YES Time: 0.005035 TRS: { concat(leaf(), y) -> y, concat(cons(u, v), y) -> cons(u, concat(v, y)), less_leaves(x, leaf()) -> false(), less_leaves(leaf(), cons(w, z)) -> true(), less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z))} RUF: Strict: { concat(cons(u, v), y) -> cons(u, concat(v, y)), less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z))} Weak: {} DP: DP: { concat#(cons(u, v), y) -> concat#(v, y), less_leaves#(cons(u, v), cons(w, z)) -> concat#(u, v), less_leaves#(cons(u, v), cons(w, z)) -> concat#(w, z), less_leaves#(cons(u, v), cons(w, z)) -> less_leaves#(concat(u, v), concat(w, z))} TRS: { concat(cons(u, v), y) -> cons(u, concat(v, y)), less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z))} EDG: {(less_leaves#(cons(u, v), cons(w, z)) -> concat#(u, v), concat#(cons(u, v), y) -> concat#(v, y)) (concat#(cons(u, v), y) -> concat#(v, y), concat#(cons(u, v), y) -> concat#(v, y)) (less_leaves#(cons(u, v), cons(w, z)) -> less_leaves#(concat(u, v), concat(w, z)), less_leaves#(cons(u, v), cons(w, z)) -> concat#(u, v)) (less_leaves#(cons(u, v), cons(w, z)) -> less_leaves#(concat(u, v), concat(w, z)), less_leaves#(cons(u, v), cons(w, z)) -> concat#(w, z)) (less_leaves#(cons(u, v), cons(w, z)) -> less_leaves#(concat(u, v), concat(w, z)), less_leaves#(cons(u, v), cons(w, z)) -> less_leaves#(concat(u, v), concat(w, z))) (less_leaves#(cons(u, v), cons(w, z)) -> concat#(w, z), concat#(cons(u, v), y) -> concat#(v, y))} SCCS (2): Scc: {less_leaves#(cons(u, v), cons(w, z)) -> less_leaves#(concat(u, v), concat(w, z))} Scc: {concat#(cons(u, v), y) -> concat#(v, y)} SCC (1): Strict: {less_leaves#(cons(u, v), cons(w, z)) -> less_leaves#(concat(u, v), concat(w, z))} Weak: { concat(cons(u, v), y) -> cons(u, concat(v, y)), less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z))} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [concat](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [less_leaves](x0, x1) = x0 + 1, [less_leaves#](x0, x1) = x0 Strict: less_leaves#(cons(u, v), cons(w, z)) -> less_leaves#(concat(u, v), concat(w, z)) 1 + 1u + 0v + 0w + 0z >= 0 + 1u + 0v + 0w + 0z Weak: Qed SCC (1): Strict: {concat#(cons(u, v), y) -> concat#(v, y)} Weak: { concat(cons(u, v), y) -> cons(u, concat(v, y)), less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z))} SPSC: Simple Projection: pi(concat#) = 0 Strict: {} Qed