Problem Transformed CSR 04 PEANO complete Z

Tool CaT

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

stdout:

MAYBE

Problem:
U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2))
U12(tt(),V2) -> U13(isNat(activate(V2)))
U13(tt()) -> tt()
U21(tt(),V1) -> U22(isNat(activate(V1)))
U22(tt()) -> tt()
U31(tt(),N) -> activate(N)
U41(tt(),M,N) -> s(plus(activate(N),activate(M)))
and(tt(),X) -> activate(X)
isNat(n__0()) -> tt()
isNat(n__plus(V1,V2)) ->
U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2))
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
isNatKind(n__0()) -> tt()
isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
isNatKind(n__s(V1)) -> isNatKind(activate(V1))
plus(N,0()) -> U31(and(isNat(N),n__isNatKind(N)),N)
plus(N,s(M)) -> U41(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N)
0() -> n__0()
plus(X1,X2) -> n__plus(X1,X2)
isNatKind(X) -> n__isNatKind(X)
s(X) -> n__s(X)
and(X1,X2) -> n__and(X1,X2)
activate(n__0()) -> 0()
activate(n__plus(X1,X2)) -> plus(X1,X2)
activate(n__isNatKind(X)) -> isNatKind(X)
activate(n__s(X)) -> s(X)
activate(n__and(X1,X2)) -> and(X1,X2)
activate(X) -> X

Proof:
Open

Tool IRC1

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

stdout:

MAYBE

Tool IRC2

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

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  U11(tt(), V1, V2) -> U12(isNat(activate(V1)), activate(V2))
     , U12(tt(), V2) -> U13(isNat(activate(V2)))
     , U13(tt()) -> tt()
     , U21(tt(), V1) -> U22(isNat(activate(V1)))
     , U22(tt()) -> tt()
     , U31(tt(), N) -> activate(N)
     , U41(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , and(tt(), X) -> activate(X)
     , isNat(n__0()) -> tt()
     , isNat(n__plus(V1, V2)) ->
       U11(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))),
           activate(V1),
           activate(V2))
     , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__plus(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatKind(activate(V2)))
     , isNatKind(n__s(V1)) -> isNatKind(activate(V1))
     , plus(N, 0()) -> U31(and(isNat(N), n__isNatKind(N)), N)
     , plus(N, s(M)) ->
       U41(and(and(isNat(M), n__isNatKind(M)),
               n__and(isNat(N), n__isNatKind(N))),
           M,
           N)
     , 0() -> n__0()
     , plus(X1, X2) -> n__plus(X1, X2)
     , isNatKind(X) -> n__isNatKind(X)
     , s(X) -> n__s(X)
     , and(X1, X2) -> n__and(X1, X2)
     , activate(n__0()) -> 0()
     , activate(n__plus(X1, X2)) -> plus(X1, X2)
     , activate(n__isNatKind(X)) -> isNatKind(X)
     , activate(n__s(X)) -> s(X)
     , activate(n__and(X1, X2)) -> and(X1, X2)
     , activate(X) -> 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 Z

stdout:

MAYBE

Tool RC2

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

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  U11(tt(), V1, V2) -> U12(isNat(activate(V1)), activate(V2))
     , U12(tt(), V2) -> U13(isNat(activate(V2)))
     , U13(tt()) -> tt()
     , U21(tt(), V1) -> U22(isNat(activate(V1)))
     , U22(tt()) -> tt()
     , U31(tt(), N) -> activate(N)
     , U41(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , and(tt(), X) -> activate(X)
     , isNat(n__0()) -> tt()
     , isNat(n__plus(V1, V2)) ->
       U11(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))),
           activate(V1),
           activate(V2))
     , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__plus(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatKind(activate(V2)))
     , isNatKind(n__s(V1)) -> isNatKind(activate(V1))
     , plus(N, 0()) -> U31(and(isNat(N), n__isNatKind(N)), N)
     , plus(N, s(M)) ->
       U41(and(and(isNat(M), n__isNatKind(M)),
               n__and(isNat(N), n__isNatKind(N))),
           M,
           N)
     , 0() -> n__0()
     , plus(X1, X2) -> n__plus(X1, X2)
     , isNatKind(X) -> n__isNatKind(X)
     , s(X) -> n__s(X)
     , and(X1, X2) -> n__and(X1, X2)
     , activate(n__0()) -> 0()
     , activate(n__plus(X1, X2)) -> plus(X1, X2)
     , activate(n__isNatKind(X)) -> isNatKind(X)
     , activate(n__s(X)) -> s(X)
     , activate(n__and(X1, X2)) -> and(X1, X2)
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds