YES(?,PRIMREC)

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

Strict Trs:
  { ite(tt(), x, y) -> x
  , ite(ff(), x, y) -> y
  , lt(x, 0()) -> ff()
  , lt(0(), s(y)) -> tt()
  , lt(s(x), s(y)) -> lt(x, y)
  , insert(a, nil()) -> cons(a, nil())
  , insert(a, cons(b, l)) ->
    ite(lt(a, b), cons(a, cons(b, l)), cons(b, insert(a, l)))
  , sort(nil()) -> nil()
  , sort(cons(a, l)) -> insert(a, sort(l)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,PRIMREC)

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

 tt > ite, tt > lt, tt > insert, tt > cons, tt > sort, ff > ite,
 ff > tt, ff > lt, ff > insert, ff > nil, ff > cons, ff > sort,
 lt > ite, lt > cons, 0 > ite, 0 > tt, 0 > lt, 0 > insert, 0 > nil,
 0 > cons, 0 > sort, s > ite, s > tt, s > lt, s > insert, s > nil,
 s > cons, s > sort, insert > ite, insert > lt, insert > cons,
 nil > ite, nil > lt, nil > insert, nil > cons, nil > sort,
 sort > ite, sort > lt, sort > insert, sort > cons, ite ~ cons,
 tt ~ nil, ff ~ 0, ff ~ s, 0 ~ s .

Hurray, we answered YES(?,PRIMREC)