/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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatList(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [U61](x0, x1) = x0 + 6x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [isNatIList](x0) = 3x0, [U43](x0) = 2x0, [U42](x0, x1) = x0 + 6x1, [U41](x0, x1, x2) = x0 + x1 + 6x2, [U32](x0) = x0, [U31](x0, x1) = x0 + x1, [U22](x0) = x0, [U21](x0, x1) = x0 + x1, [isNatList](x0) = x0, [U12](x0) = x0, [U11](x0, x1) = x0 + x1, [and](x0, x1) = 2x0 + 2x1, [isNatKind](x0) = x0, [isNat](x0) = x0, [nil] = 2, [isNatIListKind](x0) = 2x0, [a__isNatKind](x0) = x0, [a__isNatIListKind](x0) = 2x0, [length](x0) = 3x0, [a__and](x0, x1) = 2x0 + 2x1, [s](x0) = 2x0, [a__length](x0) = 3x0, [mark](x0) = x0, [a__U61](x0, x1) = x0 + 6x1, [a__U53](x0) = x0, [a__U52](x0, x1) = x0 + x1, [a__U51](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0) = 2x0, [a__isNatIList](x0) = 3x0, [a__U42](x0, x1) = x0 + 6x1, [a__U41](x0, x1, x2) = x0 + x1 + 6x2, [a__U32](x0) = x0, [a__U31](x0, x1) = x0 + x1, [a__U22](x0) = x0, [a__isNat](x0) = x0, [a__U21](x0, x1) = x0 + x1, [a__U12](x0) = x0, [a__isNatList](x0) = x0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [cons](x0, x1) = 3x0 + 7x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = V1 >= V1 = a__U12(a__isNatList(V1)) a__U12(tt()) = 0 >= 0 = tt() a__U21(tt(),V1) = V1 >= V1 = a__U22(a__isNat(V1)) a__U22(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= V = a__U32(a__isNatList(V)) a__U32(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + 6V2 >= V1 + 6V2 = a__U42(a__isNat(V1),V2) a__U42(tt(),V2) = 6V2 >= 6V2 = a__U43(a__isNatIList(V2)) a__U43(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52(a__isNat(V1),V2) a__U52(tt(),V2) = V2 >= V2 = a__U53(a__isNatList(V2)) a__U53(tt()) = 0 >= 0 = tt() a__U61(tt(),L) = 6L >= 6L = s(a__length(mark(L))) a__and(tt(),X) = 2X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 3V1 >= 3V1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 2V1 >= 2V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 3V >= 3V = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 9V1 + 21V2 >= 3V1 + 10V2 = a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(nil()) = 4 >= 0 = tt() a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 6V1 + 14V2 >= 2V1 + 4V2 = a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 3V1 >= 2V1 = a__isNatIListKind(V1) a__isNatKind(s(V1)) = 2V1 >= V1 = a__isNatKind(V1) a__isNatList(nil()) = 2 >= 0 = tt() a__isNatList(cons(V1,V2)) = 3V1 + 7V2 >= 3V1 + 5V2 = a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(nil()) = 6 >= 0 = 0() a__length(cons(N,L)) = 21L + 9N >= 18L + 8N = a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X)) = X >= X = a__U12(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = a__U21(mark(X1),X2) mark(U22(X)) = X >= X = a__U22(mark(X)) mark(isNat(X)) = X >= X = a__isNat(X) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X)) = X >= X = a__U32(mark(X)) mark(U41(X1,X2,X3)) = X1 + X2 + 6X3 >= X1 + X2 + 6X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = X1 + 6X2 >= X1 + 6X2 = a__U42(mark(X1),X2) mark(U43(X)) = 2X >= 2X = a__U43(mark(X)) mark(isNatIList(X)) = 3X >= 3X = a__isNatIList(X) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = a__U52(mark(X1),X2) mark(U53(X)) = X >= X = a__U53(mark(X)) mark(U61(X1,X2)) = X1 + 6X2 >= X1 + 6X2 = a__U61(mark(X1),X2) mark(length(X)) = 3X >= 3X = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNatIListKind(X)) = 2X >= 2X = a__isNatIListKind(X) mark(isNatKind(X)) = X >= X = a__isNatKind(X) mark(cons(X1,X2)) = 3X1 + 7X2 >= 3X1 + 7X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 2X >= 2X = s(mark(X)) mark(nil()) = 2 >= 2 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X) = X >= X = U12(X) a__isNatList(X) = X >= X = isNatList(X) a__U21(X1,X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) a__U22(X) = X >= X = U22(X) a__isNat(X) = X >= X = isNat(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X) = X >= X = U32(X) a__U41(X1,X2,X3) = X1 + X2 + 6X3 >= X1 + X2 + 6X3 = U41(X1,X2,X3) a__U42(X1,X2) = X1 + 6X2 >= X1 + 6X2 = U42(X1,X2) a__U43(X) = 2X >= 2X = U43(X) a__isNatIList(X) = 3X >= 3X = isNatIList(X) a__U51(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) a__U53(X) = X >= X = U53(X) a__U61(X1,X2) = X1 + 6X2 >= X1 + 6X2 = U61(X1,X2) a__length(X) = 3X >= 3X = length(X) a__and(X1,X2) = 2X1 + 2X2 >= 2X1 + 2X2 = and(X1,X2) a__isNatIListKind(X) = 2X >= 2X = isNatIListKind(X) a__isNatKind(X) = X >= X = isNatKind(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatList(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Matrix Interpretation Processor: dim=1 interpretation: [U61](x0, x1) = x0 + 4x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [isNatIList](x0) = 2x0, [U43](x0) = x0, [U42](x0, x1) = x0 + 3x1, [U41](x0, x1, x2) = x0 + x1 + 3x2, [U32](x0) = x0, [U31](x0, x1) = x0 + x1, [U22](x0) = x0, [U21](x0, x1) = x0 + 3x1, [isNatList](x0) = x0, [U12](x0) = x0, [U11](x0, x1) = x0 + x1, [and](x0, x1) = x0 + x1, [isNatKind](x0) = x0, [isNat](x0) = x0, [nil] = 6, [isNatIListKind](x0) = x0, [a__isNatKind](x0) = x0, [a__isNatIListKind](x0) = x0, [length](x0) = x0, [a__and](x0, x1) = x0 + 2x1, [s](x0) = 2x0, [a__length](x0) = x0, [mark](x0) = 2x0, [a__U61](x0, x1) = x0 + 4x1, [a__U53](x0) = x0, [a__U52](x0, x1) = x0 + x1, [a__U51](x0, x1, x2) = x0 + 2x1 + x2, [a__U43](x0) = x0, [a__isNatIList](x0) = 2x0, [a__U42](x0, x1) = x0 + 3x1, [a__U41](x0, x1, x2) = x0 + 2x1 + 3x2, [a__U32](x0) = x0, [a__U31](x0, x1) = x0 + x1, [a__U22](x0) = x0, [a__isNat](x0) = 2x0, [a__U21](x0, x1) = x0 + 3x1, [a__U12](x0) = x0, [a__isNatList](x0) = x0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [cons](x0, x1) = 4x0 + 7x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = V1 >= V1 = a__U12(a__isNatList(V1)) a__U12(tt()) = 0 >= 0 = tt() a__U21(tt(),V1) = 3V1 >= 2V1 = a__U22(a__isNat(V1)) a__U22(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V >= V = a__U32(a__isNatList(V)) a__U32(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 2V1 + 3V2 >= 2V1 + 3V2 = a__U42(a__isNat(V1),V2) a__U42(tt(),V2) = 3V2 >= 2V2 = a__U43(a__isNatIList(V2)) a__U43(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 2V1 + V2 >= 2V1 + V2 = a__U52(a__isNat(V1),V2) a__U52(tt(),V2) = V2 >= V2 = a__U53(a__isNatList(V2)) a__U53(tt()) = 0 >= 0 = tt() a__U61(tt(),L) = 4L >= 4L = s(a__length(mark(L))) a__and(tt(),X) = 2X >= 2X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 2V1 >= 2V1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 4V1 >= 4V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 2V >= 2V = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 8V1 + 14V2 >= 3V1 + 5V2 = a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 4V1 + 7V2 >= V1 + 2V2 = a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = V1 >= V1 = a__isNatIListKind(V1) a__isNatKind(s(V1)) = 2V1 >= V1 = a__isNatKind(V1) a__isNatList(cons(V1,V2)) = 4V1 + 7V2 >= 3V1 + 3V2 = a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) = 7L + 4N >= 7L + 4N = a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = a__U11(mark(X1),X2) mark(U12(X)) = 2X >= 2X = a__U12(mark(X)) mark(isNatList(X)) = 2X >= X = a__isNatList(X) mark(U21(X1,X2)) = 2X1 + 6X2 >= 2X1 + 3X2 = a__U21(mark(X1),X2) mark(U22(X)) = 2X >= 2X = a__U22(mark(X)) mark(isNat(X)) = 2X >= 2X = a__isNat(X) mark(U31(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = a__U31(mark(X1),X2) mark(U32(X)) = 2X >= 2X = a__U32(mark(X)) mark(U41(X1,X2,X3)) = 2X1 + 2X2 + 6X3 >= 2X1 + 2X2 + 3X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = 2X1 + 6X2 >= 2X1 + 3X2 = a__U42(mark(X1),X2) mark(U43(X)) = 2X >= 2X = a__U43(mark(X)) mark(isNatIList(X)) = 4X >= 2X = a__isNatIList(X) mark(U51(X1,X2,X3)) = 2X1 + 2X2 + 2X3 >= 2X1 + 2X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = a__U52(mark(X1),X2) mark(U53(X)) = 2X >= 2X = a__U53(mark(X)) mark(U61(X1,X2)) = 2X1 + 8X2 >= 2X1 + 4X2 = a__U61(mark(X1),X2) mark(length(X)) = 2X >= 2X = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNatIListKind(X)) = 2X >= X = a__isNatIListKind(X) mark(isNatKind(X)) = 2X >= X = a__isNatKind(X) mark(cons(X1,X2)) = 8X1 + 14X2 >= 8X1 + 7X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 4X >= 4X = s(mark(X)) mark(nil()) = 12 >= 6 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X) = X >= X = U12(X) a__isNatList(X) = X >= X = isNatList(X) a__U21(X1,X2) = X1 + 3X2 >= X1 + 3X2 = U21(X1,X2) a__U22(X) = X >= X = U22(X) a__isNat(X) = 2X >= X = isNat(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X) = X >= X = U32(X) a__U41(X1,X2,X3) = X1 + 2X2 + 3X3 >= X1 + X2 + 3X3 = U41(X1,X2,X3) a__U42(X1,X2) = X1 + 3X2 >= X1 + 3X2 = U42(X1,X2) a__U43(X) = X >= X = U43(X) a__isNatIList(X) = 2X >= 2X = isNatIList(X) a__U51(X1,X2,X3) = X1 + 2X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) a__U53(X) = X >= X = U53(X) a__U61(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U61(X1,X2) a__length(X) = X >= X = length(X) a__and(X1,X2) = X1 + 2X2 >= X1 + X2 = and(X1,X2) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__isNatKind(X) = X >= X = isNatKind(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatList(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Matrix Interpretation Processor: dim=1 interpretation: [U61](x0, x1) = x0 + 6x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + x2, [isNatIList](x0) = 2x0 + 1, [U43](x0) = x0, [U42](x0, x1) = 2x0 + 2x1 + 1, [U41](x0, x1, x2) = 2x0 + 2x1 + 2x2 + 1, [U32](x0) = x0, [U31](x0, x1) = x0 + x1 + 1, [U22](x0) = x0, [U21](x0, x1) = x0 + x1, [isNatList](x0) = x0, [U12](x0) = x0, [U11](x0, x1) = x0 + x1, [and](x0, x1) = 2x0 + 2x1, [isNatKind](x0) = 2x0, [isNat](x0) = x0, [isNatIListKind](x0) = x0, [a__isNatKind](x0) = 2x0, [a__isNatIListKind](x0) = x0, [length](x0) = 2x0, [a__and](x0, x1) = 2x0 + 2x1, [s](x0) = 3x0, [a__length](x0) = 2x0, [mark](x0) = x0, [a__U61](x0, x1) = x0 + 6x1, [a__U53](x0) = x0, [a__U52](x0, x1) = x0 + x1, [a__U51](x0, x1, x2) = x0 + x1 + x2, [a__U43](x0) = x0, [a__isNatIList](x0) = 2x0 + 1, [a__U42](x0, x1) = 2x0 + 2x1 + 1, [a__U41](x0, x1, x2) = 2x0 + 2x1 + 2x2 + 1, [a__U32](x0) = x0, [a__U31](x0, x1) = x0 + x1 + 1, [a__U22](x0) = x0, [a__isNat](x0) = x0, [a__U21](x0, x1) = x0 + x1, [a__U12](x0) = x0, [a__isNatList](x0) = x0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [cons](x0, x1) = 6x0 + 7x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = V1 >= V1 = a__U12(a__isNatList(V1)) a__U12(tt()) = 0 >= 0 = tt() a__U21(tt(),V1) = V1 >= V1 = a__U22(a__isNat(V1)) a__U22(tt()) = 0 >= 0 = tt() a__U31(tt(),V) = V + 1 >= V = a__U32(a__isNatList(V)) a__U32(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 2V1 + 2V2 + 1 >= 2V1 + 2V2 + 1 = a__U42(a__isNat(V1),V2) a__U42(tt(),V2) = 2V2 + 1 >= 2V2 + 1 = a__U43(a__isNatIList(V2)) a__U43(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + V2 >= V1 + V2 = a__U52(a__isNat(V1),V2) a__U52(tt(),V2) = V2 >= V2 = a__U53(a__isNatList(V2)) a__U53(tt()) = 0 >= 0 = tt() a__U61(tt(),L) = 6L >= 6L = s(a__length(mark(L))) a__and(tt(),X) = 2X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 2V1 >= 2V1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 3V1 >= 3V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 2V + 1 >= 2V + 1 = a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 12V1 + 14V2 + 1 >= 10V1 + 6V2 + 1 = a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 6V1 + 7V2 >= 4V1 + 2V2 = a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 4V1 >= V1 = a__isNatIListKind(V1) a__isNatKind(s(V1)) = 6V1 >= 2V1 = a__isNatKind(V1) a__isNatList(cons(V1,V2)) = 6V1 + 7V2 >= 5V1 + 3V2 = a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) = 14L + 12N >= 14L + 12N = a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X)) = X >= X = a__U12(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = a__U21(mark(X1),X2) mark(U22(X)) = X >= X = a__U22(mark(X)) mark(isNat(X)) = X >= X = a__isNat(X) mark(U31(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__U31(mark(X1),X2) mark(U32(X)) = X >= X = a__U32(mark(X)) mark(U41(X1,X2,X3)) = 2X1 + 2X2 + 2X3 + 1 >= 2X1 + 2X2 + 2X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = a__U42(mark(X1),X2) mark(U43(X)) = X >= X = a__U43(mark(X)) mark(isNatIList(X)) = 2X + 1 >= 2X + 1 = a__isNatIList(X) mark(U51(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = a__U52(mark(X1),X2) mark(U53(X)) = X >= X = a__U53(mark(X)) mark(U61(X1,X2)) = X1 + 6X2 >= X1 + 6X2 = a__U61(mark(X1),X2) mark(length(X)) = 2X >= 2X = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNatIListKind(X)) = X >= X = a__isNatIListKind(X) mark(isNatKind(X)) = 2X >= 2X = a__isNatKind(X) mark(cons(X1,X2)) = 6X1 + 7X2 >= 6X1 + 7X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 3X >= 3X = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = X1 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X) = X >= X = U12(X) a__isNatList(X) = X >= X = isNatList(X) a__U21(X1,X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) a__U22(X) = X >= X = U22(X) a__isNat(X) = X >= X = isNat(X) a__U31(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = U31(X1,X2) a__U32(X) = X >= X = U32(X) a__U41(X1,X2,X3) = 2X1 + 2X2 + 2X3 + 1 >= 2X1 + 2X2 + 2X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2) = 2X1 + 2X2 + 1 >= 2X1 + 2X2 + 1 = U42(X1,X2) a__U43(X) = X >= X = U43(X) a__isNatIList(X) = 2X + 1 >= 2X + 1 = isNatIList(X) a__U51(X1,X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) a__U53(X) = X >= X = U53(X) a__U61(X1,X2) = X1 + 6X2 >= X1 + 6X2 = U61(X1,X2) a__length(X) = 2X >= 2X = length(X) a__and(X1,X2) = 2X1 + 2X2 >= 2X1 + 2X2 = and(X1,X2) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__isNatKind(X) = 2X >= 2X = isNatKind(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Matrix Interpretation Processor: dim=1 interpretation: [U61](x0, x1) = x0 + 6x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + x1 + 2x2, [isNatIList](x0) = 4x0, [U43](x0) = x0, [U42](x0, x1) = x0 + 5x1, [U41](x0, x1, x2) = x0 + x1 + 5x2, [U32](x0) = x0 + 4, [U31](x0, x1) = x0 + x1, [U22](x0) = x0, [U21](x0, x1) = x0 + x1, [isNatList](x0) = x0, [U12](x0) = x0, [U11](x0, x1) = x0 + x1, [and](x0, x1) = 2x0 + 2x1, [isNatKind](x0) = x0, [isNat](x0) = x0, [isNatIListKind](x0) = 2x0, [a__isNatKind](x0) = x0, [a__isNatIListKind](x0) = 2x0, [length](x0) = 3x0, [a__and](x0, x1) = 2x0 + 2x1, [s](x0) = 2x0, [a__length](x0) = 3x0, [mark](x0) = x0, [a__U61](x0, x1) = x0 + 6x1, [a__U53](x0) = x0, [a__U52](x0, x1) = x0 + x1, [a__U51](x0, x1, x2) = x0 + x1 + 2x2, [a__U43](x0) = x0, [a__isNatIList](x0) = 4x0, [a__U42](x0, x1) = x0 + 5x1, [a__U41](x0, x1, x2) = x0 + x1 + 5x2, [a__U32](x0) = x0 + 4, [a__U31](x0, x1) = x0 + x1, [a__U22](x0) = x0, [a__isNat](x0) = x0, [a__U21](x0, x1) = x0 + x1, [a__U12](x0) = x0, [a__isNatList](x0) = x0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [cons](x0, x1) = 3x0 + 6x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = V1 >= V1 = a__U12(a__isNatList(V1)) a__U12(tt()) = 0 >= 0 = tt() a__U21(tt(),V1) = V1 >= V1 = a__U22(a__isNat(V1)) a__U22(tt()) = 0 >= 0 = tt() a__U32(tt()) = 4 >= 0 = tt() a__U41(tt(),V1,V2) = V1 + 5V2 >= V1 + 5V2 = a__U42(a__isNat(V1),V2) a__U42(tt(),V2) = 5V2 >= 4V2 = a__U43(a__isNatIList(V2)) a__U43(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = V1 + 2V2 >= V1 + V2 = a__U52(a__isNat(V1),V2) a__U52(tt(),V2) = V2 >= V2 = a__U53(a__isNatList(V2)) a__U53(tt()) = 0 >= 0 = tt() a__U61(tt(),L) = 6L >= 6L = s(a__length(mark(L))) a__and(tt(),X) = 2X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 3V1 >= 3V1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 2V1 >= 2V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 4V >= 3V = a__U31(a__isNatIListKind(V),V) a__isNatIList(cons(V1,V2)) = 12V1 + 24V2 >= 3V1 + 9V2 = a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 6V1 + 12V2 >= 2V1 + 4V2 = a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 3V1 >= 2V1 = a__isNatIListKind(V1) a__isNatKind(s(V1)) = 2V1 >= V1 = a__isNatKind(V1) a__isNatList(cons(V1,V2)) = 3V1 + 6V2 >= 3V1 + 6V2 = a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) = 18L + 9N >= 18L + 8N = a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = X1 + X2 >= X1 + X2 = a__U11(mark(X1),X2) mark(U12(X)) = X >= X = a__U12(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = a__U21(mark(X1),X2) mark(U22(X)) = X >= X = a__U22(mark(X)) mark(isNat(X)) = X >= X = a__isNat(X) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X)) = X + 4 >= X + 4 = a__U32(mark(X)) mark(U41(X1,X2,X3)) = X1 + X2 + 5X3 >= X1 + X2 + 5X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = X1 + 5X2 >= X1 + 5X2 = a__U42(mark(X1),X2) mark(U43(X)) = X >= X = a__U43(mark(X)) mark(isNatIList(X)) = 4X >= 4X = a__isNatIList(X) mark(U51(X1,X2,X3)) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = a__U52(mark(X1),X2) mark(U53(X)) = X >= X = a__U53(mark(X)) mark(U61(X1,X2)) = X1 + 6X2 >= X1 + 6X2 = a__U61(mark(X1),X2) mark(length(X)) = 3X >= 3X = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNatIListKind(X)) = 2X >= 2X = a__isNatIListKind(X) mark(isNatKind(X)) = X >= X = a__isNatKind(X) mark(cons(X1,X2)) = 3X1 + 6X2 >= 3X1 + 6X2 = 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 + X2 >= X1 + X2 = U11(X1,X2) a__U12(X) = X >= X = U12(X) a__isNatList(X) = X >= X = isNatList(X) a__U21(X1,X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) a__U22(X) = X >= X = U22(X) a__isNat(X) = X >= X = isNat(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X) = X + 4 >= X + 4 = U32(X) a__U41(X1,X2,X3) = X1 + X2 + 5X3 >= X1 + X2 + 5X3 = U41(X1,X2,X3) a__U42(X1,X2) = X1 + 5X2 >= X1 + 5X2 = U42(X1,X2) a__U43(X) = X >= X = U43(X) a__isNatIList(X) = 4X >= 4X = isNatIList(X) a__U51(X1,X2,X3) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = U51(X1,X2,X3) a__U52(X1,X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) a__U53(X) = X >= X = U53(X) a__U61(X1,X2) = X1 + 6X2 >= X1 + 6X2 = U61(X1,X2) a__length(X) = 3X >= 3X = length(X) a__and(X1,X2) = 2X1 + 2X2 >= 2X1 + 2X2 = and(X1,X2) a__isNatIListKind(X) = 2X >= 2X = isNatIListKind(X) a__isNatKind(X) = X >= X = isNatKind(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Matrix Interpretation Processor: dim=1 interpretation: [U61](x0, x1) = x0 + 7x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + 4x1 + x2, [isNatIList](x0) = 2x0 + 1, [U43](x0) = x0, [U42](x0, x1) = x0 + 4x1 + 1, [U41](x0, x1, x2) = 3x0 + 2x1 + 4x2 + 1, [U32](x0) = x0 + 1, [U31](x0, x1) = x0 + x1, [U22](x0) = x0, [U21](x0, x1) = 2x0 + 2x1, [isNatList](x0) = x0, [U12](x0) = x0, [U11](x0, x1) = x0 + 4x1, [and](x0, x1) = 2x0 + 2x1, [isNatKind](x0) = x0, [isNat](x0) = 2x0, [isNatIListKind](x0) = x0, [a__isNatKind](x0) = x0, [a__isNatIListKind](x0) = x0, [length](x0) = 3x0, [a__and](x0, x1) = 2x0 + 2x1, [s](x0) = 2x0, [a__length](x0) = 3x0, [mark](x0) = x0, [a__U61](x0, x1) = x0 + 7x1, [a__U53](x0) = x0, [a__U52](x0, x1) = x0 + x1, [a__U51](x0, x1, x2) = x0 + 4x1 + x2, [a__U43](x0) = x0, [a__isNatIList](x0) = 2x0 + 1, [a__U42](x0, x1) = x0 + 4x1 + 1, [a__U41](x0, x1, x2) = 3x0 + 2x1 + 4x2 + 1, [a__U32](x0) = x0 + 1, [a__U31](x0, x1) = x0 + x1, [a__U22](x0) = x0, [a__isNat](x0) = 2x0, [a__U21](x0, x1) = 2x0 + 2x1, [a__U12](x0) = x0, [a__isNatList](x0) = x0, [a__U11](x0, x1) = x0 + 4x1, [tt] = 0, [cons](x0, x1) = 6x0 + 5x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = 4V1 >= V1 = a__U12(a__isNatList(V1)) a__U12(tt()) = 0 >= 0 = tt() a__U21(tt(),V1) = 2V1 >= 2V1 = a__U22(a__isNat(V1)) a__U22(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 2V1 + 4V2 + 1 >= 2V1 + 4V2 + 1 = a__U42(a__isNat(V1),V2) a__U42(tt(),V2) = 4V2 + 1 >= 2V2 + 1 = a__U43(a__isNatIList(V2)) a__U43(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 4V1 + V2 >= 2V1 + V2 = a__U52(a__isNat(V1),V2) a__U52(tt(),V2) = V2 >= V2 = a__U53(a__isNatList(V2)) a__U53(tt()) = 0 >= 0 = tt() a__U61(tt(),L) = 7L >= 6L = s(a__length(mark(L))) a__and(tt(),X) = 2X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 6V1 >= 5V1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 4V1 >= 4V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(V) = 2V + 1 >= 2V = a__U31(a__isNatIListKind(V),V) a__isNatIList(cons(V1,V2)) = 12V1 + 10V2 + 1 >= 8V1 + 10V2 + 1 = a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 6V1 + 5V2 >= 2V1 + 2V2 = a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = 3V1 >= V1 = a__isNatIListKind(V1) a__isNatKind(s(V1)) = 2V1 >= V1 = a__isNatKind(V1) a__isNatList(cons(V1,V2)) = 6V1 + 5V2 >= 6V1 + 3V2 = a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) = 15L + 18N >= 15L + 12N = a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = a__U11(mark(X1),X2) mark(U12(X)) = X >= X = a__U12(mark(X)) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(U21(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__U21(mark(X1),X2) mark(U22(X)) = X >= X = a__U22(mark(X)) mark(isNat(X)) = 2X >= 2X = a__isNat(X) mark(U31(X1,X2)) = X1 + X2 >= X1 + X2 = a__U31(mark(X1),X2) mark(U32(X)) = X + 1 >= X + 1 = a__U32(mark(X)) mark(U41(X1,X2,X3)) = 3X1 + 2X2 + 4X3 + 1 >= 3X1 + 2X2 + 4X3 + 1 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = X1 + 4X2 + 1 >= X1 + 4X2 + 1 = a__U42(mark(X1),X2) mark(U43(X)) = X >= X = a__U43(mark(X)) mark(isNatIList(X)) = 2X + 1 >= 2X + 1 = a__isNatIList(X) mark(U51(X1,X2,X3)) = X1 + 4X2 + X3 >= X1 + 4X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = X1 + X2 >= X1 + X2 = a__U52(mark(X1),X2) mark(U53(X)) = X >= X = a__U53(mark(X)) mark(U61(X1,X2)) = X1 + 7X2 >= X1 + 7X2 = a__U61(mark(X1),X2) mark(length(X)) = 3X >= 3X = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNatIListKind(X)) = X >= X = a__isNatIListKind(X) mark(isNatKind(X)) = X >= X = a__isNatKind(X) mark(cons(X1,X2)) = 6X1 + 5X2 >= 6X1 + 5X2 = 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 + 4X2 >= X1 + 4X2 = U11(X1,X2) a__U12(X) = X >= X = U12(X) a__isNatList(X) = X >= X = isNatList(X) a__U21(X1,X2) = 2X1 + 2X2 >= 2X1 + 2X2 = U21(X1,X2) a__U22(X) = X >= X = U22(X) a__isNat(X) = 2X >= 2X = isNat(X) a__U31(X1,X2) = X1 + X2 >= X1 + X2 = U31(X1,X2) a__U32(X) = X + 1 >= X + 1 = U32(X) a__U41(X1,X2,X3) = 3X1 + 2X2 + 4X3 + 1 >= 3X1 + 2X2 + 4X3 + 1 = U41(X1,X2,X3) a__U42(X1,X2) = X1 + 4X2 + 1 >= X1 + 4X2 + 1 = U42(X1,X2) a__U43(X) = X >= X = U43(X) a__isNatIList(X) = 2X + 1 >= 2X + 1 = isNatIList(X) a__U51(X1,X2,X3) = X1 + 4X2 + X3 >= X1 + 4X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) a__U53(X) = X >= X = U53(X) a__U61(X1,X2) = X1 + 7X2 >= X1 + 7X2 = U61(X1,X2) a__length(X) = 3X >= 3X = length(X) a__and(X1,X2) = 2X1 + 2X2 >= 2X1 + 2X2 = and(X1,X2) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__isNatKind(X) = X >= X = isNatKind(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Matrix Interpretation Processor: dim=1 interpretation: [U61](x0, x1) = x0 + 4x1, [U53](x0) = x0, [U52](x0, x1) = x0 + x1, [U51](x0, x1, x2) = x0 + 4x1 + x2, [isNatIList](x0) = x0, [U43](x0) = x0, [U42](x0, x1) = x0 + x1, [U41](x0, x1, x2) = 2x0 + 3x1 + x2, [U32](x0) = 2x0 + 4, [U31](x0, x1) = x0 + 4x1, [U22](x0) = x0, [U21](x0, x1) = 2x0 + 3x1, [isNatList](x0) = x0, [U12](x0) = x0, [U11](x0, x1) = 2x0 + x1, [and](x0, x1) = x0 + x1, [isNatKind](x0) = x0, [isNat](x0) = 2x0, [isNatIListKind](x0) = x0, [a__isNatKind](x0) = x0, [a__isNatIListKind](x0) = x0, [length](x0) = x0, [a__and](x0, x1) = x0 + 2x1, [s](x0) = 2x0, [a__length](x0) = x0, [mark](x0) = 2x0, [a__U61](x0, x1) = x0 + 4x1, [a__U53](x0) = x0, [a__U52](x0, x1) = x0 + x1, [a__U51](x0, x1, x2) = x0 + 5x1 + x2, [a__U43](x0) = x0, [a__isNatIList](x0) = x0, [a__U42](x0, x1) = x0 + x1, [a__U41](x0, x1, x2) = 2x0 + 3x1 + x2, [a__U32](x0) = 2x0 + 7, [a__U31](x0, x1) = x0 + 6x1, [a__U22](x0) = x0, [a__isNat](x0) = 3x0, [a__U21](x0, x1) = 2x0 + 3x1, [a__U12](x0) = x0, [a__isNatList](x0) = x0, [a__U11](x0, x1) = 2x0 + x1, [tt] = 0, [cons](x0, x1) = 6x0 + 7x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = V1 >= V1 = a__U12(a__isNatList(V1)) a__U12(tt()) = 0 >= 0 = tt() a__U21(tt(),V1) = 3V1 >= 3V1 = a__U22(a__isNat(V1)) a__U22(tt()) = 0 >= 0 = tt() a__U41(tt(),V1,V2) = 3V1 + V2 >= 3V1 + V2 = a__U42(a__isNat(V1),V2) a__U42(tt(),V2) = V2 >= V2 = a__U43(a__isNatIList(V2)) a__U43(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 5V1 + V2 >= 3V1 + V2 = a__U52(a__isNat(V1),V2) a__U52(tt(),V2) = V2 >= V2 = a__U53(a__isNatList(V2)) a__U53(tt()) = 0 >= 0 = tt() a__U61(tt(),L) = 4L >= 4L = s(a__length(mark(L))) a__and(tt(),X) = 2X >= 2X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 3V1 >= 3V1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 6V1 >= 5V1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(cons(V1,V2)) = 6V1 + 7V2 >= 5V1 + 5V2 = a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) = 0 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = 6V1 + 7V2 >= V1 + 2V2 = a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) = 0 >= 0 = tt() a__isNatKind(length(V1)) = V1 >= V1 = a__isNatIListKind(V1) a__isNatKind(s(V1)) = 2V1 >= V1 = a__isNatKind(V1) a__isNatList(cons(V1,V2)) = 6V1 + 7V2 >= 6V1 + 3V2 = a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) = 7L + 6N >= 7L + 6N = a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 4X1 + 2X2 >= 4X1 + X2 = a__U11(mark(X1),X2) mark(U12(X)) = 2X >= 2X = a__U12(mark(X)) mark(isNatList(X)) = 2X >= X = a__isNatList(X) mark(U21(X1,X2)) = 4X1 + 6X2 >= 4X1 + 3X2 = a__U21(mark(X1),X2) mark(U22(X)) = 2X >= 2X = a__U22(mark(X)) mark(isNat(X)) = 4X >= 3X = a__isNat(X) mark(U31(X1,X2)) = 2X1 + 8X2 >= 2X1 + 6X2 = a__U31(mark(X1),X2) mark(U32(X)) = 4X + 8 >= 4X + 7 = a__U32(mark(X)) mark(U41(X1,X2,X3)) = 4X1 + 6X2 + 2X3 >= 4X1 + 3X2 + X3 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = a__U42(mark(X1),X2) mark(U43(X)) = 2X >= 2X = a__U43(mark(X)) mark(isNatIList(X)) = 2X >= X = a__isNatIList(X) mark(U51(X1,X2,X3)) = 2X1 + 8X2 + 2X3 >= 2X1 + 5X2 + X3 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = a__U52(mark(X1),X2) mark(U53(X)) = 2X >= 2X = a__U53(mark(X)) mark(U61(X1,X2)) = 2X1 + 8X2 >= 2X1 + 4X2 = a__U61(mark(X1),X2) mark(length(X)) = 2X >= 2X = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNatIListKind(X)) = 2X >= X = a__isNatIListKind(X) mark(isNatKind(X)) = 2X >= X = a__isNatKind(X) mark(cons(X1,X2)) = 12X1 + 14X2 >= 12X1 + 7X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 4X >= 4X = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 2X1 + X2 >= 2X1 + X2 = U11(X1,X2) a__U12(X) = X >= X = U12(X) a__isNatList(X) = X >= X = isNatList(X) a__U21(X1,X2) = 2X1 + 3X2 >= 2X1 + 3X2 = U21(X1,X2) a__U22(X) = X >= X = U22(X) a__isNat(X) = 3X >= 2X = isNat(X) a__U31(X1,X2) = X1 + 6X2 >= X1 + 4X2 = U31(X1,X2) a__U32(X) = 2X + 7 >= 2X + 4 = U32(X) a__U41(X1,X2,X3) = 2X1 + 3X2 + X3 >= 2X1 + 3X2 + X3 = U41(X1,X2,X3) a__U42(X1,X2) = X1 + X2 >= X1 + X2 = U42(X1,X2) a__U43(X) = X >= X = U43(X) a__isNatIList(X) = X >= X = isNatIList(X) a__U51(X1,X2,X3) = X1 + 5X2 + X3 >= X1 + 4X2 + X3 = U51(X1,X2,X3) a__U52(X1,X2) = X1 + X2 >= X1 + X2 = U52(X1,X2) a__U53(X) = X >= X = U53(X) a__U61(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U61(X1,X2) a__length(X) = X >= X = length(X) a__and(X1,X2) = X1 + 2X2 >= X1 + X2 = and(X1,X2) a__isNatIListKind(X) = X >= X = isNatIListKind(X) a__isNatKind(X) = X >= X = isNatKind(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) DP Processor: DPs: a__U11#(tt(),V1) -> a__isNatList#(V1) a__U11#(tt(),V1) -> a__U12#(a__isNatList(V1)) a__U21#(tt(),V1) -> a__isNat#(V1) a__U21#(tt(),V1) -> a__U22#(a__isNat(V1)) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__U42#(tt(),V2) -> a__U43#(a__isNatIList(V2)) a__U51#(tt(),V1,V2) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) a__U52#(tt(),V2) -> a__U53#(a__isNatList(V2)) a__U61#(tt(),L) -> mark#(L) a__U61#(tt(),L) -> a__length#(mark(L)) a__and#(tt(),X) -> mark#(X) 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#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> a__U12#(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(X)) -> mark#(X) mark#(U22(X)) -> a__U22#(mark(X)) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> a__U43#(mark(X)) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> a__U53#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) TDG Processor: DPs: a__U11#(tt(),V1) -> a__isNatList#(V1) a__U11#(tt(),V1) -> a__U12#(a__isNatList(V1)) a__U21#(tt(),V1) -> a__isNat#(V1) a__U21#(tt(),V1) -> a__U22#(a__isNat(V1)) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__U42#(tt(),V2) -> a__U43#(a__isNatIList(V2)) a__U51#(tt(),V1,V2) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) a__U52#(tt(),V2) -> a__U53#(a__isNatList(V2)) a__U61#(tt(),L) -> mark#(L) a__U61#(tt(),L) -> a__length#(mark(L)) a__and#(tt(),X) -> mark#(X) 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#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> a__U12#(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(X)) -> mark#(X) mark#(U22(X)) -> a__U22#(mark(X)) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> a__U43#(mark(X)) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> a__U53#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) graph: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) -> a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) -> a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) -> a__and#(tt(),X) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) a__and#(tt(),X) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(length(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U53(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__and#(tt(),X) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U43(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) a__and#(tt(),X) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U22(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U12(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(zeros()) -> a__zeros#() a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) -> a__and#(tt(),X) -> mark#(X) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) -> a__and#(tt(),X) -> mark#(X) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) -> a__U61#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) -> a__U61#(tt(),L) -> mark#(L) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) -> a__U61#(tt(),L) -> a__length#(mark(L)) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) -> a__U61#(tt(),L) -> mark#(L) mark#(U53(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U53(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U53(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U53(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U53(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U53(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U53(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U53(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U52(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) -> a__U52#(tt(),V2) -> a__U53#(a__isNatList(V2)) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) -> a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) -> a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) -> a__U51#(tt(),V1,V2) -> a__isNat#(V1) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) mark#(U43(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U43(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U43(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U43(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U43(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U43(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U43(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U43(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U42(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) -> a__U42#(tt(),V2) -> a__U43#(a__isNatIList(V2)) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) -> a__U42#(tt(),V2) -> a__isNatIList#(V2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) -> a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) -> a__U41#(tt(),V1,V2) -> a__isNat#(V1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U22(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U22(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U22(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U22(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U22(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U22(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U22(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U22(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U21(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) -> a__U21#(tt(),V1) -> a__U22#(a__isNat(V1)) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) -> a__U21#(tt(),V1) -> a__isNat#(V1) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) mark#(U12(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U12(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U12(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U12(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U12(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U12(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U12(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),V1) -> a__U12#(a__isNatList(V1)) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),V1) -> a__isNatList#(V1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) -> a__and#(tt(),X) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(isNatKind(X)) -> a__isNatKind#(X) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) mark#(isNatKind(X)) -> a__isNatKind#(X) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(s(V1)) -> a__isNatKind#(V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(length(V1)) -> a__isNatIListKind#(V1) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) -> a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) -> a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__isNatList#(L) mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(length(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(length(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(length(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(length(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(length(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(length(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(s(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(s(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(s(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(s(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() a__U61#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) a__U61#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__U61#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__U61#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__isNatList#(L) a__U61#(tt(),L) -> mark#(L) -> mark#(s(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(cons(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(isNatKind(X)) -> a__isNatKind#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(and(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(length(X)) -> a__length#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(length(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U61(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(U53(X)) -> a__U53#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U53(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U52(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__U61#(tt(),L) -> mark#(L) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(isNatIList(X)) -> a__isNatIList#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U43(X)) -> a__U43#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U43(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U42(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) a__U61#(tt(),L) -> mark#(L) -> mark#(U41(X1,X2,X3)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U31(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(isNat(X)) -> a__isNat#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U22(X)) -> a__U22#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U22(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U21(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(isNatList(X)) -> a__isNatList#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U12(X)) -> a__U12#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U12(