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(s(x)) -> s(inc(x))
inc(0()) -> s(0())
logarithm(x) -> logIter(x,0())
logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),half(x),inc(y))
if(false(),b,x,y) -> logZeroError()
if(true(),false(),x,s(y)) -> y
if(true(),true(),x,y) -> logIter(x,y)
f() -> g()
f() -> h()
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(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, logarithm(x) -> logIter(x, 0())
, logIter(x, y) ->
if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y))
, if(false(), b, x, y) -> logZeroError()
, if(true(), false(), x, s(y)) -> y
, if(true(), true(), x, y) -> logIter(x, y)
, f() -> g()
, f() -> h()}
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(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, logarithm(x) -> logIter(x, 0())
, logIter(x, y) ->
if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y))
, if(false(), b, x, y) -> logZeroError()
, if(true(), false(), x, s(y)) -> y
, if(true(), true(), x, y) -> logIter(x, y)
, f() -> g()
, f() -> h()}
Proof Output:
Computation stopped due to timeout after 60.0 seconds