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