Tool CaT
stdout:
MAYBE
Problem:
lt(x,0()) -> false()
lt(0(),s(y)) -> true()
lt(s(x),s(y)) -> lt(x,y)
plus(x,0()) -> x
plus(x,s(y)) -> s(plus(x,y))
quot(x,s(y)) -> help(x,s(y),0())
help(x,s(y),c) -> if(lt(c,x),x,s(y),c)
if(true(),x,s(y),c) -> s(help(x,s(y),plus(c,s(y))))
if(false(),x,s(y),c) -> 0()
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:
{ lt(x, 0()) -> false()
, lt(0(), s(y)) -> true()
, lt(s(x), s(y)) -> lt(x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, quot(x, s(y)) -> help(x, s(y), 0())
, help(x, s(y), c) -> if(lt(c, x), x, s(y), c)
, if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y))))
, if(false(), x, s(y), c) -> 0()}
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:
{ lt(x, 0()) -> false()
, lt(0(), s(y)) -> true()
, lt(s(x), s(y)) -> lt(x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, quot(x, s(y)) -> help(x, s(y), 0())
, help(x, s(y), c) -> if(lt(c, x), x, s(y), c)
, if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y))))
, if(false(), x, s(y), c) -> 0()}
Proof Output:
Computation stopped due to timeout after 60.0 seconds