Tool CaT
stdout:
MAYBE
Problem:
f(g(x)) -> g(g(f(x)))
g(s(x)) -> s(s(g(x)))
s(x) -> h(0(),x)
s(x) -> h(x,0())
f(0()) -> 0()
s(s(s(0()))) -> f(s(0()))
f(s(0())) -> s(0())
h(f(x),g(x)) -> f(s(x))
g(x) -> h(h(h(h(x,x),x),x),x)
f(s(s(x))) -> h(f(x),g(h(x,x)))
s(0()) -> r(0())
s(s(s(0()))) -> r(s(0()))
r(s(0())) -> s(0())
g(x) -> r(x)
s(0()) -> p(0())
s(s(0())) -> p(s(0()))
p(s(0())) -> 0()
s(s(s(s(s(0()))))) -> p(s(s(0())))
p(s(s(0()))) -> s(s(s(0())))
h(p(x),g(x)) -> p(s(x))
s(0()) -> k(0())
s(s(p(p(a())))) -> s(k(p(a())))
s(k(p(a()))) -> p(p(a()))
g(x) -> k(x)
a() -> 0()
s(h(r(k(p(x))),r(x))) -> h(r(r(p(x))),k(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:
{ f(g(x)) -> g(g(f(x)))
, g(s(x)) -> s(s(g(x)))
, s(x) -> h(0(), x)
, s(x) -> h(x, 0())
, f(0()) -> 0()
, s(s(s(0()))) -> f(s(0()))
, f(s(0())) -> s(0())
, h(f(x), g(x)) -> f(s(x))
, g(x) -> h(h(h(h(x, x), x), x), x)
, f(s(s(x))) -> h(f(x), g(h(x, x)))
, s(0()) -> r(0())
, s(s(s(0()))) -> r(s(0()))
, r(s(0())) -> s(0())
, g(x) -> r(x)
, s(0()) -> p(0())
, s(s(0())) -> p(s(0()))
, p(s(0())) -> 0()
, s(s(s(s(s(0()))))) -> p(s(s(0())))
, p(s(s(0()))) -> s(s(s(0())))
, h(p(x), g(x)) -> p(s(x))
, s(0()) -> k(0())
, s(s(p(p(a())))) -> s(k(p(a())))
, s(k(p(a()))) -> p(p(a()))
, g(x) -> k(x)
, a() -> 0()
, s(h(r(k(p(x))), r(x))) -> h(r(r(p(x))), k(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:
{ f(g(x)) -> g(g(f(x)))
, g(s(x)) -> s(s(g(x)))
, s(x) -> h(0(), x)
, s(x) -> h(x, 0())
, f(0()) -> 0()
, s(s(s(0()))) -> f(s(0()))
, f(s(0())) -> s(0())
, h(f(x), g(x)) -> f(s(x))
, g(x) -> h(h(h(h(x, x), x), x), x)
, f(s(s(x))) -> h(f(x), g(h(x, x)))
, s(0()) -> r(0())
, s(s(s(0()))) -> r(s(0()))
, r(s(0())) -> s(0())
, g(x) -> r(x)
, s(0()) -> p(0())
, s(s(0())) -> p(s(0()))
, p(s(0())) -> 0()
, s(s(s(s(s(0()))))) -> p(s(s(0())))
, p(s(s(0()))) -> s(s(s(0())))
, h(p(x), g(x)) -> p(s(x))
, s(0()) -> k(0())
, s(s(p(p(a())))) -> s(k(p(a())))
, s(k(p(a()))) -> p(p(a()))
, g(x) -> k(x)
, a() -> 0()
, s(h(r(k(p(x))), r(x))) -> h(r(r(p(x))), k(x))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds