LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), M, N) -> a__U102(a__isNatKind(M), M, N)
, a__U102(tt(), M, N) -> a__U103(a__isNat(N), M, N)
, a__U103(tt(), M, N) -> a__U104(a__isNatKind(N), M, N)
, a__U104(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
, a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
, a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
, a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2)
, a__U15(tt(), V2) -> a__U16(a__isNat(V2))
, a__U16(tt()) -> tt()
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
, a__U32(tt(), V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
, a__U33(tt(), V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
, a__U34(tt(), V1, V2) -> a__U35(a__isNat(V1), V2)
, a__U35(tt(), V2) -> a__U36(a__isNat(V2))
, a__U36(tt()) -> tt()
, a__U41(tt(), V2) -> a__U42(a__isNatKind(V2))
, a__U42(tt()) -> tt()
, a__U51(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt(), N) -> a__U72(a__isNatKind(N), N)
, a__U72(tt(), N) -> mark(N)
, a__U81(tt(), M, N) -> a__U82(a__isNatKind(M), M, N)
, a__U82(tt(), M, N) -> a__U83(a__isNat(N), M, N)
, a__U83(tt(), M, N) -> a__U84(a__isNatKind(N), M, N)
, a__U84(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U91(tt(), N) -> a__U92(a__isNatKind(N))
, a__U92(tt()) -> 0()
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
, a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
, a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
, a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
, a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__plus(N, 0()) -> a__U71(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
, a__x(N, 0()) -> a__U91(a__isNat(N), N)
, a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNat(X)) -> a__isNat(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
, mark(U16(X)) -> a__U16(mark(X))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
, mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
, mark(U36(X)) -> a__U36(mark(X))
, mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
, mark(U42(X)) -> a__U42(mark(X))
, mark(U51(X)) -> a__U51(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
, mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
, mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
, mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNat(X) -> isNat(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__x(X1, X2) -> x(X1, X2)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U15(X1, X2) -> U15(X1, X2)
, a__U16(X) -> U16(X)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U34(X1, X2, X3) -> U34(X1, X2, X3)
, a__U35(X1, X2) -> U35(X1, X2)
, a__U36(X) -> U36(X)
, a__U41(X1, X2) -> U41(X1, X2)
, a__U42(X) -> U42(X)
, a__U51(X) -> U51(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U81(X1, X2, X3) -> U81(X1, X2, X3)
, a__U82(X1, X2, X3) -> U82(X1, X2, X3)
, a__U83(X1, X2, X3) -> U83(X1, X2, X3)
, a__U84(X1, X2, X3) -> U84(X1, X2, X3)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), M, N) -> a__U102(a__isNatKind(M), M, N)
, a__U102(tt(), M, N) -> a__U103(a__isNat(N), M, N)
, a__U103(tt(), M, N) -> a__U104(a__isNatKind(N), M, N)
, a__U104(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
, a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
, a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
, a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2)
, a__U15(tt(), V2) -> a__U16(a__isNat(V2))
, a__U16(tt()) -> tt()
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
, a__U32(tt(), V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
, a__U33(tt(), V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
, a__U34(tt(), V1, V2) -> a__U35(a__isNat(V1), V2)
, a__U35(tt(), V2) -> a__U36(a__isNat(V2))
, a__U36(tt()) -> tt()
, a__U41(tt(), V2) -> a__U42(a__isNatKind(V2))
, a__U42(tt()) -> tt()
, a__U51(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt(), N) -> a__U72(a__isNatKind(N), N)
, a__U72(tt(), N) -> mark(N)
, a__U81(tt(), M, N) -> a__U82(a__isNatKind(M), M, N)
, a__U82(tt(), M, N) -> a__U83(a__isNat(N), M, N)
, a__U83(tt(), M, N) -> a__U84(a__isNatKind(N), M, N)
, a__U84(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U91(tt(), N) -> a__U92(a__isNatKind(N))
, a__U92(tt()) -> 0()
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
, a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
, a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
, a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
