Problem Transformed CSR 04 MYNAT complete FR

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 MYNAT complete FR

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(),V1,V2) -> U32(isNat(activate(V1)),activate(V2))
U32(tt(),V2) -> U33(isNat(activate(V2)))
U33(tt()) -> tt()
U41(tt(),N) -> activate(N)
U51(tt(),M,N) -> s(plus(activate(N),activate(M)))
U61(tt()) -> 0()
U71(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
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))
isNat(n__x(V1,V2)) ->
U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2))
isNatKind(n__0()) -> tt()
isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
isNatKind(n__s(V1)) -> isNatKind(activate(V1))
isNatKind(n__x(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
plus(N,0()) -> U41(and(isNat(N),n__isNatKind(N)),N)
plus(N,s(M)) -> U51(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N)
x(N,0()) -> U61(and(isNat(N),n__isNatKind(N)))
x(N,s(M)) -> U71(and(and(isNat(M),n__isNatKind(M)),n__and(n__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)
x(X1,X2) -> n__x(X1,X2)
and(X1,X2) -> n__and(X1,X2)
isNat(X) -> n__isNat(X)
activate(n__0()) -> 0()
activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
activate(n__isNatKind(X)) -> isNatKind(X)
activate(n__s(X)) -> s(activate(X))
activate(n__x(X1,X2)) -> x(activate(X1),activate(X2))
activate(n__and(X1,X2)) -> and(activate(X1),X2)
activate(n__isNat(X)) -> isNat(X)
activate(X) -> X

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 MYNAT complete FR

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 MYNAT complete FR

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(), V1, V2) -> U32(isNat(activate(V1)), activate(V2))
     , U32(tt(), V2) -> U33(isNat(activate(V2)))
     , U33(tt()) -> tt()
     , U41(tt(), N) -> activate(N)
     , U51(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , U61(tt()) -> 0()
     , U71(tt(), M, N) -> plus(x(activate(N), activate(M)), activate(N))
     , 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))
     , isNat(n__x(V1, V2)) ->
       U31(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))),
           activate(V1),
           activate(V2))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__plus(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatKind(activate(V2)))
     , isNatKind(n__s(V1)) -> isNatKind(activate(V1))
     , isNatKind(n__x(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatKind(activate(V2)))
     , plus(N, 0()) -> U41(and(isNat(N), n__isNatKind(N)), N)
     , plus(N, s(M)) ->
       U51(and(and(isNat(M), n__isNatKind(M)),
               n__and(n__isNat(N), n__isNatKind(N))),
           M,
           N)
     , x(N, 0()) -> U61(and(isNat(N), n__isNatKind(N)))
     , x(N, s(M)) ->
       U71(and(and(isNat(M), n__isNatKind(M)),
               n__and(n__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)
     , x(X1, X2) -> n__x(X1, X2)
     , and(X1, X2) -> n__and(X1, X2)
     , isNat(X) -> n__isNat(X)
     , activate(n__0()) -> 0()
     , activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2))
     , activate(n__isNatKind(X)) -> isNatKind(X)
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__x(X1, X2)) -> x(activate(X1), activate(X2))
     , activate(n__and(X1, X2)) -> and(activate(X1), X2)
     , activate(n__isNat(X)) -> isNat(X)
     , 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 MYNAT complete FR

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 MYNAT complete FR

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(), V1, V2) -> U32(isNat(activate(V1)), activate(V2))
     , U32(tt(), V2) -> U33(isNat(activate(V2)))
     , U33(tt()) -> tt()
     , U41(tt(), N) -> activate(N)
     , U51(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , U61(tt()) -> 0()
     , U71(tt(), M, N) -> plus(x(activate(N), activate(M)), activate(N))
     , 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))
     , isNat(n__x(V1, V2)) ->
       U31(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))),
           activate(V1),
           activate(V2))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__plus(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatKind(activate(V2)))
     , isNatKind(n__s(V1)) -> isNatKind(activate(V1))
     , isNatKind(n__x(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatKind(activate(V2)))
     , plus(N, 0()) -> U41(and(isNat(N), n__isNatKind(N)), N)
     , plus(N, s(M)) ->
       U51(and(and(isNat(M), n__isNatKind(M)),
               n__and(n__isNat(N), n__isNatKind(N))),
           M,
           N)
     , x(N, 0()) -> U61(and(isNat(N), n__isNatKind(N)))
     , x(N, s(M)) ->
       U71(and(and(isNat(M), n__isNatKind(M)),
               n__and(n__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)
     , x(X1, X2) -> n__x(X1, X2)
     , and(X1, X2) -> n__and(X1, X2)
     , isNat(X) -> n__isNat(X)
     , activate(n__0()) -> 0()
     , activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2))
     , activate(n__isNatKind(X)) -> isNatKind(X)
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__x(X1, X2)) -> x(activate(X1), activate(X2))
     , activate(n__and(X1, X2)) -> and(activate(X1), X2)
     , activate(n__isNat(X)) -> isNat(X)
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds