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 = [and^#(_0,or(_1,_2)) -> and^#(_0,_1), and^#(_0,or(_1,_2)) -> and^#(_0,_2), and^#(_0,and(_1,_1)) -> and^#(_0,_1)] TRS = {and(_0,or(_1,_2)) -> or(and(_0,_1),and(_0,_2)), and(_0,and(_1,_1)) -> and(_0,_1), or(or(_0,_1),and(_1,_2)) -> or(_0,_1), or(_0,and(_0,_1)) -> _0, or(true,_0) -> true, or(_0,false) -> _0, or(_0,_0) -> _0, or(_0,or(_1,_1)) -> or(_0,_1), and(_0,true) -> _0, and(false,_0) -> false, and(_0,_0) -> _0} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [or^#(or(_0,_1),and(_1,_2)) -> or^#(_0,_1), or^#(_0,or(_1,_1)) -> or^#(_0,_1)] TRS = {and(_0,or(_1,_2)) -> or(and(_0,_1),and(_0,_2)), and(_0,and(_1,_1)) -> and(_0,_1), or(or(_0,_1),and(_1,_2)) -> or(_0,_1), or(_0,and(_0,_1)) -> _0, or(true,_0) -> true, or(_0,false) -> _0, or(_0,_0) -> _0, or(_0,or(_1,_1)) -> or(_0,_1), and(_0,true) -> _0, and(false,_0) -> false, and(_0,_0) -> _0} ## 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