Problem Transformed CSR 04 ExIntrod Zan97 C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 C

stdout:

MAYBE

Problem:
active(fact(X)) -> mark(if(zero(X),s(0()),prod(X,fact(p(X)))))
active(add(0(),X)) -> mark(X)
active(add(s(X),Y)) -> mark(s(add(X,Y)))
active(prod(0(),X)) -> mark(0())
active(prod(s(X),Y)) -> mark(add(Y,prod(X,Y)))
active(if(true(),X,Y)) -> mark(X)
active(if(false(),X,Y)) -> mark(Y)
active(zero(0())) -> mark(true())
active(zero(s(X))) -> mark(false())
active(p(s(X))) -> mark(X)
active(fact(X)) -> fact(active(X))
active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
active(zero(X)) -> zero(active(X))
active(s(X)) -> s(active(X))
active(prod(X1,X2)) -> prod(active(X1),X2)
active(prod(X1,X2)) -> prod(X1,active(X2))
active(p(X)) -> p(active(X))
active(add(X1,X2)) -> add(active(X1),X2)
active(add(X1,X2)) -> add(X1,active(X2))
fact(mark(X)) -> mark(fact(X))
if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
zero(mark(X)) -> mark(zero(X))
s(mark(X)) -> mark(s(X))
prod(mark(X1),X2) -> mark(prod(X1,X2))
prod(X1,mark(X2)) -> mark(prod(X1,X2))
p(mark(X)) -> mark(p(X))
add(mark(X1),X2) -> mark(add(X1,X2))
add(X1,mark(X2)) -> mark(add(X1,X2))
proper(fact(X)) -> fact(proper(X))
proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
proper(zero(X)) -> zero(proper(X))
proper(s(X)) -> s(proper(X))
proper(0()) -> ok(0())
proper(prod(X1,X2)) -> prod(proper(X1),proper(X2))
proper(p(X)) -> p(proper(X))
proper(add(X1,X2)) -> add(proper(X1),proper(X2))
proper(true()) -> ok(true())
proper(false()) -> ok(false())
fact(ok(X)) -> ok(fact(X))
if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
zero(ok(X)) -> ok(zero(X))
s(ok(X)) -> ok(s(X))
prod(ok(X1),ok(X2)) -> ok(prod(X1,X2))
p(ok(X)) -> ok(p(X))
add(ok(X1),ok(X2)) -> ok(add(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 ExIntrod Zan97 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  active(fact(X)) ->
       mark(if(zero(X), s(0()), prod(X, fact(p(X)))))
     , active(add(0(), X)) -> mark(X)
     , active(add(s(X), Y)) -> mark(s(add(X, Y)))
     , active(prod(0(), X)) -> mark(0())
     , active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
     , active(if(true(), X, Y)) -> mark(X)
     , active(if(false(), X, Y)) -> mark(Y)
     , active(zero(0())) -> mark(true())
     , active(zero(s(X))) -> mark(false())
     , active(p(s(X))) -> mark(X)
     , active(fact(X)) -> fact(active(X))
     , active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
     , active(zero(X)) -> zero(active(X))
     , active(s(X)) -> s(active(X))
     , active(prod(X1, X2)) -> prod(active(X1), X2)
     , active(prod(X1, X2)) -> prod(X1, active(X2))
     , active(p(X)) -> p(active(X))
     , active(add(X1, X2)) -> add(active(X1), X2)
     , active(add(X1, X2)) -> add(X1, active(X2))
     , fact(mark(X)) -> mark(fact(X))
     , if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
     , zero(mark(X)) -> mark(zero(X))
     , s(mark(X)) -> mark(s(X))
     , prod(mark(X1), X2) -> mark(prod(X1, X2))
     , prod(X1, mark(X2)) -> mark(prod(X1, X2))
     , p(mark(X)) -> mark(p(X))
     , add(mark(X1), X2) -> mark(add(X1, X2))
     , add(X1, mark(X2)) -> mark(add(X1, X2))
     , proper(fact(X)) -> fact(proper(X))
     , proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
     , proper(zero(X)) -> zero(proper(X))
     , proper(s(X)) -> s(proper(X))
     , proper(0()) -> ok(0())
     , proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
     , proper(p(X)) -> p(proper(X))
     , proper(add(X1, X2)) -> add(proper(X1), proper(X2))
     , proper(true()) -> ok(true())
     , proper(false()) -> ok(false())
     , fact(ok(X)) -> ok(fact(X))
     , if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
     , zero(ok(X)) -> ok(zero(X))
     , s(ok(X)) -> ok(s(X))
     , prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
     , p(ok(X)) -> ok(p(X))
     , add(ok(X1), ok(X2)) -> ok(add(X1, X2))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 ExIntrod Zan97 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(fact(X)) ->
       mark(if(zero(X), s(0()), prod(X, fact(p(X)))))
     , active(add(0(), X)) -> mark(X)
     , active(add(s(X), Y)) -> mark(s(add(X, Y)))
     , active(prod(0(), X)) -> mark(0())
     , active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
     , active(if(true(), X, Y)) -> mark(X)
     , active(if(false(), X, Y)) -> mark(Y)
     , active(zero(0())) -> mark(true())
     , active(zero(s(X))) -> mark(false())
     , active(p(s(X))) -> mark(X)
     , active(fact(X)) -> fact(active(X))
     , active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
     , active(zero(X)) -> zero(active(X))
     , active(s(X)) -> s(active(X))
     , active(prod(X1, X2)) -> prod(active(X1), X2)
     , active(prod(X1, X2)) -> prod(X1, active(X2))
     , active(p(X)) -> p(active(X))
     , active(add(X1, X2)) -> add(active(X1), X2)
     , active(add(X1, X2)) -> add(X1, active(X2))
     , fact(mark(X)) -> mark(fact(X))
     , if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
     , zero(mark(X)) -> mark(zero(X))
     , s(mark(X)) -> mark(s(X))
     , prod(mark(X1), X2) -> mark(prod(X1, X2))
     , prod(X1, mark(X2)) -> mark(prod(X1, X2))
     , p(mark(X)) -> mark(p(X))
     , add(mark(X1), X2) -> mark(add(X1, X2))
     , add(X1, mark(X2)) -> mark(add(X1, X2))
     , proper(fact(X)) -> fact(proper(X))
     , proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
     , proper(zero(X)) -> zero(proper(X))
     , proper(s(X)) -> s(proper(X))
     , proper(0()) -> ok(0())
     , proper(prod(X1, X2)) -> prod(proper(X1), proper(X2))
     , proper(p(X)) -> p(proper(X))
     , proper(add(X1, X2)) -> add(proper(X1), proper(X2))
     , proper(true()) -> ok(true())
     , proper(false()) -> ok(false())
     , fact(ok(X)) -> ok(fact(X))
     , if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
     , zero(ok(X)) -> ok(zero(X))
     , s(ok(X)) -> ok(s(X))
     , prod(ok(X1), ok(X2)) -> ok(prod(X1, X2))
     , p(ok(X)) -> ok(p(X))
     , add(ok(X1), ok(X2)) -> ok(add(X1, X2))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds