YES(?,ELEMENTARY)

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

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