NO Prover = TRS(tech=GUIDED_UNF, nb_unfoldings=unlimited, unfold_variables=true, strategy=LEFTMOST_NE) ** BEGIN proof argument ** The following rule was generated while unfolding the analyzed TRS: [iteration = 5] adx(cons(_0,n__zeros)) -> adx(cons(n__0,n__zeros)) Let l be the left-hand side and r be the right-hand side of this rule. Let p = epsilon, theta1 = {} and theta2 = {_0->n__0}. We have r|p = adx(cons(n__0,n__zeros)) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = adx(cons(_0,n__zeros)) loops w.r.t. the analyzed TRS. ** 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! ## Searching for a loop by unfolding (unfolding of variable subterms: ON)... # Iteration 0: no loop detected, 6 unfolded rules generated. # Iteration 1: no loop detected, 6 unfolded rules generated. # Iteration 2: no loop detected, 36 unfolded rules generated. # Iteration 3: no loop detected, 228 unfolded rules generated. # Iteration 4: no loop detected, 1822 unfolded rules generated. # Iteration 5: loop detected, 18141 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = [adx^#(cons(_0,_1)) -> incr^#(cons(activate(_0),n__adx(activate(_1)))), incr^#(cons(_2,_3)) -> activate^#(_3), activate^#(n__adx(_4)) -> adx^#(activate(_4))] is in U_IR^0. We merge the first and the second rule of L0. ==> L1 = [adx^#(cons(_0,_1)) -> activate^#(n__adx(activate(_1))), activate^#(n__adx(_2)) -> adx^#(activate(_2))] is in U_IR^1. We merge the first and the second rule of L1. ==> L2 = adx^#(cons(_0,_1)) -> adx^#(activate(activate(_1))) is in U_IR^2. Let p2 = [0]. We unfold the rule of L2 forwards at position p2 with the rule activate(_0) -> _0. ==> L3 = adx^#(cons(_0,_1)) -> adx^#(activate(_1)) is in U_IR^3. Let p3 = [0]. We unfold the rule of L3 forwards at position p3 with the rule activate(n__zeros) -> zeros. ==> L4 = adx^#(cons(_0,n__zeros)) -> adx^#(zeros) is in U_IR^4. Let p4 = [0]. We unfold the rule of L4 forwards at position p4 with the rule zeros -> cons(n__0,n__zeros). ==> L5 = adx^#(cons(_0,n__zeros)) -> adx^#(cons(n__0,n__zeros)) is in U_IR^5. ** END proof description ** Proof stopped at iteration 5 Number of unfolded rules generated by this proof = 20239 Number of unfolded rules generated by all the parallel proofs = 47752