Tool CaT
stdout:
MAYBE
Problem:
minus(0(),y) -> 0()
minus(x,0()) -> x
minus(s(x),s(y)) -> minus(x,y)
plus(0(),y) -> y
plus(s(x),y) -> plus(x,s(y))
zero(s(x)) -> false()
zero(0()) -> true()
p(s(x)) -> x
div(x,y) -> quot(x,y,0())
quot(x,y,z) -> if(zero(x),x,y,plus(z,s(0())))
if(true(),x,y,z) -> p(z)
if(false(),x,s(y),z) -> quot(minus(x,s(y)),s(y),z)
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(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), y) -> y
, plus(s(x), y) -> plus(x, s(y))
, zero(s(x)) -> false()
, zero(0()) -> true()
, p(s(x)) -> x
, div(x, y) -> quot(x, y, 0())
, quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0())))
, if(true(), x, y, z) -> p(z)
, if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z)}
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(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), y) -> y
, plus(s(x), y) -> plus(x, s(y))
, zero(s(x)) -> false()
, zero(0()) -> true()
, p(s(x)) -> x
, div(x, y) -> quot(x, y, 0())
, quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0())))
, if(true(), x, y, z) -> p(z)
, if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds