YES Prover = TRS(tech=GUIDED_UNF_TRIPLES, nb_unfoldings=unlimited, unfold_variables=false, max_nb_coefficients=12, max_nb_unfolded_rules=-1, strategy=LEFTMOST_NE) ** 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 = [times^#(_0,s(_1)) -> times^#(_0,_1)] TRS = {times(_0,0) -> 0, times(_0,s(_1)) -> plus(times(_0,_1),_0), plus(_0,0) -> _0, plus(0,_0) -> _0, plus(_0,s(_1)) -> s(plus(_0,_1)), plus(s(_0),_1) -> s(plus(_0,_1))} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [plus^#(_0,s(_1)) -> plus^#(_0,_1), plus^#(s(_0),_1) -> plus^#(_0,_1)] TRS = {times(_0,0) -> 0, times(_0,s(_1)) -> plus(times(_0,_1),_0), plus(_0,0) -> _0, plus(0,_0) -> _0, plus(_0,s(_1)) -> s(plus(_0,_1)), plus(s(_0),_1) -> s(plus(_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