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:
 Open