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