Tool CaT
stdout:
MAYBE
Problem:
half(0()) -> 0()
half(s(0())) -> 0()
half(s(s(x))) -> s(half(x))
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
inc(0()) -> 0()
inc(s(x)) -> s(inc(x))
log(x) -> log2(x,0())
log2(x,y) -> if(le(x,s(0())),x,inc(y))
if(true(),x,s(y)) -> y
if(false(),x,y) -> log2(half(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:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, s(0())), x, inc(y))
, if(true(), x, s(y)) -> y
, if(false(), x, y) -> log2(half(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:
{ half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, s(0())), x, inc(y))
, if(true(), x, s(y)) -> y
, if(false(), x, y) -> log2(half(x), y)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds