active(zeros) → mark(cons(0, zeros))
active(U11(tt, V1)) → mark(U12(isNatIListKind(V1), V1))
active(U12(tt, V1)) → mark(U13(isNatList(V1)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isNatIListKind(V), V))
active(U32(tt, V)) → mark(U33(isNatList(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isNatKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isNatIListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isNatIListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isNat(V1), V2))
active(U45(tt, V2)) → mark(U46(isNatIList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatIListKind(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt)) → mark(tt)
active(U71(tt)) → mark(tt)
active(U81(tt, V1, V2)) → mark(U82(isNatKind(V1), V1, V2))
active(U82(tt, V1, V2)) → mark(U83(isNatIListKind(V2), V1, V2))
active(U83(tt, V1, V2)) → mark(U84(isNatIListKind(V2), V1, V2))
active(U84(tt, V1, V2)) → mark(U85(isNat(V1), V2))
active(U85(tt, V2)) → mark(U86(isNatList(V2)))
active(U86(tt)) → mark(tt)
active(U91(tt, L, N)) → mark(U92(isNatIListKind(L), L, N))
active(U92(tt, L, N)) → mark(U93(isNat(N), L, N))
active(U93(tt, L, N)) → mark(U94(isNatKind(N), L))
active(U94(tt, L)) → mark(s(length(L)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatIListKind(V1), V1))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatIList(V)) → mark(U31(isNatIListKind(V), V))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNatKind(V1), V1, V2))
active(isNatIListKind(nil)) → mark(tt)
active(isNatIListKind(zeros)) → mark(tt)
active(isNatIListKind(cons(V1, V2))) → mark(U51(isNatKind(V1), V2))
active(isNatKind(0)) → mark(tt)
active(isNatKind(length(V1))) → mark(U61(isNatIListKind(V1)))
active(isNatKind(s(V1))) → mark(U71(isNatKind(V1)))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U81(isNatKind(V1), V1, V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U91(isNatList(L), L, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2)) → U21(active(X1), X2)
active(U22(X1, X2)) → U22(active(X1), X2)
active(U23(X)) → U23(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2)) → U51(active(X1), X2)
active(U52(X)) → U52(active(X))
active(U61(X)) → U61(active(X))
active(U71(X)) → U71(active(X))
active(U81(X1, X2, X3)) → U81(active(X1), X2, X3)
active(U82(X1, X2, X3)) → U82(active(X1), X2, X3)
active(U83(X1, X2, X3)) → U83(active(X1), X2, X3)
active(U84(X1, X2, X3)) → U84(active(X1), X2, X3)
active(U85(X1, X2)) → U85(active(X1), X2)
active(U86(X)) → U86(active(X))
active(U91(X1, X2, X3)) → U91(active(X1), X2, X3)
active(U92(X1, X2, X3)) → U92(active(X1), X2, X3)
active(U93(X1, X2, X3)) → U93(active(X1), X2, X3)
active(U94(X1, X2)) → U94(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2) → mark(U21(X1, X2))
U22(mark(X1), X2) → mark(U22(X1, X2))
U23(mark(X)) → mark(U23(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2) → mark(U51(X1, X2))
U52(mark(X)) → mark(U52(X))
U61(mark(X)) → mark(U61(X))
U71(mark(X)) → mark(U71(X))
U81(mark(X1), X2, X3) → mark(U81(X1, X2, X3))
U82(mark(X1), X2, X3) → mark(U82(X1, X2, X3))
U83(mark(X1), X2, X3) → mark(U83(X1, X2, X3))
U84(mark(X1), X2, X3) → mark(U84(X1, X2, X3))
U85(mark(X1), X2) → mark(U85(X1, X2))
U86(mark(X)) → mark(U86(X))
U91(mark(X1), X2, X3) → mark(U91(X1, X2, X3))
U92(mark(X1), X2, X3) → mark(U92(X1, X2, X3))
U93(mark(X1), X2, X3) → mark(U93(X1, X2, X3))
U94(mark(X1), X2) → mark(U94(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isNatIListKind(X)) → isNatIListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNatList(X)) → isNatList(proper(X))
proper(U21(X1, X2)) → U21(proper(X1), proper(X2))
proper(U22(X1, X2)) → U22(proper(X1), proper(X2))
proper(isNatKind(X)) → isNatKind(proper(X))
proper(U23(X)) → U23(proper(X))
proper(isNat(X)) → isNat(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(isNatIList(X)) → isNatIList(proper(X))
proper(U51(X1, X2)) → U51(proper(X1), proper(X2))
proper(U52(X)) → U52(proper(X))
proper(U61(X)) → U61(proper(X))
proper(U71(X)) → U71(proper(X))
proper(U81(X1, X2, X3)) → U81(proper(X1), proper(X2), proper(X3))
proper(U82(X1, X2, X3)) → U82(proper(X1), proper(X2), proper(X3))
proper(U83(X1, X2, X3)) → U83(proper(X1), proper(X2), proper(X3))
proper(U84(X1, X2, X3)) → U84(proper(X1), proper(X2), proper(X3))
proper(U85(X1, X2)) → U85(proper(X1), proper(X2))
proper(U86(X)) → U86(proper(X))
proper(U91(X1, X2, X3)) → U91(proper(X1), proper(X2), proper(X3))
proper(U92(X1, X2, X3)) → U92(proper(X1), proper(X2), proper(X3))
proper(U93(X1, X2, X3)) → U93(proper(X1), proper(X2), proper(X3))
proper(U94(X1, X2)) → U94(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isNatIListKind(ok(X)) → ok(isNatIListKind(X))
U13(ok(X)) → ok(U13(X))
isNatList(ok(X)) → ok(isNatList(X))
U21(ok(X1), ok(X2)) → ok(U21(X1, X2))
U22(ok(X1), ok(X2)) → ok(U22(X1, X2))
isNatKind(ok(X)) → ok(isNatKind(X))
U23(ok(X)) → ok(U23(X))
isNat(ok(X)) → ok(isNat(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
isNatIList(ok(X)) → ok(isNatIList(X))
U51(ok(X1), ok(X2)) → ok(U51(X1, X2))
U52(ok(X)) → ok(U52(X))
U61(ok(X)) → ok(U61(X))
U71(ok(X)) → ok(U71(X))
U81(ok(X1), ok(X2), ok(X3)) → ok(U81(X1, X2, X3))
U82(ok(X1), ok(X2), ok(X3)) → ok(U82(X1, X2, X3))
U83(ok(X1), ok(X2), ok(X3)) → ok(U83(X1, X2, X3))
U84(ok(X1), ok(X2), ok(X3)) → ok(U84(X1, X2, X3))
U85(ok(X1), ok(X2)) → ok(U85(X1, X2))
U86(ok(X)) → ok(U86(X))
U91(ok(X1), ok(X2), ok(X3)) → ok(U91(X1, X2, X3))
U92(ok(X1), ok(X2), ok(X3)) → ok(U92(X1, X2, X3))
U93(ok(X1), ok(X2), ok(X3)) → ok(U93(X1, X2, X3))
U94(ok(X1), ok(X2)) → ok(U94(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

↳ QTRS

  ↳ DependencyPairsProof

active(zeros) → mark(cons(0, zeros))
active(U11(tt, V1)) → mark(U12(isNatIListKind(V1), V1))
active(U12(tt, V1)) → mark(U13(isNatList(V1)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isNatIListKind(V), V))
active(U32(tt, V)) → mark(U33(isNatList(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isNatKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isNatIListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isNatIListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isNat(V1), V2))
active(U45(tt, V2)) → mark(U46(isNatIList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatIListKind(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt)) → mark(tt)
active(U71(tt)) → mark(tt)
active(U81(tt, V1, V2)) → mark(U82(isNatKind(V1), V1, V2))
active(U82(tt, V1, V2)) → mark(U83(isNatIListKind(V2), V1, V2))
active(U83(tt, V1, V2)) → mark(U84(isNatIListKind(V2), V1, V2))
active(U84(tt, V1, V2)) → mark(U85(isNat(V1), V2))
active(U85(tt, V2)) → mark(U86(isNatList(V2)))
active(U86(tt)) → mark(tt)
active(U91(tt, L, N)) → mark(U92(isNatIListKind(L), L, N))
active(U92(tt, L, N)) → mark(U93(isNat(N), L, N))
active(U93(tt, L, N)) → mark(U94(isNatKind(N), L))
active(U94(tt, L)) → mark(s(length(L)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatIListKind(V1), V1))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatIList(V)) → mark(U31(isNatIListKind(V), V))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNatKind(V1), V1, V2))
active(isNatIListKind(nil)) → mark(tt)
active(isNatIListKind(zeros)) → mark(tt)
active(isNatIListKind(cons(V1, V2))) → mark(U51(isNatKind(V1), V2))
active(isNatKind(0)) → mark(tt)
active(isNatKind(length(V1))) → mark(U61(isNatIListKind(V1)))
active(isNatKind(s(V1))) → mark(U71(isNatKind(V1)))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U81(isNatKind(V1), V1, V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U91(isNatList(L), L, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2)) → U21(active(X1), X2)
active(U22(X1, X2)) → U22(active(X1), X2)
active(U23(X)) → U23(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2)) → U51(active(X1), X2)
active(U52(X)) → U52(active(X))
active(U61(X)) → U61(active(X))
active(U71(X)) → U71(active(X))
active(U81(X1, X2, X3)) → U81(active(X1), X2, X3)
active(U82(X1, X2, X3)) → U82(active(X1), X2, X3)
active(U83(X1, X2, X3)) → U83(active(X1), X2, X3)
active(U84(X1, X2, X3)) → U84(active(X1), X2, X3)
active(U85(X1, X2)) → U85(active(X1), X2)
active(U86(X)) → U86(active(X))
active(U91(X1, X2, X3)) → U91(active(X1), X2, X3)
active(U92(X1, X2, X3)) → U92(active(X1), X2, X3)
active(U93(X1, X2, X3)) → U93(active(X1), X2, X3)
active(U94(X1, X2)) → U94(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2) → mark(U21(X1, X2))
U22(mark(X1), X2) → mark(U22(X1, X2))
U23(mark(X)) → mark(U23(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2) → mark(U51(X1, X2))
U52(mark(X)) → mark(U52(X))
U61(mark(X)) → mark(U61(X))
U71(mark(X)) → mark(U71(X))
U81(mark(X1), X2, X3) → mark(U81(X1, X2, X3))
U82(mark(X1), X2, X3) → mark(U82(X1, X2, X3))
U83(mark(X1), X2, X3) → mark(U83(X1, X2, X3))
U84(mark(X1), X2, X3) → mark(U84(X1, X2, X3))
U85(mark(X1), X2) → mark(U85(X1, X2))
U86(mark(X)) → mark(U86(X))
U91(mark(X1), X2, X3) → mark(U91(X1, X2, X3))
U92(mark(X1), X2, X3) → mark(U92(X1, X2, X3))
U93(mark(X1), X2, X3) → mark(U93(X1, X2, X3))
U94(mark(X1), X2) → mark(U94(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isNatIListKind(X)) → isNatIListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNatList(X)) → isNatList(proper(X))
proper(U21(X1, X2)) → U21(proper(X1), proper(X2))
proper(U22(X1, X2)) → U22(proper(X1), proper(X2))
proper(isNatKind(X)) → isNatKind(proper(X))
proper(U23(X)) → U23(proper(X))
proper(isNat(X)) → isNat(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(isNatIList(X)) → isNatIList(proper(X))
proper(U51(X1, X2)) → U51(proper(X1), proper(X2))
proper(U52(X)) → U52(proper(X))
proper(U61(X)) → U61(proper(X))
proper(U71(X)) → U71(proper(X))
proper(U81(X1, X2, X3)) → U81(proper(X1), proper(X2), proper(X3))
proper(U82(X1, X2, X3)) → U82(proper(X1), proper(X2), proper(X3))
proper(U83(X1, X2, X3)) → U83(proper(X1), proper(X2), proper(X3))
proper(U84(X1, X2, X3)) → U84(proper(X1), proper(X2), proper(X3))
proper(U85(X1, X2)) → U85(proper(X1), proper(X2))
proper(U86(X)) → U86(proper(X))
proper(U91(X1, X2, X3)) → U91(proper(X1), proper(X2), proper(X3))
proper(U92(X1, X2, X3)) → U92(proper(X1), proper(X2), proper(X3))
proper(U93(X1, X2, X3)) → U93(proper(X1), proper(X2), proper(X3))
proper(U94(X1, X2)) → U94(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isNatIListKind(ok(X)) → ok(isNatIListKind(X))
U13(ok(X)) → ok(U13(X))
isNatList(ok(X)) → ok(isNatList(X))
U21(ok(X1), ok(X2)) → ok(U21(X1, X2))
U22(ok(X1), ok(X2)) → ok(U22(X1, X2))
isNatKind(ok(X)) → ok(isNatKind(X))
U23(ok(X)) → ok(U23(X))
isNat(ok(X)) → ok(isNat(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
isNatIList(ok(X)) → ok(isNatIList(X))
U51(ok(X1), ok(X2)) → ok(U51(X1, X2))
U52(ok(X)) → ok(U52(X))
U61(ok(X)) → ok(U61(X))
U71(ok(X)) → ok(U71(X))
U81(ok(X1), ok(X2), ok(X3)) → ok(U81(X1, X2, X3))
U82(ok(X1), ok(X2), ok(X3)) → ok(U82(X1, X2, X3))
U83(ok(X1), ok(X2), ok(X3)) → ok(U83(X1, X2, X3))
U84(ok(X1), ok(X2), ok(X3)) → ok(U84(X1, X2, X3))
U85(ok(X1), ok(X2)) → ok(U85(X1, X2))
U86(ok(X)) → ok(U86(X))
U91(ok(X1), ok(X2), ok(X3)) → ok(U91(X1, X2, X3))
U92(ok(X1), ok(X2), ok(X3)) → ok(U92(X1, X2, X3))
U93(ok(X1), ok(X2), ok(X3)) → ok(U93(X1, X2, X3))
U94(ok(X1), ok(X2)) → ok(U94(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

ACTIVE(U51(X1, X2)) → ACTIVE(X1)
U71¹(mark(X)) → U71¹(X)
PROPER(U32(X1, X2)) → PROPER(X2)
ACTIVE(cons(X1, X2)) → CONS(active(X1), X2)
PROPER(U86(X)) → PROPER(X)
PROPER(U11(X1, X2)) → U11¹(proper(X1), proper(X2))
PROPER(U31(X1, X2)) → PROPER(X1)
U33¹(ok(X)) → U33¹(X)
PROPER(U45(X1, X2)) → PROPER(X2)
U81¹(mark(X1), X2, X3) → U81¹(X1, X2, X3)
ACTIVE(isNatIList(cons(V1, V2))) → ISNATKIND(V1)
PROPER(U91(X1, X2, X3)) → U91¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U52(X)) → U52¹(active(X))
PROPER(U81(X1, X2, X3)) → PROPER(X3)
ACTIVE(U21(X1, X2)) → U21¹(active(X1), X2)
ACTIVE(U22(tt, V1)) → ISNAT(V1)
U31¹(mark(X1), X2) → U31¹(X1, X2)
U82¹(mark(X1), X2, X3) → U82¹(X1, X2, X3)
U91¹(ok(X1), ok(X2), ok(X3)) → U91¹(X1, X2, X3)
PROPER(U11(X1, X2)) → PROPER(X2)
ACTIVE(isNatList(cons(V1, V2))) → ISNATKIND(V1)
PROPER(U12(X1, X2)) → PROPER(X2)
PROPER(U32(X1, X2)) → PROPER(X1)
U86¹(ok(X)) → U86¹(X)
ACTIVE(U44(tt, V1, V2)) → U45¹(isNat(V1), V2)
ACTIVE(U82(X1, X2, X3)) → U82¹(active(X1), X2, X3)
PROPER(U82(X1, X2, X3)) → PROPER(X2)
PROPER(U43(X1, X2, X3)) → U43¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U32(X1, X2)) → ACTIVE(X1)
PROPER(isNatList(X)) → ISNATLIST(proper(X))
U43¹(ok(X1), ok(X2), ok(X3)) → U43¹(X1, X2, X3)
U46¹(ok(X)) → U46¹(X)
PROPER(U45(X1, X2)) → U45¹(proper(X1), proper(X2))
ACTIVE(U91(X1, X2, X3)) → U91¹(active(X1), X2, X3)
U61¹(ok(X)) → U61¹(X)
U81¹(ok(X1), ok(X2), ok(X3)) → U81¹(X1, X2, X3)
ACTIVE(U32(tt, V)) → U33¹(isNatList(V))
U42¹(ok(X1), ok(X2), ok(X3)) → U42¹(X1, X2, X3)
ACTIVE(U93(X1, X2, X3)) → U93¹(active(X1), X2, X3)
ACTIVE(U84(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U84(X1, X2, X3)) → U84¹(active(X1), X2, X3)
ACTIVE(U86(X)) → ACTIVE(X)
PROPER(U94(X1, X2)) → PROPER(X2)
S(ok(X)) → S(X)
PROPER(U22(X1, X2)) → U22¹(proper(X1), proper(X2))
CONS(mark(X1), X2) → CONS(X1, X2)
PROPER(U44(X1, X2, X3)) → PROPER(X3)
PROPER(isNatKind(X)) → ISNATKIND(proper(X))
PROPER(U41(X1, X2, X3)) → U41¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U41(X1, X2, X3)) → U41¹(active(X1), X2, X3)
ACTIVE(U83(X1, X2, X3)) → ACTIVE(X1)
PROPER(cons(X1, X2)) → PROPER(X1)
U31¹(ok(X1), ok(X2)) → U31¹(X1, X2)
U93¹(mark(X1), X2, X3) → U93¹(X1, X2, X3)
PROPER(U45(X1, X2)) → PROPER(X1)
ACTIVE(U91(X1, X2, X3)) → ACTIVE(X1)
U51¹(mark(X1), X2) → U51¹(X1, X2)
S(mark(X)) → S(X)
PROPER(cons(X1, X2)) → CONS(proper(X1), proper(X2))
ISNATLIST(ok(X)) → ISNATLIST(X)
PROPER(U84(X1, X2, X3)) → PROPER(X1)
ACTIVE(isNatIListKind(cons(V1, V2))) → U51¹(isNatKind(V1), V2)
U13¹(mark(X)) → U13¹(X)
ACTIVE(U42(tt, V1, V2)) → U43¹(isNatIListKind(V2), V1, V2)
ACTIVE(U83(tt, V1, V2)) → U84¹(isNatIListKind(V2), V1, V2)
ACTIVE(U33(X)) → ACTIVE(X)
ACTIVE(U45(X1, X2)) → ACTIVE(X1)
U51¹(ok(X1), ok(X2)) → U51¹(X1, X2)
ACTIVE(U12(X1, X2)) → ACTIVE(X1)
PROPER(U83(X1, X2, X3)) → PROPER(X2)
ACTIVE(U31(tt, V)) → U32¹(isNatIListKind(V), V)
U92¹(mark(X1), X2, X3) → U92¹(X1, X2, X3)
ACTIVE(U93(tt, L, N)) → U94¹(isNatKind(N), L)
U12¹(ok(X1), ok(X2)) → U12¹(X1, X2)
ACTIVE(isNatList(cons(V1, V2))) → U81¹(isNatKind(V1), V1, V2)
ACTIVE(U41(tt, V1, V2)) → ISNATKIND(V1)
U23¹(mark(X)) → U23¹(X)
PROPER(U44(X1, X2, X3)) → PROPER(X1)
ACTIVE(U71(X)) → U71¹(active(X))
PROPER(U84(X1, X2, X3)) → U84¹(proper(X1), proper(X2), proper(X3))
PROPER(U23(X)) → PROPER(X)
PROPER(U92(X1, X2, X3)) → U92¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U81(X1, X2, X3)) → U81¹(active(X1), X2, X3)
PROPER(U82(X1, X2, X3)) → U82¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U33(X)) → U33¹(active(X))
ACTIVE(zeros) → CONS(0, zeros)
ACTIVE(U84(tt, V1, V2)) → U85¹(isNat(V1), V2)
ACTIVE(cons(X1, X2)) → ACTIVE(X1)
PROPER(U46(X)) → U46¹(proper(X))
ACTIVE(U82(tt, V1, V2)) → ISNATILISTKIND(V2)
ACTIVE(U51(tt, V2)) → ISNATILISTKIND(V2)
ISNATILIST(ok(X)) → ISNATILIST(X)
ACTIVE(U46(X)) → U46¹(active(X))
PROPER(U21(X1, X2)) → PROPER(X1)
U93¹(ok(X1), ok(X2), ok(X3)) → U93¹(X1, X2, X3)
PROPER(U12(X1, X2)) → U12¹(proper(X1), proper(X2))
U11¹(ok(X1), ok(X2)) → U11¹(X1, X2)
PROPER(U46(X)) → PROPER(X)
U86¹(mark(X)) → U86¹(X)
PROPER(isNatIList(X)) → ISNATILIST(proper(X))
ACTIVE(U45(X1, X2)) → U45¹(active(X1), X2)
PROPER(isNatIListKind(X)) → PROPER(X)
ACTIVE(isNatIList(V)) → ISNATILISTKIND(V)
ACTIVE(isNat(length(V1))) → U11¹(isNatIListKind(V1), V1)
PROPER(U41(X1, X2, X3)) → PROPER(X2)
ACTIVE(U86(X)) → U86¹(active(X))
PROPER(U22(X1, X2)) → PROPER(X2)
ISNATKIND(ok(X)) → ISNATKIND(X)
ACTIVE(U52(X)) → ACTIVE(X)
PROPER(U61(X)) → PROPER(X)
U92¹(ok(X1), ok(X2), ok(X3)) → U92¹(X1, X2, X3)
PROPER(U82(X1, X2, X3)) → PROPER(X1)
ACTIVE(U41(tt, V1, V2)) → U42¹(isNatKind(V1), V1, V2)
ACTIVE(U45(tt, V2)) → ISNATILIST(V2)
ACTIVE(U94(X1, X2)) → ACTIVE(X1)
ACTIVE(U92(tt, L, N)) → ISNAT(N)
U32¹(mark(X1), X2) → U32¹(X1, X2)
ACTIVE(U11(tt, V1)) → U12¹(isNatIListKind(V1), V1)
TOP(ok(X)) → TOP(active(X))
ACTIVE(U43(X1, X2, X3)) → U43¹(active(X1), X2, X3)
U45¹(ok(X1), ok(X2)) → U45¹(X1, X2)
ACTIVE(U22(tt, V1)) → U23¹(isNat(V1))
PROPER(U43(X1, X2, X3)) → PROPER(X3)
ISNAT(ok(X)) → ISNAT(X)
CONS(ok(X1), ok(X2)) → CONS(X1, X2)
ACTIVE(U41(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(length(cons(N, L))) → ISNATLIST(L)
PROPER(U52(X)) → U52¹(proper(X))
PROPER(U44(X1, X2, X3)) → U44¹(proper(X1), proper(X2), proper(X3))
PROPER(U33(X)) → U33¹(proper(X))
ACTIVE(U83(tt, V1, V2)) → ISNATILISTKIND(V2)
PROPER(U81(X1, X2, X3)) → PROPER(X2)
ACTIVE(isNat(s(V1))) → U21¹(isNatKind(V1), V1)
PROPER(U42(X1, X2, X3)) → PROPER(X1)
ACTIVE(U91(tt, L, N)) → U92¹(isNatIListKind(L), L, N)
PROPER(U81(X1, X2, X3)) → PROPER(X1)
U43¹(mark(X1), X2, X3) → U43¹(X1, X2, X3)
ACTIVE(U92(tt, L, N)) → U93¹(isNat(N), L, N)
PROPER(U13(X)) → U13¹(proper(X))
ACTIVE(U92(X1, X2, X3)) → ACTIVE(X1)
PROPER(U94(X1, X2)) → U94¹(proper(X1), proper(X2))
PROPER(U11(X1, X2)) → PROPER(X1)
ACTIVE(s(X)) → S(active(X))
PROPER(U51(X1, X2)) → PROPER(X2)
ACTIVE(U45(tt, V2)) → U46¹(isNatIList(V2))
U22¹(ok(X1), ok(X2)) → U22¹(X1, X2)
ACTIVE(U13(X)) → ACTIVE(X)
ACTIVE(U81(X1, X2, X3)) → ACTIVE(X1)
PROPER(isNatList(X)) → PROPER(X)
ACTIVE(U44(tt, V1, V2)) → ISNAT(V1)
ACTIVE(U94(X1, X2)) → U94¹(active(X1), X2)
ACTIVE(isNatKind(length(V1))) → ISNATILISTKIND(V1)
PROPER(length(X)) → LENGTH(proper(X))
PROPER(U84(X1, X2, X3)) → PROPER(X3)
PROPER(U12(X1, X2)) → PROPER(X1)
U21¹(mark(X1), X2) → U21¹(X1, X2)
ACTIVE(isNatKind(length(V1))) → U61¹(isNatIListKind(V1))
ACTIVE(U51(tt, V2)) → U52¹(isNatIListKind(V2))
ACTIVE(U31(X1, X2)) → ACTIVE(X1)
PROPER(U84(X1, X2, X3)) → PROPER(X2)
ACTIVE(U42(X1, X2, X3)) → ACTIVE(X1)
U21¹(ok(X1), ok(X2)) → U21¹(X1, X2)
ACTIVE(U94(tt, L)) → LENGTH(L)
ACTIVE(isNatIListKind(cons(V1, V2))) → ISNATKIND(V1)
PROPER(length(X)) → PROPER(X)
PROPER(U86(X)) → U86¹(proper(X))
PROPER(U83(X1, X2, X3)) → PROPER(X3)
PROPER(U93(X1, X2, X3)) → PROPER(X2)
ACTIVE(U11(X1, X2)) → ACTIVE(X1)
PROPER(U83(X1, X2, X3)) → PROPER(X1)
ACTIVE(s(X)) → ACTIVE(X)
ACTIVE(U46(X)) → ACTIVE(X)
U83¹(mark(X1), X2, X3) → U83¹(X1, X2, X3)
PROPER(U71(X)) → U71¹(proper(X))
ACTIVE(U82(X1, X2, X3)) → ACTIVE(X1)
PROPER(U92(X1, X2, X3)) → PROPER(X3)
ACTIVE(U42(tt, V1, V2)) → ISNATILISTKIND(V2)
U91¹(mark(X1), X2, X3) → U91¹(X1, X2, X3)
U46¹(mark(X)) → U46¹(X)
TOP(mark(X)) → PROPER(X)
ACTIVE(U71(X)) → ACTIVE(X)
ACTIVE(U43(tt, V1, V2)) → ISNATILISTKIND(V2)
PROPER(U31(X1, X2)) → U31¹(proper(X1), proper(X2))
ACTIVE(U92(X1, X2, X3)) → U92¹(active(X1), X2, X3)
TOP(ok(X)) → ACTIVE(X)
ACTIVE(length(X)) → ACTIVE(X)
PROPER(U44(X1, X2, X3)) → PROPER(X2)
ACTIVE(U21(tt, V1)) → ISNATKIND(V1)
ACTIVE(isNat(length(V1))) → ISNATILISTKIND(V1)
PROPER(U23(X)) → U23¹(proper(X))
U44¹(ok(X1), ok(X2), ok(X3)) → U44¹(X1, X2, X3)
ACTIVE(U82(tt, V1, V2)) → U83¹(isNatIListKind(V2), V1, V2)
LENGTH(mark(X)) → LENGTH(X)
PROPER(isNatKind(X)) → PROPER(X)
U82¹(ok(X1), ok(X2), ok(X3)) → U82¹(X1, X2, X3)
U23¹(ok(X)) → U23¹(X)
U32¹(ok(X1), ok(X2)) → U32¹(X1, X2)
ACTIVE(U22(X1, X2)) → ACTIVE(X1)
ACTIVE(U12(tt, V1)) → U13¹(isNatList(V1))
ACTIVE(length(X)) → LENGTH(active(X))
ACTIVE(U91(tt, L, N)) → ISNATILISTKIND(L)
ACTIVE(U94(tt, L)) → S(length(L))
PROPER(U43(X1, X2, X3)) → PROPER(X2)
PROPER(U93(X1, X2, X3)) → PROPER(X3)
ACTIVE(U61(X)) → ACTIVE(X)
PROPER(U82(X1, X2, X3)) → PROPER(X3)
ACTIVE(U51(X1, X2)) → U51¹(active(X1), X2)
PROPER(U51(X1, X2)) → PROPER(X1)
U41¹(ok(X1), ok(X2), ok(X3)) → U41¹(X1, X2, X3)
U94¹(mark(X1), X2) → U94¹(X1, X2)
PROPER(U33(X)) → PROPER(X)
U12¹(mark(X1), X2) → U12¹(X1, X2)
PROPER(isNatIListKind(X)) → ISNATILISTKIND(proper(X))
U61¹(mark(X)) → U61¹(X)
U94¹(ok(X1), ok(X2)) → U94¹(X1, X2)
PROPER(U91(X1, X2, X3)) → PROPER(X2)
PROPER(U42(X1, X2, X3)) → U42¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U43(tt, V1, V2)) → U44¹(isNatIListKind(V2), V1, V2)
PROPER(U22(X1, X2)) → PROPER(X1)
ACTIVE(U85(X1, X2)) → ACTIVE(X1)
PROPER(U94(X1, X2)) → PROPER(X1)
PROPER(U21(X1, X2)) → U21¹(proper(X1), proper(X2))
U13¹(ok(X)) → U13¹(X)
PROPER(U91(X1, X2, X3)) → PROPER(X1)
U84¹(ok(X1), ok(X2), ok(X3)) → U84¹(X1, X2, X3)
U42¹(mark(X1), X2, X3) → U42¹(X1, X2, X3)
ACTIVE(U21(X1, X2)) → ACTIVE(X1)
ACTIVE(U21(tt, V1)) → U22¹(isNatKind(V1), V1)
ACTIVE(U32(X1, X2)) → U32¹(active(X1), X2)
U41¹(mark(X1), X2, X3) → U41¹(X1, X2, X3)
PROPER(U13(X)) → PROPER(X)
PROPER(U85(X1, X2)) → PROPER(X2)
ACTIVE(U42(X1, X2, X3)) → U42¹(active(X1), X2, X3)
U45¹(mark(X1), X2) → U45¹(X1, X2)
ACTIVE(U61(X)) → U61¹(active(X))
PROPER(cons(X1, X2)) → PROPER(X2)
ISNATILISTKIND(ok(X)) → ISNATILISTKIND(X)
U33¹(mark(X)) → U33¹(X)
PROPER(U42(X1, X2, X3)) → PROPER(X3)
PROPER(U41(X1, X2, X3)) → PROPER(X1)
