Problem Transformed CSR 04 MYNAT nokinds GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds GM

stdout:

MAYBE

Problem:
a__U11(tt(),N) -> mark(N)
a__U21(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
a__U31(tt()) -> 0()
a__U41(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
a__and(tt(),X) -> mark(X)
a__isNat(0()) -> tt()
a__isNat(plus(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
a__isNat(s(V1)) -> a__isNat(V1)
a__isNat(x(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
a__plus(N,0()) -> a__U11(a__isNat(N),N)
a__plus(N,s(M)) -> a__U21(a__and(a__isNat(M),isNat(N)),M,N)
a__x(N,0()) -> a__U31(a__isNat(N))
a__x(N,s(M)) -> a__U41(a__and(a__isNat(M),isNat(N)),M,N)
mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
mark(U31(X)) -> a__U31(mark(X))
mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(isNat(X)) -> a__isNat(X)
mark(tt()) -> tt()
mark(s(X)) -> s(mark(X))
mark(0()) -> 0()
a__U11(X1,X2) -> U11(X1,X2)
a__U21(X1,X2,X3) -> U21(X1,X2,X3)
a__plus(X1,X2) -> plus(X1,X2)
a__U31(X) -> U31(X)
a__U41(X1,X2,X3) -> U41(X1,X2,X3)
a__x(X1,X2) -> x(X1,X2)
a__and(X1,X2) -> and(X1,X2)
a__isNat(X) -> isNat(X)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 MYNAT nokinds GM

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 MYNAT nokinds GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 MYNAT nokinds GM

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds