Problem Transformed CSR 04 PEANO complete-noand Z

Tool CaT

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

stdout:

MAYBE

Problem:
U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
U15(tt(),V2) -> U16(isNat(activate(V2)))
U16(tt()) -> tt()
U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
U22(tt(),V1) -> U23(isNat(activate(V1)))
U23(tt()) -> tt()
U31(tt(),V2) -> U32(isNatKind(activate(V2)))
U32(tt()) -> tt()
U41(tt()) -> tt()
U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
U52(tt(),N) -> activate(N)
U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
isNat(n__0()) -> tt()
isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
isNatKind(n__0()) -> tt()
isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
plus(N,0()) -> U51(isNat(N),N)
plus(N,s(M)) -> U61(isNat(M),M,N)
0() -> n__0()
plus(X1,X2) -> n__plus(X1,X2)
s(X) -> n__s(X)
activate(n__0()) -> 0()
activate(n__plus(X1,X2)) -> plus(X1,X2)
activate(n__s(X)) -> s(X)
activate(X) -> X

Proof:
Open

Tool IRC1

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

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 PEANO complete-noand 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(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U12(tt(), V1, V2) ->
       U13(isNatKind(activate(V2)), activate(V1), activate(V2))
     , U13(tt(), V1, V2) ->
       U14(isNatKind(activate(V2)), activate(V1), activate(V2))
     , U14(tt(), V1, V2) -> U15(isNat(activate(V1)), activate(V2))
     , U15(tt(), V2) -> U16(isNat(activate(V2)))
     , U16(tt()) -> tt()
     , U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1))
     , U22(tt(), V1) -> U23(isNat(activate(V1)))
     , U23(tt()) -> tt()
     , U31(tt(), V2) -> U32(isNatKind(activate(V2)))
     , U32(tt()) -> tt()
     , U41(tt()) -> tt()
     , U51(tt(), N) -> U52(isNatKind(activate(N)), activate(N))
     , U52(tt(), N) -> activate(N)
     , U61(tt(), M, N) ->
       U62(isNatKind(activate(M)), activate(M), activate(N))
     , U62(tt(), M, N) ->
       U63(isNat(activate(N)), activate(M), activate(N))
     , U63(tt(), M, N) ->
       U64(isNatKind(activate(N)), activate(M), activate(N))
     , U64(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , isNat(n__0()) -> tt()
     , isNat(n__plus(V1, V2)) ->
       U11(isNatKind(activate(V1)), activate(V1), activate(V2))
     , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__plus(V1, V2)) ->
       U31(isNatKind(activate(V1)), activate(V2))
     , isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
     , plus(N, 0()) -> U51(isNat(N), N)
     , plus(N, s(M)) -> U61(isNat(M), M, N)
     , 0() -> n__0()
     , plus(X1, X2) -> n__plus(X1, X2)
     , s(X) -> n__s(X)
     , activate(n__0()) -> 0()
     , activate(n__plus(X1, X2)) -> plus(X1, X2)
     , activate(n__s(X)) -> s(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 PEANO complete-noand Z

stdout:

MAYBE

Tool RC2

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

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  U11(tt(), V1, V2) ->
       U12(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U12(tt(), V1, V2) ->
       U13(isNatKind(activate(V2)), activate(V1), activate(V2))
     , U13(tt(), V1, V2) ->
       U14(isNatKind(activate(V2)), activate(V1), activate(V2))
     , U14(tt(), V1, V2) -> U15(isNat(activate(V1)), activate(V2))
     , U15(tt(), V2) -> U16(isNat(activate(V2)))
     , U16(tt()) -> tt()
     , U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1))
     , U22(tt(), V1) -> U23(isNat(activate(V1)))
     , U23(tt()) -> tt()
     , U31(tt(), V2) -> U32(isNatKind(activate(V2)))
     , U32(tt()) -> tt()
     , U41(tt()) -> tt()
     , U51(tt(), N) -> U52(isNatKind(activate(N)), activate(N))
     , U52(tt(), N) -> activate(N)
     , U61(tt(), M, N) ->
       U62(isNatKind(activate(M)), activate(M), activate(N))
     , U62(tt(), M, N) ->
       U63(isNat(activate(N)), activate(M), activate(N))
     , U63(tt(), M, N) ->
       U64(isNatKind(activate(N)), activate(M), activate(N))
     , U64(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , isNat(n__0()) -> tt()
     , isNat(n__plus(V1, V2)) ->
       U11(isNatKind(activate(V1)), activate(V1), activate(V2))
     , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__plus(V1, V2)) ->
       U31(isNatKind(activate(V1)), activate(V2))
     , isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
     , plus(N, 0()) -> U51(isNat(N), N)
     , plus(N, s(M)) -> U61(isNat(M), M, N)
     , 0() -> n__0()
     , plus(X1, X2) -> n__plus(X1, X2)
     , s(X) -> n__s(X)
     , activate(n__0()) -> 0()
     , activate(n__plus(X1, X2)) -> plus(X1, X2)
     , activate(n__s(X)) -> s(X)
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds