Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
fib(0) → 0
fib(s(0)) → s(0)
fib(s(s(x))) → +(fib(s(x)), fib(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
fib(0) → 0
fib(s(0)) → s(0)
fib(s(s(x))) → +(fib(s(x)), fib(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
Q is empty.
We use [23] with the following order to prove termination.
Lexicographic path order with status [19].
Quasi-Precedence:
fib1 > +2 > [0, s1]
Status: +2: [1,2]
s1: [1]
0: multiset
fib1: [1]