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