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