Problem AProVE 07 wiehe12

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 07 wiehe12

stdout:

MAYBE

Problem:
g(s(x),s(y)) ->
if(and(f(s(x)),f(s(y))),t(g(k(minus(m(x,y),n(x,y)),s(s(0()))),k(n(s(x),s(y)),s(s(0()))))),
g(minus(m(x,y),n(x,y)),n(s(x),s(y))))
n(0(),y) -> 0()
n(x,0()) -> 0()
n(s(x),s(y)) -> s(n(x,y))
m(0(),y) -> y
m(x,0()) -> x
m(s(x),s(y)) -> s(m(x,y))
k(0(),s(y)) -> 0()
k(s(x),s(y)) -> s(k(minus(x,y),s(y)))
t(x) -> p(x,x)
p(s(x),s(y)) -> s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
p(s(x),x) -> p(if(gt(x,x),id(x),id(x)),s(x))
p(0(),y) -> y
p(id(x),s(y)) -> s(p(x,if(gt(s(y),y),y,s(y))))
minus(x,0()) -> x
minus(s(x),s(y)) -> minus(x,y)
id(x) -> x
if(true(),x,y) -> x
if(false(),x,y) -> y
not(x) -> if(x,false(),true())
and(x,false()) -> false()
and(true(),true()) -> true()
f(0()) -> true()
f(s(x)) -> h(x)
h(0()) -> false()
h(s(x)) -> f(x)
gt(s(x),0()) -> true()
gt(0(),y) -> false()
gt(s(x),s(y)) -> gt(x,y)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 07 wiehe12

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 07 wiehe12

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  g(s(x), s(y)) ->
       if(and(f(s(x)), f(s(y))),
          t(g(k(minus(m(x, y), n(x, y)), s(s(0()))),
              k(n(s(x), s(y)), s(s(0()))))),
          g(minus(m(x, y), n(x, y)), n(s(x), s(y))))
     , n(0(), y) -> 0()
     , n(x, 0()) -> 0()
     , n(s(x), s(y)) -> s(n(x, y))
     , m(0(), y) -> y
     , m(x, 0()) -> x
     , m(s(x), s(y)) -> s(m(x, y))
     , k(0(), s(y)) -> 0()
     , k(s(x), s(y)) -> s(k(minus(x, y), s(y)))
     , t(x) -> p(x, x)
     , p(s(x), s(y)) ->
       s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
     , p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x))
     , p(0(), y) -> y
     , p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y))))
     , minus(x, 0()) -> x
     , minus(s(x), s(y)) -> minus(x, y)
     , id(x) -> x
     , if(true(), x, y) -> x
     , if(false(), x, y) -> y
     , not(x) -> if(x, false(), true())
     , and(x, false()) -> false()
     , and(true(), true()) -> true()
     , f(0()) -> true()
     , f(s(x)) -> h(x)
     , h(0()) -> false()
     , h(s(x)) -> f(x)
     , gt(s(x), 0()) -> true()
     , gt(0(), y) -> false()
     , gt(s(x), s(y)) -> gt(x, y)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 07 wiehe12

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 07 wiehe12

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  g(s(x), s(y)) ->
       if(and(f(s(x)), f(s(y))),
          t(g(k(minus(m(x, y), n(x, y)), s(s(0()))),
              k(n(s(x), s(y)), s(s(0()))))),
          g(minus(m(x, y), n(x, y)), n(s(x), s(y))))
     , n(0(), y) -> 0()
     , n(x, 0()) -> 0()
     , n(s(x), s(y)) -> s(n(x, y))
     , m(0(), y) -> y
     , m(x, 0()) -> x
     , m(s(x), s(y)) -> s(m(x, y))
     , k(0(), s(y)) -> 0()
     , k(s(x), s(y)) -> s(k(minus(x, y), s(y)))
     , t(x) -> p(x, x)
     , p(s(x), s(y)) ->
       s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
     , p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x))
     , p(0(), y) -> y
     , p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y))))
     , minus(x, 0()) -> x
     , minus(s(x), s(y)) -> minus(x, y)
     , id(x) -> x
     , if(true(), x, y) -> x
     , if(false(), x, y) -> y
     , not(x) -> if(x, false(), true())
     , and(x, false()) -> false()
     , and(true(), true()) -> true()
     , f(0()) -> true()
     , f(s(x)) -> h(x)
     , h(0()) -> false()
     , h(s(x)) -> f(x)
     , gt(s(x), 0()) -> true()
     , gt(0(), y) -> false()
     , gt(s(x), s(y)) -> gt(x, y)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds