MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { lt(x, 0()) -> false()
  , lt(0(), s(x)) -> true()
  , lt(s(x), s(y)) -> lt(x, y)
  , times(0(), y) -> 0()
  , times(s(x), y) -> plus(y, times(x, y))
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(x, y))
  , fac(x) -> loop(x, s(0()), s(0()))
  , loop(x, c, y) -> if(lt(x, c), x, c, y)
  , if(true(), x, c, y) -> y
  , if(false(), x, c, y) -> loop(x, s(c), times(y, s(c))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..