YES(?,PRIMREC)

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

Strict Trs:
  { norm(nil()) -> 0()
  , norm(g(x, y)) -> s(norm(x))
  , f(x, nil()) -> g(nil(), x)
  , f(x, g(y, z)) -> g(f(x, y), z)
  , rem(nil(), y) -> nil()
  , rem(g(x, y), 0()) -> g(x, y)
  , rem(g(x, y), s(z)) -> rem(x, z) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,PRIMREC)

The input was oriented with the instance of'multiset path order' as
induced by the precedence

 norm > s, nil > norm, nil > 0, nil > g, nil > s, nil > rem,
 0 > norm, 0 > g, 0 > s, 0 > rem, g > s, f > norm, f > 0, f > g,
 f > s, f > rem, rem > s, norm ~ g, norm ~ rem, nil ~ f, g ~ rem .

Hurray, we answered YES(?,PRIMREC)