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