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