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)) , head(add(n, x)) -> n , tail(nil()) -> nil() , tail(add(n, x)) -> x , null(nil()) -> true() , null(add(n, x)) -> false() , 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(x) -> mins(x, nil(), nil()) , mins(x, y, z) -> if(null(x), x, y, z) , if(true(), x, y, z) -> z , if(false(), x, y, z) -> if2(eq(head(x), min(x)), x, y, z) , if2(true(), x, y, z) -> mins(app(rm(head(x), tail(x)), y), nil(), app(z, add(head(x), nil()))) , if2(false(), x, y, z) -> mins(tail(x), add(head(x), y), z) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..