, a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__plus(N, 0()) -> a__U71(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
, a__x(N, 0()) -> a__U91(a__isNat(N), N)
, a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNat(X)) -> a__isNat(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
, mark(U16(X)) -> a__U16(mark(X))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
, mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
, mark(U36(X)) -> a__U36(mark(X))
, mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
, mark(U42(X)) -> a__U42(mark(X))
, mark(U51(X)) -> a__U51(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
, mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
, mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
, mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNat(X) -> isNat(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__x(X1, X2) -> x(X1, X2)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U15(X1, X2) -> U15(X1, X2)
, a__U16(X) -> U16(X)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U34(X1, X2, X3) -> U34(X1, X2, X3)
, a__U35(X1, X2) -> U35(X1, X2)
, a__U36(X) -> U36(X)
, a__U41(X1, X2) -> U41(X1, X2)
, a__U42(X) -> U42(X)
, a__U51(X) -> U51(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U81(X1, X2, X3) -> U81(X1, X2, X3)
, a__U82(X1, X2, X3) -> U82(X1, X2, X3)
, a__U83(X1, X2, X3) -> U83(X1, X2, X3)
, a__U84(X1, X2, X3) -> U84(X1, X2, X3)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), M, N) -> a__U102(a__isNatKind(M), M, N)
, a__U102(tt(), M, N) -> a__U103(a__isNat(N), M, N)
, a__U103(tt(), M, N) -> a__U104(a__isNatKind(N), M, N)
, a__U104(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
, a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
, a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
, a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2)
, a__U15(tt(), V2) -> a__U16(a__isNat(V2))
, a__U16(tt()) -> tt()
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
, a__U32(tt(), V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
, a__U33(tt(), V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
, a__U34(tt(), V1, V2) -> a__U35(a__isNat(V1), V2)
, a__U35(tt(), V2) -> a__U36(a__isNat(V2))
, a__U36(tt()) -> tt()
, a__U41(tt(), V2) -> a__U42(a__isNatKind(V2))
, a__U42(tt()) -> tt()
, a__U51(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt(), N) -> a__U72(a__isNatKind(N), N)
, a__U72(tt(), N) -> mark(N)
, a__U81(tt(), M, N) -> a__U82(a__isNatKind(M), M, N)
, a__U82(tt(), M, N) -> a__U83(a__isNat(N), M, N)
, a__U83(tt(), M, N) -> a__U84(a__isNatKind(N), M, N)
, a__U84(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U91(tt(), N) -> a__U92(a__isNatKind(N))
, a__U92(tt()) -> 0()
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
, a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
, a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
, a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
, a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__plus(N, 0()) -> a__U71(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
, a__x(N, 0()) -> a__U91(a__isNat(N), N)
, a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNat(X)) -> a__isNat(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
, mark(U16(X)) -> a__U16(mark(X))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
, mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
, mark(U36(X)) -> a__U36(mark(X))
, mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
, mark(U42(X)) -> a__U42(mark(X))
, mark(U51(X)) -> a__U51(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
, mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
, mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
, mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNat(X) -> isNat(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__x(X1, X2) -> x(X1, X2)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U15(X1, X2) -> U15(X1, X2)
, a__U16(X) -> U16(X)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U34(X1, X2, X3) -> U34(X1, X2, X3)
, a__U35(X1, X2) -> U35(X1, X2)
, a__U36(X) -> U36(X)
, a__U41(X1, X2) -> U41(X1, X2)
, a__U42(X) -> U42(X)
, a__U51(X) -> U51(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U81(X1, X2, X3) -> U81(X1, X2, X3)
, a__U82(X1, X2, X3) -> U82(X1, X2, X3)
, a__U83(X1, X2, X3) -> U83(X1, X2, X3)
, a__U84(X1, X2, X3) -> U84(X1, X2, X3)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), M, N) -> a__U102(a__isNatKind(M), M, N)
, a__U102(tt(), M, N) -> a__U103(a__isNat(N), M, N)
, a__U103(tt(), M, N) -> a__U104(a__isNatKind(N), M, N)
, a__U104(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
, a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
, a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
, a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2)
, a__U15(tt(), V2) -> a__U16(a__isNat(V2))
, a__U16(tt()) -> tt()
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
, a__U32(tt(), V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
, a__U33(tt(), V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
, a__U34(tt(), V1, V2) -> a__U35(a__isNat(V1), V2)
, a__U35(tt(), V2) -> a__U36(a__isNat(V2))
, a__U36(tt()) -> tt()
, a__U41(tt(), V2) -> a__U42(a__isNatKind(V2))
, a__U42(tt()) -> tt()
, a__U51(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt(), N) -> a__U72(a__isNatKind(N), N)
, a__U72(tt(), N) -> mark(N)
, a__U81(tt(), M, N) -> a__U82(a__isNatKind(M), M, N)
, a__U82(tt(), M, N) -> a__U83(a__isNat(N), M, N)
, a__U83(tt(), M, N) -> a__U84(a__isNatKind(N), M, N)
, a__U84(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U91(tt(), N) -> a__U92(a__isNatKind(N))
, a__U92(tt()) -> 0()
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
, a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
, a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
, a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
, a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__plus(N, 0()) -> a__U71(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
, a__x(N, 0()) -> a__U91(a__isNat(N), N)
, a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNat(X)) -> a__isNat(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
, mark(U16(X)) -> a__U16(mark(X))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
, mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
, mark(U36(X)) -> a__U36(mark(X))
, mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
, mark(U42(X)) -> a__U42(mark(X))
, mark(U51(X)) -> a__U51(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
, mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
, mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
, mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNat(X) -> isNat(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__x(X1, X2) -> x(X1, X2)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U15(X1, X2) -> U15(X1, X2)
, a__U16(X) -> U16(X)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U34(X1, X2, X3) -> U34(X1, X2, X3)
, a__U35(X1, X2) -> U35(X1, X2)
, a__U36(X) -> U36(X)
, a__U41(X1, X2) -> U41(X1, X2)
, a__U42(X) -> U42(X)
, a__U51(X) -> U51(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U81(X1, X2, X3) -> U81(X1, X2, X3)
, a__U82(X1, X2, X3) -> U82(X1, X2, X3)
, a__U83(X1, X2, X3) -> U83(X1, X2, X3)
, a__U84(X1, X2, X3) -> U84(X1, X2, X3)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), M, N) -> a__U102(a__isNatKind(M), M, N)
, a__U102(tt(), M, N) -> a__U103(a__isNat(N), M, N)
, a__U103(tt(), M, N) -> a__U104(a__isNatKind(N), M, N)
, a__U104(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
, a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
, a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
, a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2)
, a__U15(tt(), V2) -> a__U16(a__isNat(V2))
, a__U16(tt()) -> tt()
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
, a__U32(tt(), V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
, a__U33(tt(), V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
, a__U34(tt(), V1, V2) -> a__U35(a__isNat(V1), V2)
, a__U35(tt(), V2) -> a__U36(a__isNat(V2))
, a__U36(tt()) -> tt()
, a__U41(tt(), V2) -> a__U42(a__isNatKind(V2))
, a__U42(tt()) -> tt()
, a__U51(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt(), N) -> a__U72(a__isNatKind(N), N)
, a__U72(tt(), N) -> mark(N)
, a__U81(tt(), M, N) -> a__U82(a__isNatKind(M), M, N)
, a__U82(tt(), M, N) -> a__U83(a__isNat(N), M, N)
, a__U83(tt(), M, N) -> a__U84(a__isNatKind(N), M, N)
, a__U84(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U91(tt(), N) -> a__U92(a__isNatKind(N))
, a__U92(tt()) -> 0()
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
, a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
, a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
, a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
, a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__plus(N, 0()) -> a__U71(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
, a__x(N, 0()) -> a__U91(a__isNat(N), N)
, a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNat(X)) -> a__isNat(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
, mark(U16(X)) -> a__U16(mark(X))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
, mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
, mark(U36(X)) -> a__U36(mark(X))
, mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
, mark(U42(X)) -> a__U42(mark(X))
, mark(U51(X)) -> a__U51(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
, mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
, mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
, mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNat(X) -> isNat(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__x(X1, X2) -> x(X1, X2)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U15(X1, X2) -> U15(X1, X2)
, a__U16(X) -> U16(X)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U34(X1, X2, X3) -> U34(X1, X2, X3)
, a__U35(X1, X2) -> U35(X1, X2)
, a__U36(X) -> U36(X)
, a__U41(X1, X2) -> U41(X1, X2)
, a__U42(X) -> U42(X)
, a__U51(X) -> U51(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U81(X1, X2, X3) -> U81(X1, X2, X3)
, a__U82(X1, X2, X3) -> U82(X1, X2, X3)
, a__U83(X1, X2, X3) -> U83(X1, X2, X3)
, a__U84(X1, X2, X3) -> U84(X1, X2, X3)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), M, N) -> a__U102(a__isNatKind(M), M, N)
, a__U102(tt(), M, N) -> a__U103(a__isNat(N), M, N)
, a__U103(tt(), M, N) -> a__U104(a__isNatKind(N), M, N)
, a__U104(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__U11(tt(), V1, V2) -> a__U12(a__isNatKind(V1), V1, V2)
, a__U12(tt(), V1, V2) -> a__U13(a__isNatKind(V2), V1, V2)
, a__U13(tt(), V1, V2) -> a__U14(a__isNatKind(V2), V1, V2)
, a__U14(tt(), V1, V2) -> a__U15(a__isNat(V1), V2)
, a__U15(tt(), V2) -> a__U16(a__isNat(V2))
, a__U16(tt()) -> tt()
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V1, V2) -> a__U32(a__isNatKind(V1), V1, V2)
, a__U32(tt(), V1, V2) -> a__U33(a__isNatKind(V2), V1, V2)
, a__U33(tt(), V1, V2) -> a__U34(a__isNatKind(V2), V1, V2)
, a__U34(tt(), V1, V2) -> a__U35(a__isNat(V1), V2)
, a__U35(tt(), V2) -> a__U36(a__isNat(V2))
, a__U36(tt()) -> tt()
, a__U41(tt(), V2) -> a__U42(a__isNatKind(V2))
, a__U42(tt()) -> tt()
, a__U51(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt(), N) -> a__U72(a__isNatKind(N), N)
, a__U72(tt(), N) -> mark(N)
, a__U81(tt(), M, N) -> a__U82(a__isNatKind(M), M, N)
, a__U82(tt(), M, N) -> a__U83(a__isNat(N), M, N)
, a__U83(tt(), M, N) -> a__U84(a__isNatKind(N), M, N)
, a__U84(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U91(tt(), N) -> a__U92(a__isNatKind(N))
, a__U92(tt()) -> 0()
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__U11(a__isNatKind(V1), V1, V2)
, a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
, a__isNat(x(V1, V2)) -> a__U31(a__isNatKind(V1), V1, V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(plus(V1, V2)) -> a__U41(a__isNatKind(V1), V2)
, a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
, a__isNatKind(x(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__plus(N, 0()) -> a__U71(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U81(a__isNat(M), M, N)
, a__x(N, 0()) -> a__U91(a__isNat(N), N)
, a__x(N, s(M)) -> a__U101(a__isNat(M), M, N)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNat(X)) -> a__isNat(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U15(X1, X2)) -> a__U15(mark(X1), X2)
, mark(U16(X)) -> a__U16(mark(X))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U34(X1, X2, X3)) -> a__U34(mark(X1), X2, X3)
, mark(U35(X1, X2)) -> a__U35(mark(X1), X2)
, mark(U36(X)) -> a__U36(mark(X))
, mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
, mark(U42(X)) -> a__U42(mark(X))
, mark(U51(X)) -> a__U51(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
, mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
, mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
, mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNat(X) -> isNat(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__x(X1, X2) -> x(X1, X2)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U15(X1, X2) -> U15(X1, X2)
, a__U16(X) -> U16(X)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U34(X1, X2, X3) -> U34(X1, X2, X3)
, a__U35(X1, X2) -> U35(X1, X2)
, a__U36(X) -> U36(X)
, a__U41(X1, X2) -> U41(X1, X2)
, a__U42(X) -> U42(X)
, a__U51(X) -> U51(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U81(X1, X2, X3) -> U81(X1, X2, X3)
, a__U82(X1, X2, X3) -> U82(X1, X2, X3)
, a__U83(X1, X2, X3) -> U83(X1, X2, X3)
, a__U84(X1, X2, X3) -> U84(X1, X2, X3)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..