MAYBE

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

Strict Trs:
  { eq(0(), 0()) -> true()
  , eq(0(), s(x)) -> false()
  , eq(s(x), 0()) -> false()
  , eq(s(x), s(y)) -> eq(x, y)
  , or(true(), y) -> true()
  , or(false(), y) -> y
  , union(empty(), h) -> h
  , union(edge(x, y, i), h) -> edge(x, y, union(i, h))
  , isEmpty(empty()) -> true()
  , isEmpty(edge(x, y, i)) -> false()
  , from(edge(x, y, i)) -> x
  , to(edge(x, y, i)) -> y
  , rest(empty()) -> empty()
  , rest(edge(x, y, i)) -> i
  , reach(x, y, i, h) ->
    if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
  , if1(true(), b1, b2, b3, x, y, i, h) -> true()
  , if1(false(), b1, b2, b3, x, y, i, h) ->
    if2(b1, b2, b3, x, y, i, h)
  , if2(true(), b2, b3, x, y, i, h) -> false()
  , if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
  , if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
  , if3(false(), b3, x, y, i, h) ->
    reach(x, y, rest(i), edge(from(i), to(i), h))
  , if4(true(), x, y, i, h) -> true()
  , if4(false(), x, y, i, h) ->
    or(reach(x, y, rest(i), h),
       reach(to(i), y, union(rest(i), h), empty())) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..