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)) , reach(x, y, empty(), h) -> false() , reach(x, y, edge(u, v, i), h) -> if_reach_1(eq(x, u), x, y, edge(u, v, i), h) , if_reach_1(true(), x, y, edge(u, v, i), h) -> if_reach_2(eq(y, v), x, y, edge(u, v, i), h) , if_reach_1(false(), x, y, edge(u, v, i), h) -> reach(x, y, i, edge(u, v, h)) , if_reach_2(true(), x, y, edge(u, v, i), h) -> true() , if_reach_2(false(), x, y, edge(u, v, i), h) -> or(reach(x, y, i, h), reach(v, y, union(i, h), empty())) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..