Tool CaT
stdout:
MAYBE
Problem:
lt(0(),s(x)) -> true()
lt(x,0()) -> false()
lt(s(x),s(y)) -> lt(x,y)
logarithm(x) -> ifa(lt(0(),x),x)
ifa(true(),x) -> help(x,1())
ifa(false(),x) -> logZeroError()
help(x,y) -> ifb(lt(y,x),x,y)
ifb(true(),x,y) -> help(half(x),s(y))
ifb(false(),x,y) -> y
half(0()) -> 0()
half(s(0())) -> 0()
half(s(s(x))) -> s(half(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, logarithm(x) -> ifa(lt(0(), x), x)
, ifa(true(), x) -> help(x, 1())
, ifa(false(), x) -> logZeroError()
, help(x, y) -> ifb(lt(y, x), x, y)
, ifb(true(), x, y) -> help(half(x), s(y))
, ifb(false(), x, y) -> y
, half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, logarithm(x) -> ifa(lt(0(), x), x)
, ifa(true(), x) -> help(x, 1())
, ifa(false(), x) -> logZeroError()
, help(x, y) -> ifb(lt(y, x), x, y)
, ifb(true(), x, y) -> help(half(x), s(y))
, ifb(false(), x, y) -> y
, half(0()) -> 0()
, half(s(0())) -> 0()
, half(s(s(x))) -> s(half(x))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds