = U111(X1,X2,X3) a__U112(X1,X2,X3) = 0 >= 0 = U112(X1,X2,X3) a__U113(X1,X2,X3) = 0 >= 0 = U113(X1,X2,X3) a__U114(X1,X2) = 0 >= 0 = U114(X1,X2) a__length(X) = 0 >= 0 = length(X) a__U13(X) = 0 >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U121(X1,X2) = 0 >= 0 = U121(X1,X2) a__U122(X) = 0 >= 0 = U122(X) a__U131(X1,X2,X3,X4) = 0 >= 0 = U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) = 0 >= 0 = U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) = 0 >= 0 = U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) = 0 >= 0 = U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) = 0 >= 0 = U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) = 0 >= 0 = U136(X1,X2,X3,X4) a__take(X1,X2) = 0 >= 0 = take(X1,X2) a__U21(X1,X2) = 0 >= 0 = U21(X1,X2) a__U22(X1,X2) = 0 >= 0 = U22(X1,X2) a__U23(X) = 0 >= 0 = U23(X) a__U31(X1,X2) = 0 >= 0 = U31(X1,X2) a__U32(X1,X2) = 0 >= 0 = U32(X1,X2) a__U33(X) = 0 >= 0 = U33(X) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 0 >= 0 = U42(X1,X2,X3) a__U43(X1,X2,X3) = 0 >= 0 = U43(X1,X2,X3) a__U44(X1,X2,X3) = 0 >= 0 = U44(X1,X2,X3) a__U45(X1,X2) = 0 >= 0 = U45(X1,X2) a__U46(X) = 0 >= 0 = U46(X) a__U51(X1,X2) = 0 >= 0 = U51(X1,X2) a__U52(X) = 0 >= 0 = U52(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__U62(X) = 0 >= 0 = U62(X) a__U71(X) = 0 >= 0 = U71(X) a__U81(X) = 0 >= 0 = U81(X) a__U91(X1,X2,X3) = 0 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 0 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 0 >= 0 = U93(X1,X2,X3) a__U94(X1,X2,X3) = 0 >= 0 = U94(X1,X2,X3) a__U95(X1,X2) = 0 >= 0 = U95(X1,X2) a__U96(X) = 0 >= 0 = U96(X) problem: DPs: a__isNatKind#(s(V1)) -> a__isNatKind#(V1) TRS: a__zeros() -> cons(0(),zeros()) a__U101(tt(),V1,V2) -> a__U102(a__isNatKind(V1),V1,V2) a__U102(tt(),V1,V2) -> a__U103(a__isNatIListKind(V2),V1,V2) a__U103(tt(),V1,V2) -> a__U104(a__isNatIListKind(V2),V1,V2) a__U104(tt(),V1,V2) -> a__U105(a__isNat(V1),V2) a__U105(tt(),V2) -> a__U106(a__isNatIList(V2)) a__U106(tt()) -> tt() a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U111(tt(),L,N) -> a__U112(a__isNatIListKind(L),L,N) a__U112(tt(),L,N) -> a__U113(a__isNat(N),L,N) a__U113(tt(),L,N) -> a__U114(a__isNatKind(N),L) a__U114(tt(),L) -> s(a__length(mark(L))) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U121(tt(),IL) -> a__U122(a__isNatIListKind(IL)) a__U122(tt()) -> nil() a__U13(tt()) -> tt() a__U131(tt(),IL,M,N) -> a__U132(a__isNatIListKind(IL),IL,M,N) a__U132(tt(),IL,M,N) -> a__U133(a__isNat(M),IL,M,N) a__U133(tt(),IL,M,N) -> a__U134(a__isNatKind(M),IL,M,N) a__U134(tt(),IL,M,N) -> a__U135(a__isNat(N),IL,M,N) a__U135(tt(),IL,M,N) -> a__U136(a__isNatKind(N),IL,M,N) a__U136(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) -> a__U23(a__isNat(V1)) a__U23(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) -> a__U33(a__isNatList(V)) a__U33(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2) a__U45(tt(),V2) -> a__U46(a__isNatIList(V2)) a__U46(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2)) a__U52(tt()) -> tt() a__U61(tt(),V2) -> a__U62(a__isNatIListKind(V2)) a__U62(tt()) -> tt() a__U71(tt()) -> tt() a__U81(tt()) -> tt() a__U91(tt(),V1,V2) -> a__U92(a__isNatKind(V1),V1,V2) a__U92(tt(),V1,V2) -> a__U93(a__isNatIListKind(V2),V1,V2) a__U93(tt(),V1,V2) -> a__U94(a__isNatIListKind(V2),V1,V2) a__U94(tt(),V1,V2) -> a__U95(a__isNat(V1),V2) a__U95(tt(),V2) -> a__U96(a__isNatList(V2)) a__U96(tt()) -> tt() a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatIListKind(take(V1,V2)) -> a__U61(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U91(a__isNatKind(V1),V1,V2) a__isNatList(take(V1,V2)) -> a__U101(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U111(a__isNatList(L),L,N) a__take(0(),IL) -> a__U121(a__isNatIList(IL),IL) a__take(s(M),cons(N,IL)) -> a__U131(a__isNatIList(IL),IL,M,N) mark(zeros()) -> a__zeros() mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3) mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3) mark(isNatKind(X)) -> a__isNatKind(X) mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3) mark(U105(X1,X2)) -> a__U105(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U106(X)) -> a__U106(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U111(X1,X2,X3)) -> a__U111(mark(X1),X2,X3) mark(U112(X1,X2,X3)) -> a__U112(mark(X1),X2,X3) mark(U113(X1,X2,X3)) -> a__U113(mark(X1),X2,X3) mark(U114(X1,X2)) -> a__U114(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U121(X1,X2)) -> a__U121(mark(X1),X2) mark(U122(X)) -> a__U122(mark(X)) mark(U131(X1,X2,X3,X4)) -> a__U131(mark(X1),X2,X3,X4) mark(U132(X1,X2,X3,X4)) -> a__U132(mark(X1),X2,X3,X4) mark(U133(X1,X2,X3,X4)) -> a__U133(mark(X1),X2,X3,X4) mark(U134(X1,X2,X3,X4)) -> a__U134(mark(X1),X2,X3,X4) mark(U135(X1,X2,X3,X4)) -> a__U135(mark(X1),X2,X3,X4) mark(U136(X1,X2,X3,X4)) -> a__U136(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(U23(X)) -> a__U23(mark(X)) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) -> a__U45(mark(X1),X2) mark(U46(X)) -> a__U46(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3) mark(U94(X1,X2,X3)) -> a__U94(mark(X1),X2,X3) mark(U95(X1,X2)) -> a__U95(mark(X1),X2) mark(U96(X)) -> a__U96(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U101(X1,X2,X3) -> U101(X1,X2,X3) a__U102(X1,X2,X3) -> U102(X1,X2,X3) a__isNatKind(X) -> isNatKind(X) a__U103(X1,X2,X3) -> U103(X1,X2,X3) a__isNatIListKind(X) -> isNatIListKind(X) a__U104(X1,X2,X3) -> U104(X1,X2,X3) a__U105(X1,X2) -> U105(X1,X2) a__isNat(X) -> isNat(X) a__U106(X) -> U106(X) a__isNatIList(X) -> isNatIList(X) a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__U111(X1,X2,X3) -> U111(X1,X2,X3) a__U112(X1,X2,X3) -> U112(X1,X2,X3) a__U113(X1,X2,X3) -> U113(X1,X2,X3) a__U114(X1,X2) -> U114(X1,X2) a__length(X) -> length(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U121(X1,X2) -> U121(X1,X2) a__U122(X) -> U122(X) a__U131(X1,X2,X3,X4) -> U131(X1,X2,X3,X4) a__U132(X1,X2,X3,X4) -> U132(X1,X2,X3,X4) a__U133(X1,X2,X3,X4) -> U133(X1,X2,X3,X4) a__U134(X1,X2,X3,X4) -> U134(X1,X2,X3,X4) a__U135(X1,X2,X3,X4) -> U135(X1,X2,X3,X4) a__U136(X1,X2,X3,X4) -> U136(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__U23(X) -> U23(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2,X3) -> U42(X1,X2,X3) a__U43(X1,X2,X3) -> U43(X1,X2,X3) a__U44(X1,X2,X3) -> U44(X1,X2,X3) a__U45(X1,X2) -> U45(X1,X2) a__U46(X) -> U46(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X1,X2) -> U61(X1,X2) a__U62(X) -> U62(X) a__U71(X) -> U71(X) a__U81(X) -> U81(X) a__U91(X1,X2,X3) -> U91(X1,X2,X3) a__U92(X1,X2,X3) -> U92(X1,X2,X3) a__U93(X1,X2,X3) -> U93(X1,X2,X3) a__U94(X1,X2,X3) -> U94(X1,X2,X3) a__U95(X1,X2) -> U95(X1,X2) a__U96(X) -> U96(X) Open