YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(0()) -> 1()
     , f(s(x)) -> g(x, s(x))
     , g(0(), y) -> y
     , g(s(x), y) -> g(x, +(y, s(x)))
     , +(x, 0()) -> x
     , +(x, s(y)) -> s(+(x, y))
     , g(s(x), y) -> g(x, s(+(y, x)))}

Proof Output:    
  Strict Rules in Predicative Notation:
   {  f(0();) -> 1()
    , f(s(; x);) -> g(x; s(; x))
    , g(0(); y) -> y
    , g(s(; x); y) -> g(x; +(s(; x); y))
    , +(0(); x) -> x
    , +(s(; y); x) -> s(; +(y; x))
    , g(s(; x); y) -> g(x; s(; +(x; y)))}
  Safe Mapping:
   safe(f) = {}, safe(0) = {}, safe(1) = {}, safe(s) = {1},
   safe(g) = {2}, safe(+) = {1}
  Argument Permutation:
   mu(f) = [1], mu(g) = [1, 2], mu(+) = [1, 2]
  Precedence:
   + ~ +, g > +, g ~ g, f > +, f > g, f ~ f