LMPO

Execution Time (secs)	0.589
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  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(), V2) -> a__U32(a__isNatKind(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt()) -> tt()
     , a__U51(tt(), N) -> a__U52(a__isNatKind(N), N)
     , a__U52(tt(), N) -> mark(N)
     , a__U61(tt(), M, N) -> a__U62(a__isNatKind(M), M, N)
     , a__U62(tt(), M, N) -> a__U63(a__isNat(N), M, N)
     , a__U63(tt(), M, N) -> a__U64(a__isNatKind(N), M, N)
     , a__U64(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , 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__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2)
     , a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
     , a__plus(N, 0()) -> a__U51(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , 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(isNat(X)) -> a__isNat(X)
     , 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)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X)) -> a__U41(mark(X))
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3)
     , mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3)
     , mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__isNatKind(X) -> isNatKind(X)
     , 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__isNat(X) -> isNat(X)
     , 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) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X) -> U41(X)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2, X3) -> U62(X1, X2, X3)
     , a__U63(X1, X2, X3) -> U63(X1, X2, X3)
     , a__U64(X1, X2, X3) -> U64(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	1.661
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  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(), V2) -> a__U32(a__isNatKind(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt()) -> tt()
     , a__U51(tt(), N) -> a__U52(a__isNatKind(N), N)
     , a__U52(tt(), N) -> mark(N)
     , a__U61(tt(), M, N) -> a__U62(a__isNatKind(M), M, N)
     , a__U62(tt(), M, N) -> a__U63(a__isNat(N), M, N)
     , a__U63(tt(), M, N) -> a__U64(a__isNatKind(N), M, N)
     , a__U64(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , 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__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2)
     , a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
     , a__plus(N, 0()) -> a__U51(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , 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(isNat(X)) -> a__isNat(X)
     , 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)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X)) -> a__U41(mark(X))
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3)
     , mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3)
     , mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__isNatKind(X) -> isNatKind(X)
     , 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__isNat(X) -> isNat(X)
     , 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) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X) -> U41(X)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2, X3) -> U62(X1, X2, X3)
     , a__U63(X1, X2, X3) -> U63(X1, X2, X3)
     , a__U64(X1, X2, X3) -> U64(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.447
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  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(), V2) -> a__U32(a__isNatKind(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt()) -> tt()
     , a__U51(tt(), N) -> a__U52(a__isNatKind(N), N)
     , a__U52(tt(), N) -> mark(N)
     , a__U61(tt(), M, N) -> a__U62(a__isNatKind(M), M, N)
     , a__U62(tt(), M, N) -> a__U63(a__isNat(N), M, N)
     , a__U63(tt(), M, N) -> a__U64(a__isNatKind(N), M, N)
     , a__U64(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , 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__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2)
     , a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
     , a__plus(N, 0()) -> a__U51(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , 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(isNat(X)) -> a__isNat(X)
     , 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)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X)) -> a__U41(mark(X))
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3)
     , mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3)
     , mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__isNatKind(X) -> isNatKind(X)
     , 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__isNat(X) -> isNat(X)
     , 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) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X) -> U41(X)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2, X3) -> U62(X1, X2, X3)
     , a__U63(X1, X2, X3) -> U63(X1, X2, X3)
     , a__U64(X1, X2, X3) -> U64(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.512
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  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(), V2) -> a__U32(a__isNatKind(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt()) -> tt()
     , a__U51(tt(), N) -> a__U52(a__isNatKind(N), N)
     , a__U52(tt(), N) -> mark(N)
     , a__U61(tt(), M, N) -> a__U62(a__isNatKind(M), M, N)
     , a__U62(tt(), M, N) -> a__U63(a__isNat(N), M, N)
     , a__U63(tt(), M, N) -> a__U64(a__isNatKind(N), M, N)
     , a__U64(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , 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__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2)
     , a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
     , a__plus(N, 0()) -> a__U51(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , 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(isNat(X)) -> a__isNat(X)
     , 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)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X)) -> a__U41(mark(X))
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3)
     , mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3)
     , mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__isNatKind(X) -> isNatKind(X)
     , 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__isNat(X) -> isNat(X)
     , 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) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X) -> U41(X)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2, X3) -> U62(X1, X2, X3)
     , a__U63(X1, X2, X3) -> U63(X1, X2, X3)
     , a__U64(X1, X2, X3) -> U64(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.479
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  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(), V2) -> a__U32(a__isNatKind(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt()) -> tt()
     , a__U51(tt(), N) -> a__U52(a__isNatKind(N), N)
     , a__U52(tt(), N) -> mark(N)
     , a__U61(tt(), M, N) -> a__U62(a__isNatKind(M), M, N)
     , a__U62(tt(), M, N) -> a__U63(a__isNat(N), M, N)
     , a__U63(tt(), M, N) -> a__U64(a__isNatKind(N), M, N)
     , a__U64(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , 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__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2)
     , a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
     , a__plus(N, 0()) -> a__U51(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , 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(isNat(X)) -> a__isNat(X)
     , 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)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X)) -> a__U41(mark(X))
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3)
     , mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3)
     , mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__isNatKind(X) -> isNatKind(X)
     , 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__isNat(X) -> isNat(X)
     , 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) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X) -> U41(X)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2, X3) -> U62(X1, X2, X3)
     , a__U63(X1, X2, X3) -> U63(X1, X2, X3)
     , a__U64(X1, X2, X3) -> U64(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.427
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  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(), V2) -> a__U32(a__isNatKind(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt()) -> tt()
     , a__U51(tt(), N) -> a__U52(a__isNatKind(N), N)
     , a__U52(tt(), N) -> mark(N)
     , a__U61(tt(), M, N) -> a__U62(a__isNatKind(M), M, N)
     , a__U62(tt(), M, N) -> a__U63(a__isNat(N), M, N)
     , a__U63(tt(), M, N) -> a__U64(a__isNatKind(N), M, N)
     , a__U64(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , 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__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) -> a__U31(a__isNatKind(V1), V2)
     , a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
     , a__plus(N, 0()) -> a__U51(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U61(a__isNat(M), M, N)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , 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(isNat(X)) -> a__isNat(X)
     , 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)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X)) -> a__U41(mark(X))
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2, X3)) -> a__U62(mark(X1), X2, X3)
     , mark(U63(X1, X2, X3)) -> a__U63(mark(X1), X2, X3)
     , mark(U64(X1, X2, X3)) -> a__U64(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__isNatKind(X) -> isNatKind(X)
     , 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__isNat(X) -> isNat(X)
     , 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) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X) -> U41(X)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2, X3) -> U62(X1, X2, X3)
     , a__U63(X1, X2, X3) -> U63(X1, X2, X3)
     , a__U64(X1, X2, X3) -> U64(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 PEANO complete noand GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)