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 = [+^#(_0,s(_1)) -> +^#(_0,_1), +^#(s(_0),_1) -> +^#(_0,_1)] TRS = {not(true) -> false, not(false) -> true, odd(0) -> false, odd(s(_0)) -> not(odd(_0)), +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), +(s(_0),_1) -> s(+(_0,_1))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [odd^#(s(_0)) -> odd^#(_0)] TRS = {not(true) -> false, not(false) -> true, odd(0) -> false, odd(s(_0)) -> not(odd(_0)), +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), +(s(_0),_1) -> s(+(_0,_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 = 0