ACTIVE(U85(tt, V2)) → U86¹(isNatList(V2))
PROPER(U61(X)) → U61¹(proper(X))
PROPER(U93(X1, X2, X3)) → U93¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U31(X1, X2)) → U31¹(active(X1), X2)
ACTIVE(U44(X1, X2, X3)) → U44¹(active(X1), X2, X3)
ACTIVE(isNatIList(cons(V1, V2))) → U41¹(isNatKind(V1), V1, V2)
PROPER(U85(X1, X2)) → U85¹(proper(X1), proper(X2))
PROPER(U41(X1, X2, X3)) → PROPER(X3)
ACTIVE(U22(X1, X2)) → U22¹(active(X1), X2)
U71¹(ok(X)) → U71¹(X)
PROPER(s(X)) → S(proper(X))
ACTIVE(U85(tt, V2)) → ISNATLIST(V2)
ACTIVE(U31(tt, V)) → ISNATILISTKIND(V)
ACTIVE(U23(X)) → U23¹(active(X))
ACTIVE(U44(X1, X2, X3)) → ACTIVE(X1)
PROPER(U92(X1, X2, X3)) → PROPER(X2)
PROPER(U52(X)) → PROPER(X)
U44¹(mark(X1), X2, X3) → U44¹(X1, X2, X3)
ACTIVE(isNat(s(V1))) → ISNATKIND(V1)
PROPER(U42(X1, X2, X3)) → PROPER(X2)
U11¹(mark(X1), X2) → U11¹(X1, X2)
PROPER(U92(X1, X2, X3)) → PROPER(X1)
PROPER(U81(X1, X2, X3)) → U81¹(proper(X1), proper(X2), proper(X3))
U22¹(mark(X1), X2) → U22¹(X1, X2)
ACTIVE(U13(X)) → U13¹(active(X))
U52¹(mark(X)) → U52¹(X)
PROPER(isNat(X)) → PROPER(X)
LENGTH(ok(X)) → LENGTH(X)
U85¹(mark(X1), X2) → U85¹(X1, X2)
ACTIVE(U93(tt, L, N)) → ISNATKIND(N)
PROPER(U32(X1, X2)) → U32¹(proper(X1), proper(X2))
PROPER(U93(X1, X2, X3)) → PROPER(X1)
PROPER(isNatIList(X)) → PROPER(X)
ACTIVE(isNatKind(s(V1))) → U71¹(isNatKind(V1))
ACTIVE(U43(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U81(tt, V1, V2)) → ISNATKIND(V1)
U84¹(mark(X1), X2, X3) → U84¹(X1, X2, X3)
PROPER(s(X)) → PROPER(X)
ACTIVE(U93(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(isNatIList(V)) → U31¹(isNatIListKind(V), V)
ACTIVE(U11(X1, X2)) → U11¹(active(X1), X2)
PROPER(U91(X1, X2, X3)) → PROPER(X3)
PROPER(isNat(X)) → ISNAT(proper(X))
ACTIVE(U23(X)) → ACTIVE(X)
ACTIVE(isNatKind(s(V1))) → ISNATKIND(V1)
ACTIVE(U12(tt, V1)) → ISNATLIST(V1)
PROPER(U43(X1, X2, X3)) → PROPER(X1)
PROPER(U31(X1, X2)) → PROPER(X2)
U85¹(ok(X1), ok(X2)) → U85¹(X1, X2)
U52¹(ok(X)) → U52¹(X)
ACTIVE(U85(X1, X2)) → U85¹(active(X1), X2)
PROPER(U71(X)) → PROPER(X)
PROPER(U85(X1, X2)) → PROPER(X1)
ACTIVE(U81(tt, V1, V2)) → U82¹(isNatKind(V1), V1, V2)
ACTIVE(U84(tt, V1, V2)) → ISNAT(V1)
PROPER(U51(X1, X2)) → U51¹(proper(X1), proper(X2))
ACTIVE(U83(X1, X2, X3)) → U83¹(active(X1), X2, X3)
ACTIVE(U32(tt, V)) → ISNATLIST(V)
ACTIVE(length(cons(N, L))) → U91¹(isNatList(L), L, N)
TOP(mark(X)) → TOP(proper(X))
U83¹(ok(X1), ok(X2), ok(X3)) → U83¹(X1, X2, X3)
PROPER(U21(X1, X2)) → PROPER(X2)
ACTIVE(U12(X1, X2)) → U12¹(active(X1), X2)
ACTIVE(U11(tt, V1)) → ISNATILISTKIND(V1)
PROPER(U83(X1, X2, X3)) → U83¹(proper(X1), proper(X2), proper(X3))

active(zeros) → mark(cons(0, zeros))
active(U11(tt, V1)) → mark(U12(isNatIListKind(V1), V1))
active(U12(tt, V1)) → mark(U13(isNatList(V1)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isNatIListKind(V), V))
active(U32(tt, V)) → mark(U33(isNatList(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isNatKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isNatIListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isNatIListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isNat(V1), V2))
active(U45(tt, V2)) → mark(U46(isNatIList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatIListKind(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt)) → mark(tt)
active(U71(tt)) → mark(tt)
active(U81(tt, V1, V2)) → mark(U82(isNatKind(V1), V1, V2))
active(U82(tt, V1, V2)) → mark(U83(isNatIListKind(V2), V1, V2))
active(U83(tt, V1, V2)) → mark(U84(isNatIListKind(V2), V1, V2))
active(U84(tt, V1, V2)) → mark(U85(isNat(V1), V2))
active(U85(tt, V2)) → mark(U86(isNatList(V2)))
active(U86(tt)) → mark(tt)
active(U91(tt, L, N)) → mark(U92(isNatIListKind(L), L, N))
active(U92(tt, L, N)) → mark(U93(isNat(N), L, N))
active(U93(tt, L, N)) → mark(U94(isNatKind(N), L))
active(U94(tt, L)) → mark(s(length(L)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatIListKind(V1), V1))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatIList(V)) → mark(U31(isNatIListKind(V), V))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNatKind(V1), V1, V2))
active(isNatIListKind(nil)) → mark(tt)
active(isNatIListKind(zeros)) → mark(tt)
active(isNatIListKind(cons(V1, V2))) → mark(U51(isNatKind(V1), V2))
active(isNatKind(0)) → mark(tt)
active(isNatKind(length(V1))) → mark(U61(isNatIListKind(V1)))
active(isNatKind(s(V1))) → mark(U71(isNatKind(V1)))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U81(isNatKind(V1), V1, V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U91(isNatList(L), L, N))
active(cons(X1, X2)) → cons(active(X1), X2)
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2)) → U21(active(X1), X2)
active(U22(X1, X2)) → U22(active(X1), X2)
active(U23(X)) → U23(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2)) → U51(active(X1), X2)
active(U52(X)) → U52(active(X))
active(U61(X)) → U61(active(X))
active(U71(X)) → U71(active(X))
active(U81(X1, X2, X3)) → U81(active(X1), X2, X3)
active(U82(X1, X2, X3)) → U82(active(X1), X2, X3)
active(U83(X1, X2, X3)) → U83(active(X1), X2, X3)
active(U84(X1, X2, X3)) → U84(active(X1), X2, X3)
active(U85(X1, X2)) → U85(active(X1), X2)
active(U86(X)) → U86(active(X))
active(U91(X1, X2, X3)) → U91(active(X1), X2, X3)
active(U92(X1, X2, X3)) → U92(active(X1), X2, X3)
active(U93(X1, X2, X3)) → U93(active(X1), X2, X3)
active(U94(X1, X2)) → U94(active(X1), X2)
active(s(X)) → s(active(X))
active(length(X)) → length(active(X))
cons(mark(X1), X2) → mark(cons(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2) → mark(U21(X1, X2))
U22(mark(X1), X2) → mark(U22(X1, X2))
U23(mark(X)) → mark(U23(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2) → mark(U51(X1, X2))
U52(mark(X)) → mark(U52(X))
U61(mark(X)) → mark(U61(X))
U71(mark(X)) → mark(U71(X))
U81(mark(X1), X2, X3) → mark(U81(X1, X2, X3))
U82(mark(X1), X2, X3) → mark(U82(X1, X2, X3))
U83(mark(X1), X2, X3) → mark(U83(X1, X2, X3))
U84(mark(X1), X2, X3) → mark(U84(X1, X2, X3))
U85(mark(X1), X2) → mark(U85(X1, X2))
U86(mark(X)) → mark(U86(X))
U91(mark(X1), X2, X3) → mark(U91(X1, X2, X3))
U92(mark(X1), X2, X3) → mark(U92(X1, X2, X3))
U93(mark(X1), X2, X3) → mark(U93(X1, X2, X3))
U94(mark(X1), X2) → mark(U94(X1, X2))
s(mark(X)) → mark(s(X))
length(mark(X)) → mark(length(X))
proper(zeros) → ok(zeros)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isNatIListKind(X)) → isNatIListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNatList(X)) → isNatList(proper(X))
proper(U21(X1, X2)) → U21(proper(X1), proper(X2))
proper(U22(X1, X2)) → U22(proper(X1), proper(X2))
proper(isNatKind(X)) → isNatKind(proper(X))
proper(U23(X)) → U23(proper(X))
proper(isNat(X)) → isNat(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(isNatIList(X)) → isNatIList(proper(X))
proper(U51(X1, X2)) → U51(proper(X1), proper(X2))
proper(U52(X)) → U52(proper(X))
proper(U61(X)) → U61(proper(X))
proper(U71(X)) → U71(proper(X))
proper(U81(X1, X2, X3)) → U81(proper(X1), proper(X2), proper(X3))
proper(U82(X1, X2, X3)) → U82(proper(X1), proper(X2), proper(X3))
proper(U83(X1, X2, X3)) → U83(proper(X1), proper(X2), proper(X3))
proper(U84(X1, X2, X3)) → U84(proper(X1), proper(X2), proper(X3))
proper(U85(X1, X2)) → U85(proper(X1), proper(X2))
proper(U86(X)) → U86(proper(X))
proper(U91(X1, X2, X3)) → U91(proper(X1), proper(X2), proper(X3))
proper(U92(X1, X2, X3)) → U92(proper(X1), proper(X2), proper(X3))
proper(U93(X1, X2, X3)) → U93(proper(X1), proper(X2), proper(X3))
proper(U94(X1, X2)) → U94(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(length(X)) → length(proper(X))
proper(nil) → ok(nil)
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isNatIListKind(ok(X)) → ok(isNatIListKind(X))
U13(ok(X)) → ok(U13(X))
isNatList(ok(X)) → ok(isNatList(X))
U21(ok(X1), ok(X2)) → ok(U21(X1, X2))
U22(ok(X1), ok(X2)) → ok(U22(X1, X2))
isNatKind(ok(X)) → ok(isNatKind(X))
U23(ok(X)) → ok(U23(X))
isNat(ok(X)) → ok(isNat(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
isNatIList(ok(X)) → ok(isNatIList(X))
U51(ok(X1), ok(X2)) → ok(U51(X1, X2))
U52(ok(X)) → ok(U52(X))
U61(ok(X)) → ok(U61(X))
U71(ok(X)) → ok(U71(X))
U81(ok(X1), ok(X2), ok(X3)) → ok(U81(X1, X2, X3))
U82(ok(X1), ok(X2), ok(X3)) → ok(U82(X1, X2, X3))
U83(ok(X1), ok(X2), ok(X3)) → ok(U83(X1, X2, X3))
U84(ok(X1), ok(X2), ok(X3)) → ok(U84(X1, X2, X3))
U85(ok(X1), ok(X2)) → ok(U85(X1, X2))
U86(ok(X)) → ok(U86(X))
U91(ok(X1), ok(X2), ok(X3)) → ok(U91(X1, X2, X3))
U92(ok(X1), ok(X2), ok(X3)) → ok(U92(X1, X2, X3))
U93(ok(X1), ok(X2), ok(X3)) → ok(U93(X1, X2, X3))
U94(ok(X1), ok(X2)) → ok(U94(X1, X2))
s(ok(X)) → ok(s(X))
length(ok(X)) → ok(length(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

ACTIVE(U51(X1, X2)) → ACTIVE(X1)
U71¹(mark(X)) → U71¹(X)
PROPER(U32(X1, X2)) → PROPER(X2)
ACTIVE(cons(X1, X2)) → CONS(active(X1), X2)
PROPER(U86(X)) → PROPER(X)
PROPER(U11(X1, X2)) → U11¹(proper(X1), proper(X2))
PROPER(U31(X1, X2)) → PROPER(X1)
U33¹(ok(X)) → U33¹(X)
PROPER(U45(X1, X2)) → PROPER(X2)
U81¹(mark(X1), X2, X3) → U81¹(X1, X2, X3)
ACTIVE(isNatIList(cons(V1, V2))) → ISNATKIND(V1)
PROPER(U91(X1, X2, X3)) → U91¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U52(X)) → U52¹(active(X))
PROPER(U81(X1, X2, X3)) → PROPER(X3)
ACTIVE(U21(X1, X2)) → U21¹(active(X1), X2)
ACTIVE(U22(tt, V1)) → ISNAT(V1)
U31¹(mark(X1), X2) → U31¹(X1, X2)
U82¹(mark(X1), X2, X3) → U82¹(X1, X2, X3)
U91¹(ok(X1), ok(X2), ok(X3)) → U91¹(X1, X2, X3)
PROPER(U11(X1, X2)) → PROPER(X2)
ACTIVE(isNatList(cons(V1, V2))) → ISNATKIND(V1)
PROPER(U12(X1, X2)) → PROPER(X2)
PROPER(U32(X1, X2)) → PROPER(X1)
U86¹(ok(X)) → U86¹(X)
ACTIVE(U44(tt, V1, V2)) → U45¹(isNat(V1), V2)
ACTIVE(U82(X1, X2, X3)) → U82¹(active(X1), X2, X3)
PROPER(U82(X1, X2, X3)) → PROPER(X2)
PROPER(U43(X1, X2, X3)) → U43¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U32(X1, X2)) → ACTIVE(X1)
PROPER(isNatList(X)) → ISNATLIST(proper(X))
U43¹(ok(X1), ok(X2), ok(X3)) → U43¹(X1, X2, X3)
U46¹(ok(X)) → U46¹(X)
PROPER(U45(X1, X2)) → U45¹(proper(X1), proper(X2))
ACTIVE(U91(X1, X2, X3)) → U91¹(active(X1), X2, X3)
U61¹(ok(X)) → U61¹(X)
U81¹(ok(X1), ok(X2), ok(X3)) → U81¹(X1, X2, X3)
ACTIVE(U32(tt, V)) → U33¹(isNatList(V))
U42¹(ok(X1), ok(X2), ok(X3)) → U42¹(X1, X2, X3)
ACTIVE(U93(X1, X2, X3)) → U93¹(active(X1), X2, X3)
ACTIVE(U84(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U84(X1, X2, X3)) → U84¹(active(X1), X2, X3)
ACTIVE(U86(X)) → ACTIVE(X)
PROPER(U94(X1, X2)) → PROPER(X2)
S(ok(X)) → S(X)
PROPER(U22(X1, X2)) → U22¹(proper(X1), proper(X2))
CONS(mark(X1), X2) → CONS(X1, X2)
PROPER(U44(X1, X2, X3)) → PROPER(X3)
PROPER(isNatKind(X)) → ISNATKIND(proper(X))
PROPER(U41(X1, X2, X3)) → U41¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U41(X1, X2, X3)) → U41¹(active(X1), X2, X3)
ACTIVE(U83(X1, X2, X3)) → ACTIVE(X1)
PROPER(cons(X1, X2)) → PROPER(X1)
U31¹(ok(X1), ok(X2)) → U31¹(X1, X2)
U93¹(mark(X1), X2, X3) → U93¹(X1, X2, X3)
PROPER(U45(X1, X2)) → PROPER(X1)
ACTIVE(U91(X1, X2, X3)) → ACTIVE(X1)
U51¹(mark(X1), X2) → U51¹(X1, X2)
S(mark(X)) → S(X)
PROPER(cons(X1, X2)) → CONS(proper(X1), proper(X2))
ISNATLIST(ok(X)) → ISNATLIST(X)
PROPER(U84(X1, X2, X3)) → PROPER(X1)
ACTIVE(isNatIListKind(cons(V1, V2))) → U51¹(isNatKind(V1), V2)
U13¹(mark(X)) → U13¹(X)
ACTIVE(U42(tt, V1, V2)) → U43¹(isNatIListKind(V2), V1, V2)
ACTIVE(U83(tt, V1, V2)) → U84¹(isNatIListKind(V2), V1, V2)
ACTIVE(U33(X)) → ACTIVE(X)
ACTIVE(U45(X1, X2)) → ACTIVE(X1)
U51¹(ok(X1), ok(X2)) → U51¹(X1, X2)
ACTIVE(U12(X1, X2)) → ACTIVE(X1)
PROPER(U83(X1, X2, X3)) → PROPER(X2)
ACTIVE(U31(tt, V)) → U32¹(isNatIListKind(V), V)
U92¹(mark(X1), X2, X3) → U92¹(X1, X2, X3)
ACTIVE(U93(tt, L, N)) → U94¹(isNatKind(N), L)
U12¹(ok(X1), ok(X2)) → U12¹(X1, X2)
ACTIVE(isNatList(cons(V1, V2))) → U81¹(isNatKind(V1), V1, V2)
ACTIVE(U41(tt, V1, V2)) → ISNATKIND(V1)
U23¹(mark(X)) → U23¹(X)
PROPER(U44(X1, X2, X3)) → PROPER(X1)
ACTIVE(U71(X)) → U71¹(active(X))
PROPER(U84(X1, X2, X3)) → U84¹(proper(X1), proper(X2), proper(X3))
PROPER(U23(X)) → PROPER(X)
PROPER(U92(X1, X2, X3)) → U92¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U81(X1, X2, X3)) → U81¹(active(X1), X2, X3)
PROPER(U82(X1, X2, X3)) → U82¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U33(X)) → U33¹(active(X))
ACTIVE(zeros) → CONS(0, zeros)
ACTIVE(U84(tt, V1, V2)) → U85¹(isNat(V1), V2)
ACTIVE(cons(X1, X2)) → ACTIVE(X1)
PROPER(U46(X)) → U46¹(proper(X))
ACTIVE(U82(tt, V1, V2)) → ISNATILISTKIND(V2)
ACTIVE(U51(tt, V2)) → ISNATILISTKIND(V2)
ISNATILIST(ok(X)) → ISNATILIST(X)
ACTIVE(U46(X)) → U46¹(active(X))
PROPER(U21(X1, X2)) → PROPER(X1)
U93¹(ok(X1), ok(X2), ok(X3)) → U93¹(X1, X2, X3)
PROPER(U12(X1, X2)) → U12¹(proper(X1), proper(X2))
U11¹(ok(X1), ok(X2)) → U11¹(X1, X2)
PROPER(U46(X)) → PROPER(X)
U86¹(mark(X)) → U86¹(X)
PROPER(isNatIList(X)) → ISNATILIST(proper(X))
ACTIVE(U45(X1, X2)) → U45¹(active(X1), X2)
PROPER(isNatIListKind(X)) → PROPER(X)
ACTIVE(isNatIList(V)) → ISNATILISTKIND(V)
ACTIVE(isNat(length(V1))) → U11¹(isNatIListKind(V1), V1)
PROPER(U41(X1, X2, X3)) → PROPER(X2)
ACTIVE(U86(X)) → U86¹(active(X))
PROPER(U22(X1, X2)) → PROPER(X2)
ISNATKIND(ok(X)) → ISNATKIND(X)
ACTIVE(U52(X)) → ACTIVE(X)
PROPER(U61(X)) → PROPER(X)
U92¹(ok(X1), ok(X2), ok(X3)) → U92¹(X1, X2, X3)
PROPER(U82(X1, X2, X3)) → PROPER(X1)
ACTIVE(U41(tt, V1, V2)) → U42¹(isNatKind(V1), V1, V2)
ACTIVE(U45(tt, V2)) → ISNATILIST(V2)
ACTIVE(U94(X1, X2)) → ACTIVE(X1)
ACTIVE(U92(tt, L, N)) → ISNAT(N)
U32¹(mark(X1), X2) → U32¹(X1, X2)
ACTIVE(U11(tt, V1)) → U12¹(isNatIListKind(V1), V1)
TOP(ok(X)) → TOP(active(X))
ACTIVE(U43(X1, X2, X3)) → U43¹(active(X1), X2, X3)
U45¹(ok(X1), ok(X2)) → U45¹(X1, X2)
ACTIVE(U22(tt, V1)) → U23¹(isNat(V1))
PROPER(U43(X1, X2, X3)) → PROPER(X3)
ISNAT(ok(X)) → ISNAT(X)
CONS(ok(X1), ok(X2)) → CONS(X1, X2)
ACTIVE(U41(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(length(cons(N, L))) → ISNATLIST(L)
PROPER(U52(X)) → U52¹(proper(X))
PROPER(U44(X1, X2, X3)) → U44¹(proper(X1), proper(X2), proper(X3))
PROPER(U33(X)) → U33¹(proper(X))
ACTIVE(U83(tt, V1, V2)) → ISNATILISTKIND(V2)
PROPER(U81(X1, X2, X3)) → PROPER(X2)
ACTIVE(isNat(s(V1))) → U21¹(isNatKind(V1), V1)
PROPER(U42(X1, X2, X3)) → PROPER(X1)
ACTIVE(U91(tt, L, N)) → U92¹(isNatIListKind(L), L, N)
PROPER(U81(X1, X2, X3)) → PROPER(X1)
U43¹(mark(X1), X2, X3) → U43¹(X1, X2, X3)
ACTIVE(U92(tt, L, N)) → U93¹(isNat(N), L, N)
PROPER(U13(X)) → U13¹(proper(X))
ACTIVE(U92(X1, X2, X3)) → ACTIVE(X1)
PROPER(U94(X1, X2)) → U94¹(proper(X1), proper(X2))
PROPER(U11(X1, X2)) → PROPER(X1)
ACTIVE(s(X)) → S(active(X))
PROPER(U51(X1, X2)) → PROPER(X2)
ACTIVE(U45(tt, V2)) → U46¹(isNatIList(V2))
U22¹(ok(X1), ok(X2)) → U22¹(X1, X2)
ACTIVE(U13(X)) → ACTIVE(X)
ACTIVE(U81(X1, X2, X3)) → ACTIVE(X1)
PROPER(isNatList(X)) → PROPER(X)
ACTIVE(U44(tt, V1, V2)) → ISNAT(V1)
ACTIVE(U94(X1, X2)) → U94¹(active(X1), X2)
ACTIVE(isNatKind(length(V1))) → ISNATILISTKIND(V1)
PROPER(length(X)) → LENGTH(proper(X))
PROPER(U84(X1, X2, X3)) → PROPER(X3)
PROPER(U12(X1, X2)) → PROPER(X1)
U21¹(mark(X1), X2) → U21¹(X1, X2)
ACTIVE(isNatKind(length(V1))) → U61¹(isNatIListKind(V1))
ACTIVE(U51(tt, V2)) → U52¹(isNatIListKind(V2))
ACTIVE(U31(X1, X2)) → ACTIVE(X1)
PROPER(U84(X1, X2, X3)) → PROPER(X2)
ACTIVE(U42(X1, X2, X3)) → ACTIVE(X1)
U21¹(ok(X1), ok(X2)) → U21¹(X1, X2)
ACTIVE(U94(tt, L)) → LENGTH(L)
ACTIVE(isNatIListKind(cons(V1, V2))) → ISNATKIND(V1)
PROPER(length(X)) → PROPER(X)
PROPER(U86(X)) → U86¹(proper(X))
PROPER(U83(X1, X2, X3)) → PROPER(X3)
PROPER(U93(X1, X2, X3)) → PROPER(X2)
ACTIVE(U11(X1, X2)) → ACTIVE(X1)
PROPER(U83(X1, X2, X3)) → PROPER(X1)
ACTIVE(s(X)) → ACTIVE(X)
ACTIVE(U46(X)) → ACTIVE(X)
U83¹(mark(X1), X2, X3) → U83¹(X1, X2, X3)
PROPER(U71(X)) → U71¹(proper(X))
ACTIVE(U82(X1, X2, X3)) → ACTIVE(X1)
PROPER(U92(X1, X2, X3)) → PROPER(X3)
ACTIVE(U42(tt, V1, V2)) → ISNATILISTKIND(V2)
U91¹(mark(X1), X2, X3) → U91¹(X1, X2, X3)
U46¹(mark(X)) → U46¹(X)
TOP(mark(X)) → PROPER(X)
ACTIVE(U71(X)) → ACTIVE(X)
ACTIVE(U43(tt, V1, V2)) → ISNATILISTKIND(V2)
PROPER(U31(X1, X2)) → U31¹(proper(X1), proper(X2))
ACTIVE(U92(X1, X2, X3)) → U92¹(active(X1), X2, X3)
TOP(ok(X)) → ACTIVE(X)
ACTIVE(length(X)) → ACTIVE(X)
PROPER(U44(X1, X2, X3)) → PROPER(X2)
ACTIVE(U21(tt, V1)) → ISNATKIND(V1)
ACTIVE(isNat(length(V1))) → ISNATILISTKIND(V1)
PROPER(U23(X)) → U23¹(proper(X))
U44¹(ok(X1), ok(X2), ok(X3)) → U44¹(X1, X2, X3)
ACTIVE(U82(tt, V1, V2)) → U83¹(isNatIListKind(V2), V1, V2)
LENGTH(mark(X)) → LENGTH(X)
PROPER(isNatKind(X)) → PROPER(X)
U82¹(ok(X1), ok(X2), ok(X3)) → U82¹(X1, X2, X3)
U23¹(ok(X)) → U23¹(X)
U32¹(ok(X1), ok(X2)) → U32¹(X1, X2)
ACTIVE(U22(X1, X2)) → ACTIVE(X1)
ACTIVE(U12(tt, V1)) → U13¹(isNatList(V1))
ACTIVE(length(X)) → LENGTH(active(X))
ACTIVE(U91(tt, L, N)) → ISNATILISTKIND(L)
ACTIVE(U94(tt, L)) → S(length(L))
PROPER(U43(X1, X2, X3)) → PROPER(X2)
PROPER(U93(X1, X2, X3)) → PROPER(X3)
ACTIVE(U61(X)) → ACTIVE(X)
PROPER(U82(X1, X2, X3)) → PROPER(X3)
ACTIVE(U51(X1, X2)) → U51¹(active(X1), X2)
PROPER(U51(X1, X2)) → PROPER(X1)
U41¹(ok(X1), ok(X2), ok(X3)) → U41¹(X1, X2, X3)
U94¹(mark(X1), X2) → U94¹(X1, X2)
PROPER(U33(X)) → PROPER(X)
U12¹(mark(X1), X2) → U12¹(X1, X2)
PROPER(isNatIListKind(X)) → ISNATILISTKIND(proper(X))
U61¹(mark(X)) → U61¹(X)
U94¹(ok(X1), ok(X2)) → U94¹(X1, X2)
PROPER(U91(X1, X2, X3)) → PROPER(X2)
PROPER(U42(X1, X2, X3)) → U42¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U43(tt, V1, V2)) → U44¹(isNatIListKind(V2), V1, V2)
PROPER(U22(X1, X2)) → PROPER(X1)
ACTIVE(U85(X1, X2)) → ACTIVE(X1)
PROPER(U94(X1, X2)) → PROPER(X1)
PROPER(U21(X1, X2)) → U21¹(proper(X1), proper(X2))
U13¹(ok(X)) → U13¹(X)
PROPER(U91(X1, X2, X3)) → PROPER(X1)
U84¹(ok(X1), ok(X2), ok(X3)) → U84¹(X1, X2, X3)
U42¹(mark(X1), X2, X3) → U42¹(X1, X2, X3)
ACTIVE(U21(X1, X2)) → ACTIVE(X1)
ACTIVE(U21(tt, V1)) → U22¹(isNatKind(V1), V1)
ACTIVE(U32(X1, X2)) → U32¹(active(X1), X2)
U41¹(mark(X1), X2, X3) → U41¹(X1, X2, X3)
PROPER(U13(X)) → PROPER(X)
PROPER(U85(X1, X2)) → PROPER(X2)
ACTIVE(U42(X1, X2, X3)) → U42¹(active(X1), X2, X3)
U45¹(mark(X1), X2) → U45¹(X1, X2)
ACTIVE(U61(X)) → U61¹(active(X))
PROPER(cons(X1, X2)) → PROPER(X2)
ISNATILISTKIND(ok(X)) → ISNATILISTKIND(X)
U33¹(mark(X)) → U33¹(X)
PROPER(U42(X1, X2, X3)) → PROPER(X3)
PROPER(U41(X1, X2, X3)) → PROPER(X1)
ACTIVE(U85(tt, V2)) → U86¹(isNatList(V2))
PROPER(U61(X)) → U61¹(proper(X))
PROPER(U93(X1, X2, X3)) → U93¹(proper(X1), proper(X2), proper(X3))
ACTIVE(U31(X1, X2)) → U31¹(active(X1), X2)
ACTIVE(U44(X1, X2, X3)) → U44¹(active(X1), X2, X3)
ACTIVE(isNatIList(cons(V1, V2))) → U41¹(isNatKind(V1), V1, V2)
PROPER(U85(X1, X2)) → U85¹(proper(X1), proper(X2))
PROPER(U41(X1, X2, X3)) → PROPER(X3)
ACTIVE(U22(X1, X2)) → U22¹(active(X1), X2)
U71¹(ok(X)) → U71¹(X)
PROPER(s(X)) → S(proper(X))
ACTIVE(U85(tt, V2)) → ISNATLIST(V2)
ACTIVE(U31(tt, V)) → ISNATILISTKIND(V)
ACTIVE(U23(X)) → U23¹(active(X))
ACTIVE(U44(X1, X2, X3)) → ACTIVE(X1)
PROPER(U92(X1, X2, X3)) → PROPER(X2)
PROPER(U52(X)) → PROPER(X)
U44¹(mark(X1), X2, X3) → U44¹(X1, X2, X3)
ACTIVE(isNat(s(V1))) → ISNATKIND(V1)
PROPER(U42(X1, X2, X3)) → PROPER(X2)
U11¹(mark(X1), X2) → U11¹(X1, X2)
PROPER(U92(X1, X2, X3)) → PROPER(X1)
PROPER(U81(X1, X2, X3)) → U81¹(proper(X1), proper(X2), proper(X3))
U22¹(mark(X1), X2) → U22¹(X1, X2)
ACTIVE(U13(X)) → U13¹(active(X))
U52¹(mark(X)) → U52¹(X)
PROPER(isNat(X)) → PROPER(X)
LENGTH(ok(X)) → LENGTH(X)
U85¹(mark(X1), X2) → U85¹(X1, X2)
ACTIVE(U93(tt, L, N)) → ISNATKIND(N)
PROPER(U32(X1, X2)) → U32¹(proper(X1), proper(X2))
PROPER(U93(X1, X2, X3)) → PROPER(X1)
PROPER(isNatIList(X)) → PROPER(X)
ACTIVE(isNatKind(s(V1))) → U71¹(isNatKind(V1))
ACTIVE(U43(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U81(tt, V1, V2)) → ISNATKIND(V1)
U84¹(mark(X1), X2, X3) → U84¹(X1, X2, X3)
PROPER(s(X)) → PROPER(X)
ACTIVE(U93(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(isNatIList(V)) → U31¹(isNatIListKind(V), V)
ACTIVE(U11(X1, X2)) → U11¹(active(X1), X2)
PROPER(U91(X1, X2, X3)) → PROPER(X3)
PROPER(isNat(X)) → ISNAT(proper(X))
ACTIVE(U23(X)) → ACTIVE(X)
ACTIVE(isNatKind(s(V1))) → ISNATKIND(V1)
ACTIVE(U12(tt, V1)) → ISNATLIST(V1)
PROPER(U43(X1, X2, X3)) → PROPER(X1)
PROPER(U31(X1, X2)) → PROPER(X2)
U85¹(ok(X1), ok(X2)) → U85¹(X1, X2)
U52¹(ok(X)) → U52¹(X)
ACTIVE(U85(X1, X2)) → U85¹(active(X1), X2)
PROPER(U71(X)) → PROPER(X)
PROPER(U85(X1, X2)) → PROPER(X1)
ACTIVE(U81(tt, V1, V2)) → U82¹(isNatKind(V1), V1, V2)
ACTIVE(U84(tt, V1, V2)) → ISNAT(V1)
PROPER(U51(X1, X2)) → U51¹(proper(X1), proper(X2))
ACTIVE(U83(X1, X2, X3)) → U83¹(active(X1), X2, X3)
ACTIVE(U32(tt, V)) → ISNATLIST(V)
ACTIVE(length(cons(N, L))) → U91¹(isNatList(L), L, N)
TOP(mark(X)) → TOP(proper(X))
U83¹(ok(X1), ok(X2), ok(X3)) → U83¹(X1, X2, X3)
PROPER(U21(X1, X2)) → PROPER(X2)
ACTIVE(U12(X1, X2)) → U12¹(active(X1), X2)
ACTIVE(U11(tt, V1)) → ISNATILISTKIND(V1)
PROPER(U83(X1, X2, X3)) → U83¹(proper(X1), proper(X2), proper(X3))