Tool CaT
stdout:
MAYBE
Problem:
le(s(x),0()) -> false()
le(0(),y) -> true()
le(s(x),s(y)) -> le(x,y)
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
log(0()) -> logError()
log(s(x)) -> loop(s(x),s(0()),0())
loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
if(true(),x,y,z) -> z
if(false(),x,y,z) -> loop(x,double(y),s(z))
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:
{ le(s(x), 0()) -> false()
, le(0(), y) -> true()
, le(s(x), s(y)) -> le(x, y)
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, log(0()) -> logError()
, log(s(x)) -> loop(s(x), s(0()), 0())
, loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
, if(true(), x, y, z) -> z
, if(false(), x, y, z) -> loop(x, double(y), s(z))}
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:
{ le(s(x), 0()) -> false()
, le(0(), y) -> true()
, le(s(x), s(y)) -> le(x, y)
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, log(0()) -> logError()
, log(s(x)) -> loop(s(x), s(0()), 0())
, loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z)
, if(true(), x, y, z) -> z
, if(false(), x, y, z) -> loop(x, double(y), s(z))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds