Problem Transformed CSR 04 PEANO complete GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete GM

stdout:

MAYBE

Problem:
a__U11(tt(),V1,V2) -> a__U12(a__isNat(V1),V2)
a__U12(tt(),V2) -> a__U13(a__isNat(V2))
a__U13(tt()) -> tt()
a__U21(tt(),V1) -> a__U22(a__isNat(V1))
a__U22(tt()) -> tt()
a__U31(tt(),N) -> mark(N)
a__U41(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
a__and(tt(),X) -> mark(X)
a__isNat(0()) -> tt()
a__isNat(plus(V1,V2)) -> a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
a__isNatKind(0()) -> tt()
a__isNatKind(plus(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
a__isNatKind(s(V1)) -> a__isNatKind(V1)
a__plus(N,0()) -> a__U31(a__and(a__isNat(N),isNatKind(N)),N)
a__plus(N,s(M)) -> a__U41(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
mark(isNat(X)) -> a__isNat(X)
mark(U13(X)) -> a__U13(mark(X))
mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
mark(U22(X)) -> a__U22(mark(X))
mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(isNatKind(X)) -> a__isNatKind(X)
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) -> U12(X1,X2)
a__isNat(X) -> isNat(X)
a__U13(X) -> U13(X)
a__U21(X1,X2) -> U21(X1,X2)
a__U22(X) -> U22(X)
a__U31(X1,X2) -> U31(X1,X2)
a__U41(X1,X2,X3) -> U41(X1,X2,X3)
a__plus(X1,X2) -> plus(X1,X2)
a__and(X1,X2) -> and(X1,X2)
a__isNatKind(X) -> isNatKind(X)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 PEANO complete GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__U11(tt(), V1, V2) -> a__U12(a__isNat(V1), V2)
     , a__U12(tt(), V2) -> a__U13(a__isNat(V2))
     , a__U13(tt()) -> tt()
     , a__U21(tt(), V1) -> a__U22(a__isNat(V1))
     , a__U22(tt()) -> tt()
     , a__U31(tt(), N) -> mark(N)
     , a__U41(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) ->
       a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2)
     , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
     , a__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) ->
       a__and(a__isNatKind(V1), isNatKind(V2))
     , a__isNatKind(s(V1)) -> a__isNatKind(V1)
     , a__plus(N, 0()) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N)
     , a__plus(N, s(M)) ->
       a__U41(a__and(a__and(a__isNat(M), isNatKind(M)),
                     and(isNat(N), isNatKind(N))),
              M,
              N)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U13(X)) -> a__U13(mark(X))
     , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
     , mark(U22(X)) -> a__U22(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , 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) -> U12(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__U13(X) -> U13(X)
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U22(X) -> U22(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatKind(X) -> isNatKind(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 PEANO complete GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 PEANO complete GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a__U11(tt(), V1, V2) -> a__U12(a__isNat(V1), V2)
     , a__U12(tt(), V2) -> a__U13(a__isNat(V2))
     , a__U13(tt()) -> tt()
     , a__U21(tt(), V1) -> a__U22(a__isNat(V1))
     , a__U22(tt()) -> tt()
     , a__U31(tt(), N) -> mark(N)
     , a__U41(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(plus(V1, V2)) ->
       a__U11(a__and(a__isNatKind(V1), isNatKind(V2)), V1, V2)
     , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
     , a__isNatKind(0()) -> tt()
     , a__isNatKind(plus(V1, V2)) ->
       a__and(a__isNatKind(V1), isNatKind(V2))
     , a__isNatKind(s(V1)) -> a__isNatKind(V1)
     , a__plus(N, 0()) -> a__U31(a__and(a__isNat(N), isNatKind(N)), N)
     , a__plus(N, s(M)) ->
       a__U41(a__and(a__and(a__isNat(M), isNatKind(M)),
                     and(isNat(N), isNatKind(N))),
              M,
              N)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U13(X)) -> a__U13(mark(X))
     , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
     , mark(U22(X)) -> a__U22(mark(X))
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNatKind(X)) -> a__isNatKind(X)
     , 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) -> U12(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__U13(X) -> U13(X)
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U22(X) -> U22(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatKind(X) -> isNatKind(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds