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) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , app(nil(), y) -> y , app(add(n, x), y) -> add(n, app(x, y)) , min(add(n, nil())) -> n , min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) , if_min(true(), add(n, add(m, x))) -> min(add(n, x)) , if_min(false(), add(n, add(m, x))) -> min(add(m, x)) , rm(n, nil()) -> nil() , rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) , if_rm(true(), n, add(m, x)) -> rm(n, x) , if_rm(false(), n, add(m, x)) -> add(m, rm(n, x)) , minsort(nil(), nil()) -> nil() , minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) , if_minsort(true(), add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil())) , if_minsort(false(), add(n, x), y) -> minsort(x, add(n, y)) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..