Tool CaT
stdout:
MAYBE
Problem:
ge(x,0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),s(y)) -> ge(x,y)
minus(x,0()) -> x
minus(s(x),s(y)) -> minus(x,y)
div(x,y) -> ify(ge(y,s(0())),x,y)
ify(false(),x,y) -> divByZeroError()
ify(true(),x,y) -> if(ge(x,y),x,y)
if(false(),x,y) -> 0()
if(true(),x,y) -> s(div(minus(x,y),y))
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:
{ ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, div(x, y) -> ify(ge(y, s(0())), x, y)
, ify(false(), x, y) -> divByZeroError()
, ify(true(), x, y) -> if(ge(x, y), x, y)
, if(false(), x, y) -> 0()
, if(true(), x, y) -> s(div(minus(x, y), y))}
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:
{ ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, div(x, y) -> ify(ge(y, s(0())), x, y)
, ify(false(), x, y) -> divByZeroError()
, ify(true(), x, y) -> if(ge(x, y), x, y)
, if(false(), x, y) -> 0()
, if(true(), x, y) -> s(div(minus(x, y), y))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds