Tool CaT
stdout:
MAYBE
Problem:
half(0()) -> 0()
half(s(0())) -> 0()
half(s(s(x))) -> s(half(x))
inc(0()) -> 0()
inc(s(x)) -> s(inc(x))
zero(0()) -> true()
zero(s(x)) -> false()
p(0()) -> 0()
p(s(x)) -> x
bits(x) -> bitIter(x,0())
bitIter(x,y) -> if(zero(x),x,inc(y))
if(true(),x,y) -> p(y)
if(false(),x,y) -> bitIter(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))
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, zero(0()) -> true()
, zero(s(x)) -> false()
, p(0()) -> 0()
, p(s(x)) -> x
, bits(x) -> bitIter(x, 0())
, bitIter(x, y) -> if(zero(x), x, inc(y))
, if(true(), x, y) -> p(y)
, if(false(), x, y) -> bitIter(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))
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, zero(0()) -> true()
, zero(s(x)) -> false()
, p(0()) -> 0()
, p(s(x)) -> x
, bits(x) -> bitIter(x, 0())
, bitIter(x, y) -> if(zero(x), x, inc(y))
, if(true(), x, y) -> p(y)
, if(false(), x, y) -> bitIter(half(x), y)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds