Problem Transformed CSR 04 Ex1 GM03 GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 GM03 GM

stdout:

MAYBE

Problem:
a__p(0()) -> 0()
a__p(s(X)) -> mark(X)
a__leq(0(),Y) -> true()
a__leq(s(X),0()) -> false()
a__leq(s(X),s(Y)) -> a__leq(mark(X),mark(Y))
a__if(true(),X,Y) -> mark(X)
a__if(false(),X,Y) -> mark(Y)
a__diff(X,Y) -> a__if(a__leq(mark(X),mark(Y)),0(),s(diff(p(X),Y)))
mark(p(X)) -> a__p(mark(X))
mark(leq(X1,X2)) -> a__leq(mark(X1),mark(X2))
mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
mark(diff(X1,X2)) -> a__diff(mark(X1),mark(X2))
mark(0()) -> 0()
mark(s(X)) -> s(mark(X))
mark(true()) -> true()
mark(false()) -> false()
a__p(X) -> p(X)
a__leq(X1,X2) -> leq(X1,X2)
a__if(X1,X2,X3) -> if(X1,X2,X3)
a__diff(X1,X2) -> diff(X1,X2)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 GM03 GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex1 GM03 GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__p(0()) -> 0()
     , a__p(s(X)) -> mark(X)
     , a__leq(0(), Y) -> true()
     , a__leq(s(X), 0()) -> false()
     , a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y))
     , a__if(true(), X, Y) -> mark(X)
     , a__if(false(), X, Y) -> mark(Y)
     , a__diff(X, Y) ->
       a__if(a__leq(mark(X), mark(Y)), 0(), s(diff(p(X), Y)))
     , mark(p(X)) -> a__p(mark(X))
     , mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2))
     , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
     , mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(true()) -> true()
     , mark(false()) -> false()
     , a__p(X) -> p(X)
     , a__leq(X1, X2) -> leq(X1, X2)
     , a__if(X1, X2, X3) -> if(X1, X2, X3)
     , a__diff(X1, X2) -> diff(X1, X2)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex1 GM03 GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex1 GM03 GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a__p(0()) -> 0()
     , a__p(s(X)) -> mark(X)
     , a__leq(0(), Y) -> true()
     , a__leq(s(X), 0()) -> false()
     , a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y))
     , a__if(true(), X, Y) -> mark(X)
     , a__if(false(), X, Y) -> mark(Y)
     , a__diff(X, Y) ->
       a__if(a__leq(mark(X), mark(Y)), 0(), s(diff(p(X), Y)))
     , mark(p(X)) -> a__p(mark(X))
     , mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2))
     , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
     , mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(true()) -> true()
     , mark(false()) -> false()
     , a__p(X) -> p(X)
     , a__leq(X1, X2) -> leq(X1, X2)
     , a__if(X1, X2, X3) -> if(X1, X2, X3)
     , a__diff(X1, X2) -> diff(X1, X2)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds