YES Prover = TRS(tech=PATTERN_RULES, nb_unfoldings=unlimited, max_nb_unfolded_rules=200) ** BEGIN proof argument ** All the DP problems were proved finite. As all the involved DP processors are sound, the TRS under analysis terminates. ** END proof argument ** ** BEGIN proof description ** ## Searching for a generalized rewrite rule (a rule whose right-hand side contains a variable that does not occur in the left-hand side)... No generalized rewrite rule found! ## Applying the DP framework... ## Round 1: ## DP problem: Dependency pairs = [div^#(s(_0),s(_1)) -> div^#(minus(_0,_1),s(_1))] TRS = {minus(_0,0) -> _0, minus(s(_0),s(_1)) -> p(minus(_0,_1)), p(s(_0)) -> _0, div(0,s(_0)) -> 0, div(s(_0),s(_1)) -> s(div(minus(_0,_1),s(_1)))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... Too many coefficients (14)! Aborting! ## Trying with lexicographic path orders... The constraints are satisfied by the lexicographic path order using the precedence: s > [p, minus], div > [s, p, minus] and the argument filtering: {minus:[0], s:[0], div:[0], p:[0], div^#:[0, 1]} This DP problem is finite. ## DP problem: Dependency pairs = [minus^#(s(_0),s(_1)) -> minus^#(_0,_1)] TRS = {minus(_0,0) -> _0, minus(s(_0),s(_1)) -> p(minus(_0,_1)), p(s(_0)) -> _0, div(0,s(_0)) -> 0, div(s(_0),s(_1)) -> s(div(minus(_0,_1),s(_1)))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ** END proof description ** Proof stopped at iteration 0 Number of unfolded rules generated by this proof = 0 Number of unfolded rules generated by all the parallel proofs = 19