LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ 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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ 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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ 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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ 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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ 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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ 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))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..