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(zeros()) -> a__zeros#() a__U52#(tt(),V2) -> a__isNatList#(V2) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U52#(tt(),V2) -> a__isNatList#(V2) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__U52#(tt(),V2) -> a__isNatList#(V2) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) -> a__U52#(tt(),V2) -> a__U53#(a__isNatList(V2)) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) -> a__U52#(tt(),V2) -> a__isNatList#(V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U51#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNatKind#(V1) a__U51#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__U51#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) -> a__and#(tt(),X) -> mark#(X) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) -> a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) -> a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U42#(tt(),V2) -> a__isNatIList#(V2) -> a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) -> a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__U42#(tt(),V2) -> a__isNatIList#(V2) -> a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) -> a__U42#(tt(),V2) -> a__U43#(a__isNatIList(V2)) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) -> a__U42#(tt(),V2) -> a__isNatIList#(V2) a__U41#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U41#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNatKind#(V1) a__U41#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__U41#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) -> a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) -> a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) -> a__U11#(tt(),V1) -> a__U12#(a__isNatList(V1)) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) -> a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) -> a__U21#(tt(),V1) -> a__U22#(a__isNat(V1)) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) -> a__U21#(tt(),V1) -> a__isNat#(V1) a__U21#(tt(),V1) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNatKind#(V1) a__U21#(tt(),V1) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__U21#(tt(),V1) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) -> a__and#(tt(),X) -> mark#(X) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) -> a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) -> a__U51#(tt(),V1,V2) -> a__isNat#(V1) a__U11#(tt(),V1) -> a__isNatList#(V1) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U11#(tt(),V1) -> a__isNatList#(V1) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__U11#(tt(),V1) -> a__isNatList#(V1) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) SCC Processor: #sccs: 1 #rules: 59 #arcs: 742/4761 DPs: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) 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__U21#(tt(),V1) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U12(X)) -> 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(X)) -> mark#(X) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) a__U61#(tt(),L) -> a__length#(mark(L)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Matrix Interpretation Processor: dim=1 usable rules: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) interpretation: [a__isNatKind#](x0) = 1, [a__isNatIListKind#](x0) = 1, [a__and#](x0, x1) = 1, [a__length#](x0) = 1, [mark#](x0) = 1, [a__U61#](x0, x1) = x0, [a__U52#](x0, x1) = 1, [a__U51#](x0, x1, x2) = 1, [a__isNatIList#](x0) = 1, [a__U42#](x0, x1) = 1, [a__U41#](x0, x1, x2) = 1, [a__isNat#](x0) = 1, [a__U21#](x0, x1) = 1, [a__isNatList#](x0) = 1, [a__U11#](x0, x1) = 1, [U61](x0, x1) = 0, [U53](x0) = x0, [U52](x0, x1) = 0, [U51](x0, x1, x2) = 0, [isNatIList](x0) = 0, [U43](x0) = 0, [U42](x0, x1) = 0, [U41](x0, x1, x2) = 0, [U31](x0, x1) = 0, [U22](x0) = 0, [U21](x0, x1) = x0, [isNatList](x0) = 0, [U12](x0) = 0, [U11](x0, x1) = 1, [and](x0, x1) = 0, [isNatKind](x0) = 0, [isNat](x0) = 1, [isNatIListKind](x0) = 0, [a__isNatKind](x0) = 1, [a__isNatIListKind](x0) = 1, [length](x0) = 0, [a__and](x0, x1) = x0, [s](x0) = 0, [a__length](x0) = 0, [mark](x0) = 1, [a__U61](x0, x1) = 0, [a__U53](x0) = x0, [a__U52](x0, x1) = 0, [a__U51](x0, x1, x2) = 0, [a__U43](x0) = x0, [a__isNatIList](x0) = 0, [a__U42](x0, x1) = 0, [a__U41](x0, x1, x2) = 0, [a__U31](x0, x1) = 1, [a__U22](x0) = 1, [a__isNat](x0) = 1, [a__U21](x0, x1) = x0, [a__U12](x0) = x0, [a__isNatList](x0) = 0, [a__U11](x0, x1) = 1, [tt] = 1, [cons](x0, x1) = x0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__isNatKind#(length(V1)) = 1 >= 1 = a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) = 1 >= 1 = a__isNatKind#(V1) a__isNatKind#(s(V1)) = 1 >= 1 = a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) = 1 >= 1 = a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) = 1 >= 1 = mark#(X) mark#(U11(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U11(X1,X2)) = 1 >= 1 = a__U11#(mark(X1),X2) a__U11#(tt(),V1) = 1 >= 1 = a__isNatList#(V1) a__isNatList#(cons(V1,V2)) = 1 >= 1 = a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) = 1 >= 1 = a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) = 1 >= 1 = a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) = 1 >= 1 = a__isNat#(V1) a__isNat#(length(V1)) = 1 >= 1 = a__isNatIListKind#(V1) a__isNat#(length(V1)) = 1 >= 1 = a__U11#(a__isNatIListKind(V1),V1) a__isNat#(s(V1)) = 1 >= 1 = a__isNatKind#(V1) a__isNat#(s(V1)) = 1 >= 1 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 1 >= 1 = a__isNat#(V1) a__U51#(tt(),V1,V2) = 1 >= 1 = a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) = 1 >= 1 = a__isNatList#(V2) mark#(U12(X)) = 1 >= 1 = mark#(X) mark#(isNatList(X)) = 1 >= 1 = a__isNatList#(X) mark#(U21(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U21(X1,X2)) = 1 >= 1 = a__U21#(mark(X1),X2) mark#(U22(X)) = 1 >= 1 = mark#(X) mark#(isNat(X)) = 1 >= 1 = a__isNat#(X) mark#(U31(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U41(X1,X2,X3)) = 1 >= 1 = a__U41#(mark(X1),X2,X3) a__U41#(tt(),V1,V2) = 1 >= 1 = a__isNat#(V1) a__U41#(tt(),V1,V2) = 1 >= 1 = a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) = 1 >= 1 = a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) = 1 >= 1 = a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) = 1 >= 1 = a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) = 1 >= 1 = a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(U42(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U42(X1,X2)) = 1 >= 1 = a__U42#(mark(X1),X2) mark#(U43(X)) = 1 >= 1 = mark#(X) mark#(isNatIList(X)) = 1 >= 1 = a__isNatIList#(X) mark#(U51(X1,X2,X3)) = 1 >= 1 = mark#(X1) mark#(U51(X1,X2,X3)) = 1 >= 1 = a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U52(X1,X2)) = 1 >= 1 = a__U52#(mark(X1),X2) mark#(U53(X)) = 1 >= 1 = mark#(X) mark#(U61(X1,X2)) = 1 >= 1 = mark#(X1) mark#(U61(X1,X2)) = 1 >= 1 = a__U61#(mark(X1),X2) a__U61#(tt(),L) = 1 >= 1 = mark#(L) mark#(length(X)) = 1 >= 1 = mark#(X) mark#(length(X)) = 1 >= 1 = a__length#(mark(X)) a__length#(cons(N,L)) = 1 >= 1 = a__isNatList#(L) a__length#(cons(N,L)) = 1 >= 1 = a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) = 1 >= 1 = a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__length#(cons(N,L)) = 1 >= 0 = a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) a__U61#(tt(),L) = 1 >= 1 = a__length#(mark(L)) mark#(and(X1,X2)) = 1 >= 1 = mark#(X1) mark#(and(X1,X2)) = 1 >= 1 = a__and#(mark(X1),X2) mark#(isNatIListKind(X)) = 1 >= 1 = a__isNatIListKind#(X) mark#(isNatKind(X)) = 1 >= 1 = a__isNatKind#(X) mark#(cons(X1,X2)) = 1 >= 1 = mark#(X1) mark#(s(X)) = 1 >= 1 = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),V1) = 1 >= 0 = a__U12(a__isNatList(V1)) a__U12(tt()) = 1 >= 1 = tt() a__U21(tt(),V1) = 1 >= 1 = a__U22(a__isNat(V1)) a__U22(tt()) = 1 >= 1 = tt() a__U41(tt(),V1,V2) = 0 >= 0 = a__U42(a__isNat(V1),V2) a__U42(tt(),V2) = 0 >= 0 = a__U43(a__isNatIList(V2)) a__U43(tt()) = 1 >= 1 = tt() a__U51(tt(),V1,V2) = 0 >= 0 = a__U52(a__isNat(V1),V2) a__U52(tt(),V2) = 0 >= 0 = a__U53(a__isNatList(V2)) a__U53(tt()) = 1 >= 1 = tt() a__U61(tt(),L) = 0 >= 0 = s(a__length(mark(L))) a__and(tt(),X) = 1 >= 1 = mark(X) a__isNat(0()) = 1 >= 1 = tt() a__isNat(length(V1)) = 1 >= 1 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 1 >= 1 = a__U21(a__isNatKind(V1),V1) a__isNatIList(cons(V1,V2)) = 0 >= 0 = a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) = 1 >= 1 = tt() a__isNatIListKind(cons(V1,V2)) = 1 >= 1 = a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) = 1 >= 1 = tt() a__isNatKind(length(V1)) = 1 >= 1 = a__isNatIListKind(V1) a__isNatKind(s(V1)) = 1 >= 1 = a__isNatKind(V1) a__isNatList(cons(V1,V2)) = 0 >= 0 = a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) = 0 >= 0 = a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) mark(zeros()) = 1 >= 0 = a__zeros() mark(U11(X1,X2)) = 1 >= 1 = a__U11(mark(X1),X2) mark(U12(X)) = 1 >= 1 = a__U12(mark(X)) mark(isNatList(X)) = 1 >= 0 = a__isNatList(X) mark(U21(X1,X2)) = 1 >= 1 = a__U21(mark(X1),X2) mark(U22(X)) = 1 >= 1 = a__U22(mark(X)) mark(isNat(X)) = 1 >= 1 = a__isNat(X) mark(U31(X1,X2)) = 1 >= 1 = a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) = 1 >= 0 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = 1 >= 0 = a__U42(mark(X1),X2) mark(U43(X)) = 1 >= 1 = a__U43(mark(X)) mark(isNatIList(X)) = 1 >= 0 = a__isNatIList(X) mark(U51(X1,X2,X3)) = 1 >= 0 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = 1 >= 0 = a__U52(mark(X1),X2) mark(U53(X)) = 1 >= 1 = a__U53(mark(X)) mark(U61(X1,X2)) = 1 >= 0 = a__U61(mark(X1),X2) mark(length(X)) = 1 >= 0 = a__length(mark(X)) mark(and(X1,X2)) = 1 >= 1 = a__and(mark(X1),X2) mark(isNatIListKind(X)) = 1 >= 1 = a__isNatIListKind(X) mark(isNatKind(X)) = 1 >= 1 = a__isNatKind(X) mark(cons(X1,X2)) = 1 >= 1 = cons(mark(X1),X2) mark(0()) = 1 >= 0 = 0() mark(tt()) = 1 >= 1 = tt() mark(s(X)) = 1 >= 0 = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 1 >= 1 = U11(X1,X2) a__U12(X) = X >= 0 = U12(X) a__isNatList(X) = 0 >= 0 = isNatList(X) a__U21(X1,X2) = X1 >= X1 = U21(X1,X2) a__U22(X) = 1 >= 0 = U22(X) a__isNat(X) = 1 >= 1 = isNat(X) a__U31(X1,X2) = 1 >= 0 = U31(X1,X2) a__U41(X1,X2,X3) = 0 >= 0 = U41(X1,X2,X3) a__U42(X1,X2) = 0 >= 0 = U42(X1,X2) a__U43(X) = X >= 0 = U43(X) a__isNatIList(X) = 0 >= 0 = isNatIList(X) a__U51(X1,X2,X3) = 0 >= 0 = U51(X1,X2,X3) a__U52(X1,X2) = 0 >= 0 = U52(X1,X2) a__U53(X) = X >= X = U53(X) a__U61(X1,X2) = 0 >= 0 = U61(X1,X2) a__length(X) = 0 >= 0 = length(X) a__and(X1,X2) = X1 >= 0 = and(X1,X2) a__isNatIListKind(X) = 1 >= 0 = isNatIListKind(X) a__isNatKind(X) = 1 >= 0 = isNatKind(X) problem: DPs: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) 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__U21#(tt(),V1) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U12(X)) -> 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(X)) -> mark#(X) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__U61#(tt(),L) -> a__length#(mark(L)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Restore Modifier: DPs: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) 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__U21#(tt(),V1) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U12(X)) -> 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(X)) -> mark#(X) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__U61#(tt(),L) -> a__length#(mark(L)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Matrix Interpretation Processor: dim=1 usable rules: interpretation: [a__isNatKind#](x0) = 0, [a__isNatIListKind#](x0) = 0, [a__and#](x0, x1) = x1, [a__length#](x0) = 4, [mark#](x0) = x0, [a__U61#](x0, x1) = x1 + 7, [a__U52#](x0, x1) = 0, [a__U51#](x0, x1, x2) = 0, [a__isNatIList#](x0) = 0, [a__U42#](x0, x1) = 0, [a__U41#](x0, x1, x2) = 0, [a__isNat#](x0) = 0, [a__U21#](x0, x1) = 0, [a__isNatList#](x0) = 0, [a__U11#](x0, x1) = 0, [U61](x0, x1) = x0 + x1 + 7, [U53](x0) = 4x0, [U52](x0, x1) = 4x0 + 4x1, [U51](x0, x1, x2) = x0, [isNatIList](x0) = 0, [U43](x0) = 4x0, [U42](x0, x1) = x0, [U41](x0, x1, x2) = 2x0 + 4x1 + x2 + 5, [U31](x0, x1) = 4x0 + x1, [U22](x0) = x0, [U21](x0, x1) = 4x0, [isNatList](x0) = x0 + 2, [U12](x0) = 5x0, [U11](x0, x1) = 4x0 + 1, [and](x0, x1) = 2x0 + 2x1 + 4, [isNatKind](x0) = 0, [isNat](x0) = 0, [isNatIListKind](x0) = 0, [a__isNatKind](x0) = 4x0, [a__isNatIListKind](x0) = x0 + 4, [length](x0) = x0 + 5, [a__and](x0, x1) = 0, [s](x0) = x0, [a__length](x0) = 2, [mark](x0) = 4x0, [a__U61](x0, x1) = 0, [a__U53](x0) = 2x0 + 6, [a__U52](x0, x1) = 0, [a__U51](x0, x1, x2) = 4, [a__U43](x0) = 3x0, [a__isNatIList](x0) = 3x0, [a__U42](x0, x1) = x0 + 6, [a__U41](x0, x1, x2) = 2, [a__U31](x0, x1) = 0, [a__U22](x0) = 2x0 + 2, [a__isNat](x0) = 0, [a__U21](x0, x1) = x0 + 4, [a__U12](x0) = 3x0 + 7, [a__isNatList](x0) = 3, [a__U11](x0, x1) = 4x0 + 2, [tt] = 0, [cons](x0, x1) = x0, [zeros] = 0, [0] = 2, [a__zeros] = 0 orientation: a__isNatKind#(length(V1)) = 0 >= 0 = a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) = 0 >= 0 = a__isNatKind#(V1) a__isNatKind#(s(V1)) = 0 >= 0 = a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) = 0 >= 0 = a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) = X >= X = mark#(X) mark#(U11(X1,X2)) = 4X1 + 1 >= X1 = mark#(X1) mark#(U11(X1,X2)) = 4X1 + 1 >= 0 = a__U11#(mark(X1),X2) a__U11#(tt(),V1) = 0 >= 0 = a__isNatList#(V1) a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) = 0 >= 0 = a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) = 0 >= 0 = a__isNat#(V1) a__isNat#(length(V1)) = 0 >= 0 = a__isNatIListKind#(V1) a__isNat#(length(V1)) = 0 >= 0 = a__U11#(a__isNatIListKind(V1),V1) a__isNat#(s(V1)) = 0 >= 0 = a__isNatKind#(V1) a__isNat#(s(V1)) = 0 >= 0 = a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) = 0 >= 0 = a__isNat#(V1) a__U51#(tt(),V1,V2) = 0 >= 0 = a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) = 0 >= 0 = a__isNatList#(V2) mark#(U12(X)) = 5X >= X = mark#(X) mark#(isNatList(X)) = X + 2 >= 0 = a__isNatList#(X) mark#(U21(X1,X2)) = 4X1 >= X1 = mark#(X1) mark#(U21(X1,X2)) = 4X1 >= 0 = a__U21#(mark(X1),X2) mark#(U22(X)) = X >= X = mark#(X) mark#(isNat(X)) = 0 >= 0 = a__isNat#(X) mark#(U31(X1,X2)) = 4X1 + X2 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = 2X1 + 4X2 + X3 + 5 >= X1 = mark#(X1) mark#(U41(X1,X2,X3)) = 2X1 + 4X2 + X3 + 5 >= 0 = a__U41#(mark(X1),X2,X3) a__U41#(tt(),V1,V2) = 0 >= 0 = a__isNat#(V1) a__U41#(tt(),V1,V2) = 0 >= 0 = a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) = 0 >= 0 = a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) = 0 >= 0 = a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(U42(X1,X2)) = X1 >= X1 = mark#(X1) mark#(U42(X1,X2)) = X1 >= 0 = a__U42#(mark(X1),X2) mark#(U43(X)) = 4X >= X = mark#(X) mark#(isNatIList(X)) = 0 >= 0 = a__isNatIList#(X) mark#(U51(X1,X2,X3)) = X1 >= X1 = mark#(X1) mark#(U51(X1,X2,X3)) = X1 >= 0 = a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) = 4X1 + 4X2 >= X1 = mark#(X1) mark#(U52(X1,X2)) = 4X1 + 4X2 >= 0 = a__U52#(mark(X1),X2) mark#(U53(X)) = 4X >= X = mark#(X) mark#(U61(X1,X2)) = X1 + X2 + 7 >= X1 = mark#(X1) mark#(U61(X1,X2)) = X1 + X2 + 7 >= X2 + 7 = a__U61#(mark(X1),X2) a__U61#(tt(),L) = L + 7 >= L = mark#(L) mark#(length(X)) = X + 5 >= X = mark#(X) mark#(length(X)) = X + 5 >= 4 = a__length#(mark(X)) a__length#(cons(N,L)) = 4 >= 0 = a__isNatList#(L) a__length#(cons(N,L)) = 4 >= 0 = a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) = 4 >= 4 = a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__U61#(tt(),L) = L + 7 >= 4 = a__length#(mark(L)) mark#(and(X1,X2)) = 2X1 + 2X2 + 4 >= X1 = mark#(X1) mark#(and(X1,X2)) = 2X1 + 2X2 + 4 >= X2 = a__and#(mark(X1),X2) mark#(isNatIListKind(X)) = 0 >= 0 = a__isNatIListKind#(X) mark#(isNatKind(X)) = 0 >= 0 = a__isNatKind#(X) mark#(cons(X1,X2)) = X1 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 2 = cons(0(),zeros()) a__U11(tt(),V1) = 2 >= 16 = a__U12(a__isNatList(V1)) a__U12(tt()) = 7 >= 0 = tt() a__U21(tt(),V1) = 4 >= 2 = a__U22(a__isNat(V1)) a__U22(tt()) = 2 >= 0 = tt() a__U41(tt(),V1,V2) = 2 >= 6 = a__U42(a__isNat(V1),V2) a__U42(tt(),V2) = 6 >= 9V2 = a__U43(a__isNatIList(V2)) a__U43(tt()) = 0 >= 0 = tt() a__U51(tt(),V1,V2) = 4 >= 0 = a__U52(a__isNat(V1),V2) a__U52(tt(),V2) = 0 >= 12 = a__U53(a__isNatList(V2)) a__U53(tt()) = 6 >= 0 = tt() a__U61(tt(),L) = 0 >= 2 = s(a__length(mark(L))) a__and(tt(),X) = 0 >= 4X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 0 >= 4V1 + 18 = a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) = 0 >= 4V1 + 4 = a__U21(a__isNatKind(V1),V1) a__isNatIList(cons(V1,V2)) = 3V1 >= 2 = a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) = 4 >= 0 = tt() a__isNatIListKind(cons(V1,V2)) = V1 + 4 >= 0 = a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) = 8 >= 0 = tt() a__isNatKind(length(V1)) = 4V1 + 20 >= V1 + 4 = a__isNatIListKind(V1) a__isNatKind(s(V1)) = 4V1 >= 4V1 = a__isNatKind(V1) a__isNatList(cons(V1,V2)) = 3 >= 4 = a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) = 2 >= 0 = a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N), isNatKind (N))),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 16X1 + 4 >= 16X1 + 2 = a__U11(mark(X1),X2) mark(U12(X)) = 20X >= 12X + 7 = a__U12(mark(X)) mark(isNatList(X)) = 4X + 8 >= 3 = a__isNatList(X) mark(U21(X1,X2)) = 16X1 >= 4X1 + 4 = a__U21(mark(X1),X2) mark(U22(X)) = 4X >= 8X + 2 = a__U22(mark(X)) mark(isNat(X)) = 0 >= 0 = a__isNat(X) mark(U31(X1,X2)) = 16X1 + 4X2 >= 0 = a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) = 8X1 + 16X2 + 4X3 + 20 >= 2 = a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) = 4X1 >= 4X1 + 6 = a__U42(mark(X1),X2) mark(U43(X)) = 16X >= 12X = a__U43(mark(X)) mark(isNatIList(X)) = 0 >= 3X = a__isNatIList(X) mark(U51(X1,X2,X3)) = 4X1 >= 4 = a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) = 16X1 + 16X2 >= 0 = a__U52(mark(X1),X2) mark(U53(X)) = 16X >= 8X + 6 = a__U53(mark(X)) mark(U61(X1,X2)) = 4X1 + 4X2 + 28 >= 0 = a__U61(mark(X1),X2) mark(length(X)) = 4X + 20 >= 2 = a__length(mark(X)) mark(and(X1,X2)) = 8X1 + 8X2 + 16 >= 0 = a__and(mark(X1),X2) mark(isNatIListKind(X)) = 0 >= X + 4 = a__isNatIListKind(X) mark(isNatKind(X)) = 0 >= 4X = a__isNatKind(X) mark(cons(X1,X2)) = 4X1 >= 4X1 = cons(mark(X1),X2) mark(0()) = 8 >= 2 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 4X >= 4X = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 4X1 + 2 >= 4X1 + 1 = U11(X1,X2) a__U12(X) = 3X + 7 >= 5X = U12(X) a__isNatList(X) = 3 >= X + 2 = isNatList(X) a__U21(X1,X2) = X1 + 4 >= 4X1 = U21(X1,X2) a__U22(X) = 2X + 2 >= X = U22(X) a__isNat(X) = 0 >= 0 = isNat(X) a__U31(X1,X2) = 0 >= 4X1 + X2 = U31(X1,X2) a__U41(X1,X2,X3) = 2 >= 2X1 + 4X2 + X3 + 5 = U41(X1,X2,X3) a__U42(X1,X2) = X1 + 6 >= X1 = U42(X1,X2) a__U43(X) = 3X >= 4X = U43(X) a__isNatIList(X) = 3X >= 0 = isNatIList(X) a__U51(X1,X2,X3) = 4 >= X1 = U51(X1,X2,X3) a__U52(X1,X2) = 0 >= 4X1 + 4X2 = U52(X1,X2) a__U53(X) = 2X + 6 >= 4X = U53(X) a__U61(X1,X2) = 0 >= X1 + X2 + 7 = U61(X1,X2) a__length(X) = 2 >= X + 5 = length(X) a__and(X1,X2) = 0 >= 2X1 + 2X2 + 4 = and(X1,X2) a__isNatIListKind(X) = X + 4 >= 0 = isNatIListKind(X) a__isNatKind(X) = 4X >= 0 = isNatKind(X) problem: DPs: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) -> mark#(X) a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) 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__U21#(tt(),V1) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U12(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X)) -> mark#(X) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))), L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Restore Modifier: DPs: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) -> mark#(X) a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) 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__U21#(tt(),V1) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U12(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X)) -> mark#(X) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))), L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) SCC Processor: #sccs: 1 #rules: 42 #arcs: 626/1936 DPs: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(U12(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) a__U21#(tt(),V1) -> a__isNat#(V1) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U22(X)) -> mark#(X) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) mark#(U43(X)) -> mark#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(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__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))), L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Subterm Criterion Processor: simple projection: pi(isNatIListKind) = [0,0,0] pi(U12) = 0 pi(U22) = [0,0] pi(U41) = 1 pi(U51) = [0,0,1,2,2,2] pi(a__U11#) = 1 pi(a__isNatList#) = 0 pi(a__U21#) = 1 pi(a__isNat#) = 0 pi(a__U41#) = [1,2,2] pi(a__U42#) = [1,1] pi(a__isNatIList#) = [0,0] pi(a__U51#) = [1,2,2,2] pi(a__U52#) = [1,1,1] pi(mark#) = 0 pi(a__and#) = [1,1] pi(a__isNatIListKind#) = [0,0,0] pi(a__isNatKind#) = [0,0] problem: DPs: mark#(U12(X)) -> mark#(X) a__U21#(tt(),V1) -> a__isNat#(V1) a__U11#(tt(),V1) -> a__isNatList#(V1) a__U42#(tt(),V2) -> a__isNatIList#(V2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)), and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) SCC Processor: #sccs: 1 #rules: 1 #arcs: 290/25 DPs: mark#(U12(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)), and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Size-Change Termination Processor: DPs: TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) 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(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)), and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(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(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) The DP: mark#(U12(X)) -> mark#(X) has the edges: 0 > 0 Qed