Tool CaT
stdout:
MAYBE
Problem:
lt(0(),s(x)) -> true()
lt(x,0()) -> false()
lt(s(x),s(y)) -> lt(x,y)
fibo(0()) -> fib(0())
fibo(s(0())) -> fib(s(0()))
fibo(s(s(x))) -> sum(fibo(s(x)),fibo(x))
fib(0()) -> s(0())
fib(s(0())) -> s(0())
fib(s(s(x))) -> if(true(),0(),s(s(x)),0(),0())
if(true(),c,s(s(x)),a,b) -> if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c)
if(false(),c,s(s(x)),a,b) -> sum(fibo(a),fibo(b))
sum(x,0()) -> x
sum(x,s(y)) -> s(sum(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, fibo(0()) -> fib(0())
, fibo(s(0())) -> fib(s(0()))
, fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
, fib(0()) -> s(0())
, fib(s(0())) -> s(0())
, fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
, if(true(), c, s(s(x)), a, b) ->
if(lt(s(c), s(s(x))), s(c), s(s(x)), b, c)
, if(false(), c, s(s(x)), a, b) -> sum(fibo(a), fibo(b))
, sum(x, 0()) -> x
, sum(x, s(y)) -> s(sum(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:
{ lt(0(), s(x)) -> true()
, lt(x, 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, fibo(0()) -> fib(0())
, fibo(s(0())) -> fib(s(0()))
, fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
, fib(0()) -> s(0())
, fib(s(0())) -> s(0())
, fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
, if(true(), c, s(s(x)), a, b) ->
if(lt(s(c), s(s(x))), s(c), s(s(x)), b, c)
, if(false(), c, s(s(x)), a, b) -> sum(fibo(a), fibo(b))
, sum(x, 0()) -> x
, sum(x, s(y)) -> s(sum(x, y))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds