YES(?,ELEMENTARY)

We are left with following problem, upon which TcT provides the
certificate YES(?,ELEMENTARY).

Strict Trs:
  { fib(0()) -> 0()
  , fib(s(0())) -> s(0())
  , fib(s(s(x))) -> +(fib(s(x)), fib(x)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,ELEMENTARY)

The input was oriented with the instance of 'Lightweight Multiset
Path Order' as induced by the safe mapping

 safe(fib) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1, 2}

and precedence

 empty .

Following symbols are considered recursive:

 {fib}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

          fib(0();) > 0()                        
                                                 
     fib(s(; 0());) > s(; 0())                   
                                                 
  fib(s(; s(; x));) > +(; fib(s(; x);),  fib(x;))
                                                 

Hurray, we answered YES(?,ELEMENTARY)