/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(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__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [U94](x0, x1) = x0 + 3x1, [U93](x0, x1, x2) = x0 + 4x1 + 2x2, [U92](x0, x1, x2) = x0 + 3x1 + 6x2, [U91](x0, x1, x2) = x0 + 4x1 + 4x2, [U86](x0) = x0, [U85](x0, x1) = x0 + x1, [U84](x0, x1, x2) = x0 + 5x1 + x2, [U83](x0, x1, x2) = x0 + 3x1 + 2x2, [U82](x0, x1, x2) = x0 + 4x1 + 2x2, [U81](x0, x1, x2) = x0 + 3x1 + 4x2, [U71](x0) = 2x0, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = 7x0 + 4x1, [isNatIList](x0) = 3x0, [U46](x0) = x0, [U45](x0, x1) = x0 + 3x1, [U44](x0, x1, x2) = x0 + 3x1 + 4x2, [U43](x0, x1, x2) = x0 + 4x1 + 4x2, [U42](x0, x1, x2) = 2x0 + 5x1 + 6x2, [U41](x0, x1, x2) = x0 + 5x1 + 5x2, [U33](x0) = x0, [U32](x0, x1) = x0 + x1, [U31](x0, x1) = x0 + x1, [isNat](x0) = 3x0, [U23](x0) = x0, [isNatKind](x0) = x0, [U22](x0, x1) = 2x0 + 5x1, [U21](x0, x1) = x0 + 4x1, [isNatList](x0) = x0, [U13](x0) = x0, [isNatIListKind](x0) = x0, [U12](x0, x1) = 2x0 + x1, [U11](x0, x1) = x0 + 3x1, [nil] = 4, [length](x0) = x0, [s](x0) = 2x0, [a__length](x0) = x0, [mark](x0) = 2x0, [a__U94](x0, x1) = x0 + 4x1, [a__U93](x0, x1, x2) = x0 + 4x1 + 2x2, [a__U92](x0, x1, x2) = x0 + 4x1 + 7x2, [a__U91](x0, x1, x2) = x0 + 5x1 + 7x2, [a__U86](x0) = x0, [a__U85](x0, x1) = x0 + x1, [a__U84](x0, x1, x2) = x0 + 5x1 + x2, [a__U83](x0, x1, x2) = x0 + 5x1 + 3x2, [a__U82](x0, x1, x2) = x0 + 5x1 + 4x2, [a__U81](x0, x1, x2) = x0 + 6x1 + 4x2, [a__U71](x0) = 2x0, [a__U61](x0) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = 7x0 + 6x1, [a__U46](x0) = x0, [a__isNatIList](x0) = 4x0, [a__U45](x0, x1) = x0 + 4x1, [a__U44](x0, x1, x2) = x0 + 5x1 + 4x2, [a__U43](x0, x1, x2) = x0 + 5x1 + 5x2, [a__U42](x0, x1, x2) = 2x0 + 5x1 + 6x2, [a__U41](x0, x1, x2) = x0 + 7x1 + 6x2, [a__U33](x0) = x0, [a__U32](x0, x1) = x0 + x1, [a__U31](x0, x1) = x0 + 2x1, [a__U23](x0) = x0, [a__isNat](x0) = 5x0, [a__U22](x0, x1) = 2x0 + 5x1, [a__isNatKind](x0) = x0, [a__U21](x0, x1) = x0 + 7x1, [a__U13](x0) = x0, [a__isNatList](x0) = x0, [a__U12](x0, x1) = 2x0 + x1, [a__isNatIListKind](x0) = x0, [a__U11](x0, x1) = x0 + 4x1, [tt] = 0, [cons](x0, x1) = 7x0 + 6x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = 4V1 >= 3V1 = a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) = V1 >= V1 = a__U13(a__isNatList(V1)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1) = 7V1 >= 7V1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 5V1 >= 5V1 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 2V >= 2V = a__U32(a__isNatIListKind(V),V) a__U32(tt(),V) = V >= V = a__U33(a__isNatList(V)) a__U33(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 7V1 + 6V2 >= 7V1 + 6V2 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 5V1 + 6V2 >= 5V1 + 6V2 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 5V1 + 5V2 >= 5V1 + 5V2 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 5V1 + 4V2 >= 5V1 + 4V2 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 4V2 >= 4V2 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 6V2 >= V2 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt(),V1,V2) = 6V1 + 4V2 >= 6V1 + 4V2 = a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) = 5V1 + 4V2 >= 5V1 + 4V2 = a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) = 5V1 + 3V2 >= 5V1 + 2V2 = a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) = 5V1 + V2 >= 5V1 + V2 = a__U85(a__isNat(V1),V2) a__U85(tt(),V2) = V2 >= V2 = a__U86(a__isNatList(V2)) a__U86(tt()) = 0 >= 0 = tt() a__U91(tt(),L,N) = 5L + 7N >= 5L + 7N = a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) = 4L + 7N >= 4L + 7N = a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) = 4L + 2N >= 4L + N = a__U94(a__isNatKind(N),L) a__U94(tt(),L) = 4L >= 4L = s(a__length(mark(L))) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 5V1 >= 5V1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 10V1 >= 8V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 4V >= 3V = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 28V1 + 24V2 >= 8V1 + 6V2 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(nil()) = 4 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 7V1 + 6V2 >= 7V1 + 6V2 = a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = V1 >= V1 = a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 2V1 >= 2V1 = a__U71(a__isNatKind(V1)) a__isNatList(nil()) = 4 >= 0 = tt() a__isNatList(cons(V1,V2)) = 7V1 + 6V2 >= 7V1 + 4V2 = a__U81(a__isNatKind(V1),V1,V2) a__length(nil()) = 4 >= 0 = 0() a__length(cons(N,L)) = 6L + 7N >= 6L + 7N = a__U91(a__isNatList(L),L,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 2X1 + 6X2 >= 2X1 + 4X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 4X1 + 2X2 >= 4X1 + X2 = a__U12(mark(X1),X2) mark(isNatIListKind(X)) = 2X >= X = a__isNatIListKind(X) mark(U13(X)) = 2X >= 2X = a__U13(mark(X)) mark(isNatList(X)) = 2X >= X = a__isNatList(X) mark(U21(X1,X2)) = 2X1 + 8X2 >= 2X1 + 7X2 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 4X1 + 10X2 >= 4X1 + 5X2 = a__U22(mark(X1),X2) mark(isNatKind(X)) = 2X >= X = a__isNatKind(X) mark(U23(X)) = 2X >= 2X = a__U23(mark(X)) mark(isNat(X)) = 6X >= 5X = a__isNat(X) mark(U31(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = a__U32(mark(X1),X2) mark(U33(X)) = 2X >= 2X = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 2X1 + 10X2 + 10X3 >= 2X1 + 7X2 + 6X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 4X1 + 10X2 + 12X3 >= 4X1 + 5X2 + 6X3 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 2X1 + 8X2 + 8X3 >= 2X1 + 5X2 + 5X3 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 2X1 + 6X2 + 8X3 >= 2X1 + 5X2 + 4X3 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 2X1 + 6X2 >= 2X1 + 4X2 = a__U45(mark(X1),X2) mark(U46(X)) = 2X >= 2X = a__U46(mark(X)) mark(isNatIList(X)) = 6X >= 4X = a__isNatIList(X) mark(U51(X1,X2)) = 14X1 + 8X2 >= 14X1 + 6X2 = a__U51(mark(X1),X2) mark(U52(X)) = 2X >= 2X = a__U52(mark(X)) mark(U61(X)) = 2X >= 2X = a__U61(mark(X)) mark(U71(X)) = 4X >= 4X = a__U71(mark(X)) mark(U81(X1,X2,X3)) = 2X1 + 6X2 + 8X3 >= 2X1 + 6X2 + 4X3 = a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) = 2X1 + 8X2 + 4X3 >= 2X1 + 5X2 + 4X3 = a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) = 2X1 + 6X2 + 4X3 >= 2X1 + 5X2 + 3X3 = a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) = 2X1 + 10X2 + 2X3 >= 2X1 + 5X2 + X3 = a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = a__U85(mark(X1),X2) mark(U86(X)) = 2X >= 2X = a__U86(mark(X)) mark(U91(X1,X2,X3)) = 2X1 + 8X2 + 8X3 >= 2X1 + 5X2 + 7X3 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 2X1 + 6X2 + 12X3 >= 2X1 + 4X2 + 7X3 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 2X1 + 8X2 + 4X3 >= 2X1 + 4X2 + 2X3 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2)) = 2X1 + 6X2 >= 2X1 + 4X2 = a__U94(mark(X1),X2) mark(length(X)) = 2X >= 2X = a__length(mark(X)) mark(cons(X1,X2)) = 14X1 + 12X2 >= 14X1 + 6X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 4X >= 4X = s(mark(X)) mark(nil()) = 8 >= 4 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = X1 + 4X2 >= X1 + 3X2 = U11(X1,X2) a__U12(X1,X2) = 2X1 + X2 >= 2X1 + X2 = U12(X1,X2) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = X >= X = isNatList(X) a__U21(X1,X2) = X1 + 7X2 >= X1 + 4X2 = U21(X1,X2) a__U22(X1,X2) = 2X1 + 5X2 >= 2X1 + 5X2 = U22(X1,X2) a__isNatKind(X) = X >= X = isNatKind(X) a__U23(X) = X >= X = U23(X) a__isNat(X) = 5X >= 3X = isNat(X) a__U31(X1,X2) = X1 + 2X2 >= X1 + X2 = U31(X1,X2) a__U32(X1,X2) = X1 + X2 >= X1 + X2 = U32(X1,X2) a__U33(X) = X >= X = U33(X) a__U41(X1,X2,X3) = X1 + 7X2 + 6X3 >= X1 + 5X2 + 5X3 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 2X1 + 5X2 + 6X3 >= 2X1 + 5X2 + 6X3 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + 5X2 + 5X3 >= X1 + 4X2 + 4X3 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + 5X2 + 4X3 >= X1 + 3X2 + 4X3 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + 4X2 >= X1 + 3X2 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__isNatIList(X) = 4X >= 3X = isNatIList(X) a__U51(X1,X2) = 7X1 + 6X2 >= 7X1 + 4X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X) = 2X >= 2X = U71(X) a__U81(X1,X2,X3) = X1 + 6X2 + 4X3 >= X1 + 3X2 + 4X3 = U81(X1,X2,X3) a__U82(X1,X2,X3) = X1 + 5X2 + 4X3 >= X1 + 4X2 + 2X3 = U82(X1,X2,X3) a__U83(X1,X2,X3) = X1 + 5X2 + 3X3 >= X1 + 3X2 + 2X3 = U83(X1,X2,X3) a__U84(X1,X2,X3) = X1 + 5X2 + X3 >= X1 + 5X2 + X3 = U84(X1,X2,X3) a__U85(X1,X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) a__U86(X) = X >= X = U86(X) a__U91(X1,X2,X3) = X1 + 5X2 + 7X3 >= X1 + 4X2 + 4X3 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 + 4X2 + 7X3 >= X1 + 3X2 + 6X3 = U92(X1,X2,X3) a__U93(X1,X2,X3) = X1 + 4X2 + 2X3 >= X1 + 4X2 + 2X3 = U93(X1,X2,X3) a__U94(X1,X2) = X1 + 4X2 >= X1 + 3X2 = U94(X1,X2) a__length(X) = X >= X = length(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) Matrix Interpretation Processor: dim=1 interpretation: [U94](x0, x1) = x0 + 2x1, [U93](x0, x1, x2) = 2x0 + 2x1 + x2, [U92](x0, x1, x2) = 4x0 + 2x1 + 7x2, [U91](x0, x1, x2) = x0 + 6x1 + 7x2, [U86](x0) = x0, [U85](x0, x1) = x0 + x1, [U84](x0, x1, x2) = x0 + 3x1 + x2, [U83](x0, x1, x2) = x0 + 3x1 + 2x2, [U82](x0, x1, x2) = x0 + 3x1 + 3x2, [U81](x0, x1, x2) = x0 + 4x1 + 4x2, [U71](x0) = 2x0, [U61](x0) = x0, [U52](x0) = 4x0, [U51](x0, x1) = x0 + 4x1, [isNatIList](x0) = 3x0 + 1, [U46](x0) = x0, [U45](x0, x1) = x0 + 3x1 + 1, [U44](x0, x1, x2) = x0 + 3x1 + 3x2 + 1, [U43](x0, x1, x2) = x0 + 4x1 + 4x2 + 1, [U42](x0, x1, x2) = 2x0 + 5x1 + 5x2 + 1, [U41](x0, x1, x2) = x0 + 7x1 + 5x2 + 1, [U33](x0) = x0 + 1, [U32](x0, x1) = x0 + x1 + 1, [U31](x0, x1) = x0 + 2x1 + 1, [isNat](x0) = 3x0, [U23](x0) = x0, [isNatKind](x0) = x0, [U22](x0, x1) = x0 + 4x1, [U21](x0, x1) = x0 + 5x1, [isNatList](x0) = x0, [U13](x0) = x0, [isNatIListKind](x0) = x0, [U12](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + 2x1, [length](x0) = x0, [s](x0) = 2x0, [a__length](x0) = x0, [mark](x0) = x0, [a__U94](x0, x1) = x0 + 2x1, [a__U93](x0, x1, x2) = 2x0 + 2x1 + x2, [a__U92](x0, x1, x2) = 4x0 + 2x1 + 7x2, [a__U91](x0, x1, x2) = x0 + 6x1 + 7x2, [a__U86](x0) = x0, [a__U85](x0, x1) = x0 + x1, [a__U84](x0, x1, x2) = x0 + 3x1 + x2, [a__U83](x0, x1, x2) = x0 + 3x1 + 2x2, [a__U82](x0, x1, x2) = x0 + 3x1 + 3x2, [a__U81](x0, x1, x2) = x0 + 4x1 + 4x2, [a__U71](x0) = 2x0, [a__U61](x0) = x0, [a__U52](x0) = 4x0, [a__U51](x0, x1) = x0 + 4x1, [a__U46](x0) = x0, [a__isNatIList](x0) = 3x0 + 1, [a__U45](x0, x1) = x0 + 3x1 + 1, [a__U44](x0, x1, x2) = x0 + 3x1 + 3x2 + 1, [a__U43](x0, x1, x2) = x0 + 4x1 + 4x2 + 1, [a__U42](x0, x1, x2) = 2x0 + 5x1 + 5x2 + 1, [a__U41](x0, x1, x2) = x0 + 7x1 + 5x2 + 1, [a__U33](x0) = x0 + 1, [a__U32](x0, x1) = x0 + x1 + 1, [a__U31](x0, x1) = x0 + 2x1 + 1, [a__U23](x0) = x0, [a__isNat](x0) = 3x0, [a__U22](x0, x1) = x0 + 4x1, [a__isNatKind](x0) = x0, [a__U21](x0, x1) = x0 + 5x1, [a__U13](x0) = x0, [a__isNatList](x0) = x0, [a__U12](x0, x1) = x0 + x1, [a__isNatIListKind](x0) = x0, [a__U11](x0, x1) = x0 + 2x1, [tt] = 0, [cons](x0, x1) = 7x0 + 7x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = 2V1 >= 2V1 = a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) = V1 >= V1 = a__U13(a__isNatList(V1)) a__U13(tt()) = 0 >= 0 = tt() a__U21(tt(),V1) = 5V1 >= 5V1 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 4V1 >= 3V1 = a__U23(a__isNat(V1)) a__U23(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = 2V + 1 >= 2V + 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) = 7V1 + 5V2 + 1 >= 7V1 + 5V2 + 1 = a__U42(a__isNatKind(V1),V1,V2) a__U42(tt(),V1,V2) = 5V1 + 5V2 + 1 >= 4V1 + 5V2 + 1 = a__U43(a__isNatIListKind(V2),V1,V2) a__U43(tt(),V1,V2) = 4V1 + 4V2 + 1 >= 3V1 + 4V2 + 1 = a__U44(a__isNatIListKind(V2),V1,V2) a__U44(tt(),V1,V2) = 3V1 + 3V2 + 1 >= 3V1 + 3V2 + 1 = a__U45(a__isNat(V1),V2) a__U45(tt(),V2) = 3V2 + 1 >= 3V2 + 1 = a__U46(a__isNatIList(V2)) a__U46(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = 4V2 >= 4V2 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt()) = 0 >= 0 = tt() a__U71(tt()) = 0 >= 0 = tt() a__U81(tt(),V1,V2) = 4V1 + 4V2 >= 4V1 + 3V2 = a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) = 3V1 + 3V2 >= 3V1 + 3V2 = a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) = 3V1 + 2V2 >= 3V1 + 2V2 = a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) = 3V1 + V2 >= 3V1 + V2 = a__U85(a__isNat(V1),V2) a__U85(tt(),V2) = V2 >= V2 = a__U86(a__isNatList(V2)) a__U86(tt()) = 0 >= 0 = tt() a__U91(tt(),L,N) = 6L + 7N >= 6L + 7N = a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) = 2L + 7N >= 2L + 7N = a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) = 2L + N >= 2L + N = a__U94(a__isNatKind(N),L) a__U94(tt(),L) = 2L >= 2L = s(a__length(mark(L))) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 3V1 >= 3V1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 6V1 >= 6V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 3V + 1 >= 3V + 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 21V1 + 21V2 + 1 >= 8V1 + 5V2 + 1 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 7V1 + 7V2 >= V1 + 4V2 = a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = V1 >= V1 = a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 2V1 >= 2V1 = a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) = 7V1 + 7V2 >= 5V1 + 4V2 = a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) = 7L + 7N >= 7L + 7N = a__U91(a__isNatList(L),L,N) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 >= X1 + X2 = a__U12(mark(X1),X2) mark(isNatIListKind(X)) = X >= X = a__isNatIListKind(X) mark(U13(X)) = X >= X = a__U13(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U21(X1,X2)) = X1 + 5X2 >= X1 + 5X2 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = a__U22(mark(X1),X2) mark(isNatKind(X)) = X >= X = a__isNatKind(X) mark(U23(X)) = X >= X = a__U23(mark(X)) mark(isNat(X)) = 3X >= 3X = a__isNat(X) mark(U31(X1,X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 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 + 7X2 + 5X3 + 1 >= X1 + 7X2 + 5X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 2X1 + 5X2 + 5X3 + 1 >= 2X1 + 5X2 + 5X3 + 1 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = X1 + 4X2 + 4X3 + 1 >= X1 + 4X2 + 4X3 + 1 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = X1 + 3X2 + 3X3 + 1 >= X1 + 3X2 + 3X3 + 1 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = X1 + 3X2 + 1 >= X1 + 3X2 + 1 = a__U45(mark(X1),X2) mark(U46(X)) = X >= X = a__U46(mark(X)) mark(isNatIList(X)) = 3X + 1 >= 3X + 1 = a__isNatIList(X) mark(U51(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = a__U51(mark(X1),X2) mark(U52(X)) = 4X >= 4X = a__U52(mark(X)) mark(U61(X)) = X >= X = a__U61(mark(X)) mark(U71(X)) = 2X >= 2X = a__U71(mark(X)) mark(U81(X1,X2,X3)) = X1 + 4X2 + 4X3 >= X1 + 4X2 + 4X3 = a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) = X1 + 3X2 + 3X3 >= X1 + 3X2 + 3X3 = a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) = X1 + 3X2 + 2X3 >= X1 + 3X2 + 2X3 = a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) = X1 + 3X2 + X3 >= X1 + 3X2 + X3 = a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) = X1 + X2 >= X1 + X2 = a__U85(mark(X1),X2) mark(U86(X)) = X >= X = a__U86(mark(X)) mark(U91(X1,X2,X3)) = X1 + 6X2 + 7X3 >= X1 + 6X2 + 7X3 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 4X1 + 2X2 + 7X3 >= 4X1 + 2X2 + 7X3 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 2X1 + 2X2 + X3 >= 2X1 + 2X2 + X3 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = a__U94(mark(X1),X2) mark(length(X)) = X >= X = a__length(mark(X)) mark(cons(X1,X2)) = 7X1 + 7X2 >= 7X1 + 7X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 2X >= 2X = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = X1 + 2X2 >= X1 + 2X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 >= X1 + X2 = U12(X1,X2) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__U13(X) = X >= X = U13(X) a__isNatList(X) = X >= X = isNatList(X) a__U21(X1,X2) = X1 + 5X2 >= X1 + 5X2 = U21(X1,X2) a__U22(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U22(X1,X2) a__isNatKind(X) = X >= X = isNatKind(X) a__U23(X) = X >= X = U23(X) a__isNat(X) = 3X >= 3X = isNat(X) a__U31(X1,X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 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 + 7X2 + 5X3 + 1 >= X1 + 7X2 + 5X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2,X3) = 2X1 + 5X2 + 5X3 + 1 >= 2X1 + 5X2 + 5X3 + 1 = U42(X1,X2,X3) a__U43(X1,X2,X3) = X1 + 4X2 + 4X3 + 1 >= X1 + 4X2 + 4X3 + 1 = U43(X1,X2,X3) a__U44(X1,X2,X3) = X1 + 3X2 + 3X3 + 1 >= X1 + 3X2 + 3X3 + 1 = U44(X1,X2,X3) a__U45(X1,X2) = X1 + 3X2 + 1 >= X1 + 3X2 + 1 = U45(X1,X2) a__U46(X) = X >= X = U46(X) a__isNatIList(X) = 3X + 1 >= 3X + 1 = isNatIList(X) a__U51(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) a__U52(X) = 4X >= 4X = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X) = 2X >= 2X = U71(X) a__U81(X1,X2,X3) = X1 + 4X2 + 4X3 >= X1 + 4X2 + 4X3 = U81(X1,X2,X3) a__U82(X1,X2,X3) = X1 + 3X2 + 3X3 >= X1 + 3X2 + 3X3 = U82(X1,X2,X3) a__U83(X1,X2,X3) = X1 + 3X2 + 2X3 >= X1 + 3X2 + 2X3 = U83(X1,X2,X3) a__U84(X1,X2,X3) = X1 + 3X2 + X3 >= X1 + 3X2 + X3 = U84(X1,X2,X3) a__U85(X1,X2) = X1 + X2 >= X1 + X2 = U85(X1,X2) a__U86(X) = X >= X = U86(X) a__U91(X1,X2,X3) = X1 + 6X2 + 7X3 >= X1 + 6X2 + 7X3 = U91(X1,X2,X3) a__U92(X1,X2,X3) = 4X1 + 2X2 + 7X3 >= 4X1 + 2X2 + 7X3 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 2X1 + 2X2 + X3 >= 2X1 + 2X2 + X3 = U93(X1,X2,X3) a__U94(X1,X2) = X1 + 2X2 >= X1 + 2X2 = U94(X1,X2) a__length(X) = X >= X = length(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) DP Processor: DPs: a__U11#(tt(),V1) -> a__isNatIListKind#(V1) a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__U12#(tt(),V1) -> a__isNatList#(V1) a__U12#(tt(),V1) -> a__U13#(a__isNatList(V1)) 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__U81#(tt(),V1,V2) -> a__isNatKind#(V1) a__U81#(tt(),V1,V2) -> a__U82#(a__isNatKind(V1),V1,V2) a__U82#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U82#(tt(),V1,V2) -> a__U83#(a__isNatIListKind(V2),V1,V2) a__U83#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U83#(tt(),V1,V2) -> a__U84#(a__isNatIListKind(V2),V1,V2) a__U84#(tt(),V1,V2) -> a__isNat#(V1) a__U84#(tt(),V1,V2) -> a__U85#(a__isNat(V1),V2) a__U85#(tt(),V2) -> a__isNatList#(V2) a__U85#(tt(),V2) -> a__U86#(a__isNatList(V2)) a__U91#(tt(),L,N) -> a__isNatIListKind#(L) a__U91#(tt(),L,N) -> a__U92#(a__isNatIListKind(L),L,N) a__U92#(tt(),L,N) -> a__isNat#(N) a__U92#(tt(),L,N) -> a__U93#(a__isNat(N),L,N) a__U93#(tt(),L,N) -> a__isNatKind#(N) a__U93#(tt(),L,N) -> a__U94#(a__isNatKind(N),L) a__U94#(tt(),L) -> mark#(L) a__U94#(tt(),L) -> a__length#(mark(L)) 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__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatKind#(length(V1)) -> a__U61#(a__isNatIListKind(V1)) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__U71#(a__isNatKind(V1)) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__U81#(a__isNatKind(V1),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__U91#(a__isNatList(L),L,N) mark#(zeros()) -> a__zeros#() 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#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> a__U13#(mark(X)) mark#(isNatList(X)) -> a__isNatList#(X) 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#(isNatKind(X)) -> a__isNatKind#(X) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> a__U23#(mark(X)) mark#(isNat(X)) -> a__isNat#(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#(isNatIList(X)) -> a__isNatIList#(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(X)) -> mark#(X) mark#(U61(X)) -> a__U61#(mark(X)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> a__U71#(mark(X)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> a__U81#(mark(X1),X2,X3) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> a__U82#(mark(X1),X2,X3) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> a__U83#(mark(X1),X2,X3) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> a__U84#(mark(X1),X2,X3) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> a__U85#(mark(X1),X2) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> a__U86#(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)) -> mark#(X1) mark#(U94(X1,X2)) -> a__U94#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) TDG Processor: DPs: a__U11#(tt(),V1) -> a__isNatIListKind#(V1) a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) a__U12#(tt(),V1) -> a__isNatList#(V1) a__U12#(tt(),V1) -> a__U13#(a__isNatList(V1)) 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__U81#(tt(),V1,V2) -> a__isNatKind#(V1) a__U81#(tt(),V1,V2) -> a__U82#(a__isNatKind(V1),V1,V2) a__U82#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U82#(tt(),V1,V2) -> a__U83#(a__isNatIListKind(V2),V1,V2) a__U83#(tt(),V1,V2) -> a__isNatIListKind#(V2) a__U83#(tt(),V1,V2) -> a__U84#(a__isNatIListKind(V2),V1,V2) a__U84#(tt(),V1,V2) -> a__isNat#(V1) a__U84#(tt(),V1,V2) -> a__U85#(a__isNat(V1),V2) a__U85#(tt(),V2) -> a__isNatList#(V2) a__U85#(tt(),V2) -> a__U86#(a__isNatList(V2)) a__U91#(tt(),L,N) -> a__isNatIListKind#(L) a__U91#(tt(),L,N) -> a__U92#(a__isNatIListKind(L),L,N) a__U92#(tt(),L,N) -> a__isNat#(N) a__U92#(tt(),L,N) -> a__U93#(a__isNat(N),L,N) a__U93#(tt(),L,N) -> a__isNatKind#(N) a__U93#(tt(),L,N) -> a__U94#(a__isNatKind(N),L) a__U94#(tt(),L) -> mark#(L) a__U94#(tt(),L) -> a__length#(mark(L)) 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__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatKind#(length(V1)) -> a__U61#(a__isNatIListKind(V1)) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__U71#(a__isNatKind(V1)) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__U81#(a__isNatKind(V1),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__U91#(a__isNatList(L),L,N) mark#(zeros()) -> a__zeros#() 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#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> a__U13#(mark(X)) mark#(isNatList(X)) -> a__isNatList#(X) 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#(isNatKind(X)) -> a__isNatKind#(X) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> a__U23#(mark(X)) mark#(isNat(X)) -> a__isNat#(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#(isNatIList(X)) -> a__isNatIList#(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(X)) -> mark#(X) mark#(U61(X)) -> a__U61#(mark(X)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> a__U71#(mark(X)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> a__U81#(mark(X1),X2,X3) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> a__U82#(mark(X1),X2,X3) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> a__U83#(mark(X1),X2,X3) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> a__U84#(mark(X1),X2,X3) mark#(U85(X1,X2)) -> mark#(X1) mark#(U85(X1,X2)) -> a__U85#(mark(X1),X2) mark#(U86(X)) -> mark#(X) mark#(U86(X)) -> a__U86#(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)) -> mark#(X1) mark#(U94(X1,X2)) -> a__U94#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) graph: ... SCC Processor: #sccs: 4 #rules: 67 #arcs: 2434/16384 DPs: a__length#(cons(N,L)) -> a__U91#(a__isNatList(L),L,N) a__U91#(tt(),L,N) -> a__U92#(a__isNatIListKind(L),L,N) a__U92#(tt(),L,N) -> a__U93#(a__isNat(N),L,N) a__U93#(tt(),L,N) -> a__U94#(a__isNatKind(N),L) a__U94#(tt(),L) -> mark#(L) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) 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(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U85(X1,X2)) -> mark#(X1) mark#(U86(X)) -> 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)) -> mark#(X1) mark#(U94(X1,X2)) -> a__U94#(mark(X1),X2) a__U94#(tt(),L) -> a__length#(mark(L)) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) Matrix Interpretation Processor: dim=1 usable rules: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) interpretation: [a__length#](x0) = 4, [mark#](x0) = 4, [a__U94#](x0, x1) = 4, [a__U93#](x0, x1, x2) = 4, [a__U92#](x0, x1, x2) = 4, [a__U91#](x0, x1, x2) = x0, [U94](x0, x1) = 0, [U93](x0, x1, x2) = 1, [U92](x0, x1, x2) = 0, [U91](x0, x1, x2) = 0, [U86](x0) = x0, [U85](x0, x1) = 0, [U84](x0, x1, x2) = 0, [U83](x0, x1, x2) = 0, [U82](x0, x1, x2) = 0, [U81](x0, x1, x2) = 0, [U71](x0) = 0, [U61](x0) = x0, [U52](x0) = 0, [U51](x0, x1) = 0, [isNatIList](x0) = 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, [isNat](x0) = 4, [U23](x0) = 0, [isNatKind](x0) = 4, [U22](x0, x1) = x0, [U21](x0, x1) = 0, [isNatList](x0) = 0, [U13](x0) = 0, [isNatIListKind](x0) = 0, [U12](x0, x1) = x0, [U11](x0, x1) = 0, [length](x0) = 0, [s](x0) = 0, [a__length](x0) = 4, [mark](x0) = 4, [a__U94](x0, x1) = 0, [a__U93](x0, x1, x2) = 1, [a__U92](x0, x1, x2) = x0, [a__U91](x0, x1, x2) = 4, [a__U86](x0) = x0, [a__U85](x0, x1) = 0, [a__U84](x0, x1, x2) = 0, [a__U83](x0, x1, x2) = 0, [a__U82](x0, x1, x2) = 0, [a__U81](x0, x1, x2) = 0, [a__U71](x0) = x0, [a__U61](x0) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = 4, [a__U46](x0) = x0, [a__isNatIList](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) = x0, [a__isNat](x0) = 4, [a__U22](x0, x1) = x0, [a__isNatKind](x0) = 4, [a__U21](x0, x1) = x0, [a__U13](x0) = x0, [a__isNatList](x0) = 0, [a__U12](x0, x1) = x0, [a__isNatIListKind](x0) = 4, [a__U11](x0, x1) = 4, [tt] = 4, [cons](x0, x1) = x0, [zeros] = 4, [0] = 4, [a__zeros] = 4 orientation: a__length#(cons(N,L)) = 4 >= 0 = a__U91#(a__isNatList(L),L,N) a__U91#(tt(),L,N) = 4 >= 4 = a__U92#(a__isNatIListKind(L),L,N) a__U92#(tt(),L,N) = 4 >= 4 = a__U93#(a__isNat(N),L,N) a__U93#(tt(),L,N) = 4 >= 4 = a__U94#(a__isNatKind(N),L) a__U94#(tt(),L) = 4 >= 4 = mark#(L) mark#(U11(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U12(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U13(X)) = 4 >= 4 = mark#(X) mark#(U21(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U22(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U23(X)) = 4 >= 4 = mark#(X) mark#(U31(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U32(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U33(X)) = 4 >= 4 = mark#(X) mark#(U41(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U42(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U43(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U44(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U45(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U46(X)) = 4 >= 4 = mark#(X) mark#(U51(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U52(X)) = 4 >= 4 = mark#(X) mark#(U61(X)) = 4 >= 4 = mark#(X) mark#(U71(X)) = 4 >= 4 = mark#(X) mark#(U81(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U82(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U83(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U84(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U85(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U86(X)) = 4 >= 4 = mark#(X) mark#(U91(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U91(X1,X2,X3)) = 4 >= 4 = a__U91#(mark(X1),X2,X3) mark#(U92(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U92(X1,X2,X3)) = 4 >= 4 = a__U92#(mark(X1),X2,X3) mark#(U93(X1,X2,X3)) = 4 >= 4 = mark#(X1) mark#(U93(X1,X2,X3)) = 4 >= 4 = a__U93#(mark(X1),X2,X3) mark#(U94(X1,X2)) = 4 >= 4 = mark#(X1) mark#(U94(X1,X2)) = 4 >= 4 = a__U94#(mark(X1),X2) a__U94#(tt(),L) = 4 >= 4 = a__length#(mark(L)) mark#(length(X)) = 4 >= 4 = mark#(X) mark#(length(X)) = 4 >= 4 = a__length#(mark(X)) mark#(cons(X1,X2)) = 4 >= 4 = mark#(X1) mark#(s(X)) = 4 >= 4 = mark#(X) a__zeros() = 4 >= 4 = cons(0(),zeros()) a__U11(tt(),V1) = 4 >= 4 = a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) = 4 >= 0 = a__U13(a__isNatList(V1)) a__U13(tt()) = 4 >= 4 = tt() a__U21(tt(),V1) = 4 >= 4 = a__U22(a__isNatKind(V1),V1) a__U22(tt(),V1) = 4 >= 4 = a__U23(a__isNat(V1)) a__U23(tt()) = 4 >= 4 = 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__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()) = 4 >= 4 = tt() a__U51(tt(),V2) = 4 >= 4 = a__U52(a__isNatIListKind(V2)) a__U52(tt()) = 4 >= 4 = tt() a__U61(tt()) = 4 >= 4 = tt() a__U71(tt()) = 4 >= 4 = tt() a__U81(tt(),V1,V2) = 0 >= 0 = a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) = 0 >= 0 = a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) = 0 >= 0 = a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) = 0 >= 0 = a__U85(a__isNat(V1),V2) a__U85(tt(),V2) = 0 >= 0 = a__U86(a__isNatList(V2)) a__U86(tt()) = 4 >= 4 = tt() a__U91(tt(),L,N) = 4 >= 4 = a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) = 4 >= 1 = a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) = 1 >= 0 = a__U94(a__isNatKind(N),L) a__U94(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__isNat(0()) = 4 >= 4 = tt() a__isNat(length(V1)) = 4 >= 4 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 4 >= 4 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 0 >= 0 = a__U31(a__isNatIListKind(V),V) a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) = 4 >= 4 = tt() a__isNatIListKind(cons(V1,V2)) = 4 >= 4 = a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) = 4 >= 4 = tt() a__isNatKind(length(V1)) = 4 >= 4 = a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) = 4 >= 4 = a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) = 4 >= 4 = a__U91(a__isNatList(L),L,N) mark(zeros()) = 4 >= 4 = a__zeros() mark(U11(X1,X2)) = 4 >= 4 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = 4 >= 4 = a__U12(mark(X1),X2) mark(isNatIListKind(X)) = 4 >= 4 = a__isNatIListKind(X) mark(U13(X)) = 4 >= 4 = a__U13(mark(X)) mark(isNatList(X)) = 4 >= 0 = a__isNatList(X) mark(U21(X1,X2)) = 4 >= 4 = a__U21(mark(X1),X2) mark(U22(X1,X2)) = 4 >= 4 = a__U22(mark(X1),X2) mark(isNatKind(X)) = 4 >= 4 = a__isNatKind(X) mark(U23(X)) = 4 >= 4 = a__U23(mark(X)) mark(isNat(X)) = 4 >= 4 = a__isNat(X) mark(U31(X1,X2)) = 4 >= 0 = a__U31(mark(X1),X2) mark(U32(X1,X2)) = 4 >= 0 = a__U32(mark(X1),X2) mark(U33(X)) = 4 >= 0 = a__U33(mark(X)) mark(U41(X1,X2,X3)) = 4 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2,X3)) = 4 >= 0 = a__U42(mark(X1),X2,X3) mark(U43(X1,X2,X3)) = 4 >= 0 = a__U43(mark(X1),X2,X3) mark(U44(X1,X2,X3)) = 4 >= 0 = a__U44(mark(X1),X2,X3) mark(U45(X1,X2)) = 4 >= 0 = a__U45(mark(X1),X2) mark(U46(X)) = 4 >= 4 = a__U46(mark(X)) mark(isNatIList(X)) = 4 >= 0 = a__isNatIList(X) mark(U51(X1,X2)) = 4 >= 4 = a__U51(mark(X1),X2) mark(U52(X)) = 4 >= 4 = a__U52(mark(X)) mark(U61(X)) = 4 >= 4 = a__U61(mark(X)) mark(U71(X)) = 4 >= 4 = a__U71(mark(X)) mark(U81(X1,X2,X3)) = 4 >= 0 = a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) = 4 >= 0 = a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) = 4 >= 0 = a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) = 4 >= 0 = a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) = 4 >= 0 = a__U85(mark(X1),X2) mark(U86(X)) = 4 >= 4 = a__U86(mark(X)) mark(U91(X1,X2,X3)) = 4 >= 4 = a__U91(mark(X1),X2,X3) mark(U92(X1,X2,X3)) = 4 >= 4 = a__U92(mark(X1),X2,X3) mark(U93(X1,X2,X3)) = 4 >= 1 = a__U93(mark(X1),X2,X3) mark(U94(X1,X2)) = 4 >= 0 = a__U94(mark(X1),X2) mark(length(X)) = 4 >= 4 = a__length(mark(X)) mark(cons(X1,X2)) = 4 >= 4 = cons(mark(X1),X2) mark(0()) = 4 >= 4 = 0() mark(tt()) = 4 >= 4 = tt() mark(s(X)) = 4 >= 0 = s(mark(X)) a__zeros() = 4 >= 4 = zeros() a__U11(X1,X2) = 4 >= 0 = U11(X1,X2) a__U12(X1,X2) = X1 >= X1 = U12(X1,X2) a__isNatIListKind(X) = 4 >= 0 = isNatIListKind(X) a__U13(X) = X >= 0 = U13(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U21(X1,X2) = X1 >= 0 = U21(X1,X2) a__U22(X1,X2) = X1 >= X1 = U22(X1,X2) a__isNatKind(X) = 4 >= 4 = isNatKind(X) a__U23(X) = X >= 0 = U23(X) a__isNat(X) = 4 >= 4 = isNat(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 >= 0 = U46(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U51(X1,X2) = 4 >= 0 = U51(X1,X2) a__U52(X) = X >= 0 = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X) = X >= 0 = U71(X) a__U81(X1,X2,X3) = 0 >= 0 = U81(X1,X2,X3) a__U82(X1,X2,X3) = 0 >= 0 = U82(X1,X2,X3) a__U83(X1,X2,X3) = 0 >= 0 = U83(X1,X2,X3) a__U84(X1,X2,X3) = 0 >= 0 = U84(X1,X2,X3) a__U85(X1,X2) = 0 >= 0 = U85(X1,X2) a__U86(X) = X >= X = U86(X) a__U91(X1,X2,X3) = 4 >= 0 = U91(X1,X2,X3) a__U92(X1,X2,X3) = X1 >= 0 = U92(X1,X2,X3) a__U93(X1,X2,X3) = 1 >= 1 = U93(X1,X2,X3) a__U94(X1,X2) = 0 >= 0 = U94(X1,X2) a__length(X) = 4 >= 0 = length(X) problem: DPs: a__U91#(tt(),L,N) -> a__U92#(a__isNatIListKind(L),L,N) a__U92#(tt(),L,N) -> a__U93#(a__isNat(N),L,N) a__U93#(tt(),L,N) -> a__U94#(a__isNatKind(N),L) a__U94#(tt(),L) -> mark#(L) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) 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(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U85(X1,X2)) -> mark#(X1) mark#(U86(X)) -> 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)) -> mark#(X1) mark#(U94(X1,X2)) -> a__U94#(mark(X1),X2) a__U94#(tt(),L) -> a__length#(mark(L)) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) Restore Modifier: DPs: a__U91#(tt(),L,N) -> a__U92#(a__isNatIListKind(L),L,N) a__U92#(tt(),L,N) -> a__U93#(a__isNat(N),L,N) a__U93#(tt(),L,N) -> a__U94#(a__isNatKind(N),L) a__U94#(tt(),L) -> mark#(L) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) 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(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U85(X1,X2)) -> mark#(X1) mark#(U86(X)) -> 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)) -> mark#(X1) mark#(U94(X1,X2)) -> a__U94#(mark(X1),X2) a__U94#(tt(),L) -> a__length#(mark(L)) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) SCC Processor: #sccs: 1 #rules: 40 #arcs: 1233/1764 DPs: mark#(U94(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) 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(X)) -> mark#(X) mark#(U71(X)) -> mark#(X) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U85(X1,X2)) -> mark#(X1) mark#(U86(X)) -> mark#(X) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> a__U91#(mark(X1),X2,X3) a__U91#(tt(),L,N) -> a__U92#(a__isNatIListKind(L),L,N) a__U92#(tt(),L,N) -> a__U93#(a__isNat(N),L,N) a__U93#(tt(),L,N) -> a__U94#(a__isNatKind(N),L) a__U94#(tt(),L) -> mark#(L) 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)) -> a__U94#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) Subterm Criterion Processor: simple projection: pi(a__U91#) = 1 pi(a__U92#) = 1 pi(a__U93#) = 1 pi(a__U94#) = 1 pi(mark#) = 0 problem: DPs: a__U91#(tt(),L,N) -> a__U92#(a__isNatIListKind(L),L,N) a__U92#(tt(),L,N) -> a__U93#(a__isNat(N),L,N) a__U93#(tt(),L,N) -> a__U94#(a__isNatKind(N),L) a__U94#(tt(),L) -> mark#(L) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) SCC Processor: #sccs: 0 #rules: 0 #arcs: 1195/16 DPs: 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) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__isNatKind(V1),V1,V2) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) Subterm Criterion Processor: simple projection: pi(a__U41#) = 2 pi(a__U42#) = 2 pi(a__U43#) = 2 pi(a__U44#) = 2 pi(a__U45#) = 1 pi(a__isNatIList#) = 0 problem: DPs: 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__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) SCC Processor: #sccs: 0 #rules: 0 #arcs: 6/25 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__U81#(a__isNatKind(V1),V1,V2) a__U81#(tt(),V1,V2) -> a__U82#(a__isNatKind(V1),V1,V2) a__U82#(tt(),V1,V2) -> a__U83#(a__isNatIListKind(V2),V1,V2) a__U83#(tt(),V1,V2) -> a__U84#(a__isNatIListKind(V2),V1,V2) a__U84#(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__U84#(tt(),V1,V2) -> a__U85#(a__isNat(V1),V2) a__U85#(tt(),V2) -> a__isNatList#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) Size-Change Termination Processor: DPs: TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) The DP: a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) has the edges: 0 > 1 The DP: a__U11#(tt(),V1) -> a__U12#(a__isNatIListKind(V1),V1) has the edges: 1 >= 1 The DP: a__U12#(tt(),V1) -> a__isNatList#(V1) has the edges: 1 >= 0 The DP: a__isNatList#(cons(V1,V2)) -> a__U81#(a__isNatKind(V1),V1,V2) has the edges: 0 > 2 0 > 1 The DP: a__U81#(tt(),V1,V2) -> a__U82#(a__isNatKind(V1),V1,V2) has the edges: 1 >= 1 2 >= 2 The DP: a__U82#(tt(),V1,V2) -> a__U83#(a__isNatIListKind(V2),V1,V2) has the edges: 1 >= 1 2 >= 2 The DP: a__U83#(tt(),V1,V2) -> a__U84#(a__isNatIListKind(V2),V1,V2) has the edges: 1 >= 1 2 >= 2 The DP: a__U84#(tt(),V1,V2) -> a__isNat#(V1) has the edges: 1 >= 0 The DP: a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) has the edges: 0 > 1 The DP: a__U21#(tt(),V1) -> a__U22#(a__isNatKind(V1),V1) has the edges: 1 >= 1 The DP: a__U22#(tt(),V1) -> a__isNat#(V1) has the edges: 1 >= 0 The DP: a__U84#(tt(),V1,V2) -> a__U85#(a__isNat(V1),V2) has the edges: 2 >= 1 The DP: a__U85#(tt(),V2) -> a__isNatList#(V2) has the edges: 1 >= 0 Qed 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__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) Subterm Criterion Processor: simple projection: pi(a__isNatIListKind#) = 0 pi(a__isNatKind#) = 0 pi(a__U51#) = 1 problem: DPs: a__U51#(tt(),V2) -> a__isNatIListKind#(V2) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1) a__U12(tt(),V1) -> a__U13(a__isNatList(V1)) a__U13(tt()) -> tt() 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__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()) -> tt() a__U71(tt()) -> tt() a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2) a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2) a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2) a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2) a__U85(tt(),V2) -> a__U86(a__isNatList(V2)) a__U86(tt()) -> tt() a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N) a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N) a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L) a__U94(tt(),L) -> s(a__length(mark(L))) 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(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1)) a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1)) a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2) a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(U13(X)) -> a__U13(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X1,X2)) -> a__U22(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) mark(U23(X)) -> a__U23(mark(X)) mark(isNat(X)) -> a__isNat(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(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X)) -> a__U71(mark(X)) mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3) mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3) mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3) mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3) mark(U85(X1,X2)) -> a__U85(mark(X1),X2) mark(U86(X)) -> a__U86(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)) -> a__U94(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__U13(X) -> U13(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X1,X2) -> U22(X1,X2) a__isNatKind(X) -> isNatKind(X) a__U23(X) -> U23(X) a__isNat(X) -> isNat(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__isNatIList(X) -> isNatIList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X) -> U71(X) a__U81(X1,X2,X3) -> U81(X1,X2,X3) a__U82(X1,X2,X3) -> U82(X1,X2,X3) a__U83(X1,X2,X3) -> U83(X1,X2,X3) a__U84(X1,X2,X3) -> U84(X1,X2,X3) a__U85(X1,X2) -> U85(X1,X2) a__U86(X) -> U86(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) -> U94(X1,X2) a__length(X) -> length(X) SCC Processor: #sccs: 0 #rules: 0 #arcs: 9/1