YES(?,PRIMREC)

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

Strict Trs:
  { lcs(x, e()) -> 0()
  , lcs(e(), y) -> 0()
  , lcs(a(x), a(y)) -> s(lcs(x, y))
  , lcs(a(x), b(y)) -> max(lcs(x, b(y)), lcs(a(x), y))
  , lcs(b(x), a(y)) -> max(lcs(x, a(y)), lcs(b(x), y))
  , lcs(b(x), b(y)) -> s(lcs(x, y))
  , max(x, 0()) -> 0()
  , max(0(), y) -> 0()
  , max(s(x), s(y)) -> max(x, y) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,PRIMREC)

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

 lcs > s, lcs > max, e > s, e > max, 0 > s, 0 > max, a > s, a > max,
 b > s, b > max, lcs ~ e, lcs ~ 0, lcs ~ a, e ~ 0, e ~ a, e ~ b,
 0 ~ a, 0 ~ b, a ~ b, s ~ max .

Hurray, we answered YES(?,PRIMREC)