Tool CaT
stdout:
MAYBE
Problem:
minus(0(),y) -> 0()
minus(s(x),0()) -> s(x)
minus(s(x),s(y)) -> minus(x,y)
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
if(true(),x,y) -> x
if(false(),x,y) -> y
perfectp(0()) -> false()
perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
f(0(),y,0(),u) -> true()
f(0(),y,s(z),u) -> false()
f(s(x),0(),z,u) -> f(x,u,minus(z,s(x)),u)
f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
Proof:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ minus(0(), y) -> 0()
, minus(s(x), 0()) -> s(x)
, minus(s(x), s(y)) -> minus(x, y)
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ minus(0(), y) -> 0()
, minus(s(x), 0()) -> s(x)
, minus(s(x), s(y)) -> minus(x, y)
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds