LMPO

Execution Time (secs)	0.287
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__U11(tt(), V2) -> a__U12(a__isNat(V2))
     , a__U12(tt()) -> tt()
     , a__U21(tt()) -> tt()
     , a__U31(tt(), V2) -> a__U32(a__isNat(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt(), N) -> mark(N)
     , a__U51(tt(), M, N) -> a__U52(a__isNat(N), M, N)
     , a__U52(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__U61(tt()) -> 0()
     , a__U71(tt(), M, N) -> a__U72(a__isNat(N), M, N)
     , a__U72(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2)
     , a__plus(N, 0()) -> a__U41(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N)
     , a__x(N, 0()) -> a__U61(a__isNat(N))
     , a__x(N, s(M)) -> a__U71(a__isNat(M), M, N)
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(U12(X)) -> a__U12(mark(X))
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
     , mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(U61(X)) -> a__U61(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3)
     , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__U12(X) -> U12(X)
     , a__isNat(X) -> isNat(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
     , a__U52(X1, X2, X3) -> U52(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__U61(X) -> U61(X)
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U72(X1, X2, X3) -> U72(X1, X2, X3)
     , a__x(X1, X2) -> x(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.683
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__U11(tt(), V2) -> a__U12(a__isNat(V2))
     , a__U12(tt()) -> tt()
     , a__U21(tt()) -> tt()
     , a__U31(tt(), V2) -> a__U32(a__isNat(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt(), N) -> mark(N)
     , a__U51(tt(), M, N) -> a__U52(a__isNat(N), M, N)
     , a__U52(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__U61(tt()) -> 0()
     , a__U71(tt(), M, N) -> a__U72(a__isNat(N), M, N)
     , a__U72(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2)
     , a__plus(N, 0()) -> a__U41(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N)
     , a__x(N, 0()) -> a__U61(a__isNat(N))
     , a__x(N, s(M)) -> a__U71(a__isNat(M), M, N)
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(U12(X)) -> a__U12(mark(X))
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
     , mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(U61(X)) -> a__U61(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3)
     , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__U12(X) -> U12(X)
     , a__isNat(X) -> isNat(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
     , a__U52(X1, X2, X3) -> U52(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__U61(X) -> U61(X)
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U72(X1, X2, X3) -> U72(X1, X2, X3)
     , a__x(X1, X2) -> x(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.403
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__U11(tt(), V2) -> a__U12(a__isNat(V2))
     , a__U12(tt()) -> tt()
     , a__U21(tt()) -> tt()
     , a__U31(tt(), V2) -> a__U32(a__isNat(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt(), N) -> mark(N)
     , a__U51(tt(), M, N) -> a__U52(a__isNat(N), M, N)
     , a__U52(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__U61(tt()) -> 0()
     , a__U71(tt(), M, N) -> a__U72(a__isNat(N), M, N)
     , a__U72(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2)
     , a__plus(N, 0()) -> a__U41(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N)
     , a__x(N, 0()) -> a__U61(a__isNat(N))
     , a__x(N, s(M)) -> a__U71(a__isNat(M), M, N)
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(U12(X)) -> a__U12(mark(X))
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
     , mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(U61(X)) -> a__U61(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3)
     , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__U12(X) -> U12(X)
     , a__isNat(X) -> isNat(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
     , a__U52(X1, X2, X3) -> U52(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__U61(X) -> U61(X)
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U72(X1, X2, X3) -> U72(X1, X2, X3)
     , a__x(X1, X2) -> x(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.356
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__U11(tt(), V2) -> a__U12(a__isNat(V2))
     , a__U12(tt()) -> tt()
     , a__U21(tt()) -> tt()
     , a__U31(tt(), V2) -> a__U32(a__isNat(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt(), N) -> mark(N)
     , a__U51(tt(), M, N) -> a__U52(a__isNat(N), M, N)
     , a__U52(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__U61(tt()) -> 0()
     , a__U71(tt(), M, N) -> a__U72(a__isNat(N), M, N)
     , a__U72(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2)
     , a__plus(N, 0()) -> a__U41(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N)
     , a__x(N, 0()) -> a__U61(a__isNat(N))
     , a__x(N, s(M)) -> a__U71(a__isNat(M), M, N)
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(U12(X)) -> a__U12(mark(X))
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
     , mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(U61(X)) -> a__U61(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3)
     , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__U12(X) -> U12(X)
     , a__isNat(X) -> isNat(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
     , a__U52(X1, X2, X3) -> U52(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__U61(X) -> U61(X)
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U72(X1, X2, X3) -> U72(X1, X2, X3)
     , a__x(X1, X2) -> x(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.304
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__U11(tt(), V2) -> a__U12(a__isNat(V2))
     , a__U12(tt()) -> tt()
     , a__U21(tt()) -> tt()
     , a__U31(tt(), V2) -> a__U32(a__isNat(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt(), N) -> mark(N)
     , a__U51(tt(), M, N) -> a__U52(a__isNat(N), M, N)
     , a__U52(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__U61(tt()) -> 0()
     , a__U71(tt(), M, N) -> a__U72(a__isNat(N), M, N)
     , a__U72(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2)
     , a__plus(N, 0()) -> a__U41(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N)
     , a__x(N, 0()) -> a__U61(a__isNat(N))
     , a__x(N, s(M)) -> a__U71(a__isNat(M), M, N)
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(U12(X)) -> a__U12(mark(X))
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
     , mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(U61(X)) -> a__U61(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3)
     , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__U12(X) -> U12(X)
     , a__isNat(X) -> isNat(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
     , a__U52(X1, X2, X3) -> U52(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__U61(X) -> U61(X)
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U72(X1, X2, X3) -> U72(X1, X2, X3)
     , a__x(X1, X2) -> x(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.387
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds noand GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__U11(tt(), V2) -> a__U12(a__isNat(V2))
     , a__U12(tt()) -> tt()
     , a__U21(tt()) -> tt()
     , a__U31(tt(), V2) -> a__U32(a__isNat(V2))
     , a__U32(tt()) -> tt()
     , a__U41(tt(), N) -> mark(N)
     , a__U51(tt(), M, N) -> a__U52(a__isNat(N), M, N)
     , a__U52(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__U61(tt()) -> 0()
     , a__U71(tt(), M, N) -> a__U72(a__isNat(N), M, N)
     , a__U72(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2)
     , a__plus(N, 0()) -> a__U41(a__isNat(N), N)
     , a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N)
     , a__x(N, 0()) -> a__U61(a__isNat(N))
     , a__x(N, s(M)) -> a__U71(a__isNat(M), M, N)
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(U12(X)) -> a__U12(mark(X))
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
     , mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(U61(X)) -> a__U61(mark(X))
     , mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3)
     , mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3)
     , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__U12(X) -> U12(X)
     , a__isNat(X) -> isNat(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
     , a__U52(X1, X2, X3) -> U52(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__U61(X) -> U61(X)
     , a__U71(X1, X2, X3) -> U71(X1, X2, X3)
     , a__U72(X1, X2, X3) -> U72(X1, X2, X3)
     , a__x(X1, X2) -> x(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 MYNAT nokinds noand GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)