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 = 2] sieve(cons(_0,n__from(_1))) -> sieve(cons(_1,n__from(s(_1)))) Let l be the left-hand side and r be the right-hand side of this rule. Let p = epsilon, theta1 = {} and theta2 = {_1->s(_1), _0->_1}. We have r|p = sieve(cons(_1,n__from(s(_1)))) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = sieve(cons(_0,n__from(_1))) 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, 5 unfolded rules generated. # Iteration 1: no loop detected, 14 unfolded rules generated. # Iteration 2: loop detected, 1 unfolded rule generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = sieve^#(cons(_0,_1)) -> sieve^#(activate(_1)) is in U_IR^0. Let p0 = [0]. We unfold the rule of L0 forwards at position p0 with the rule activate(n__from(_0)) -> from(_0). ==> L1 = sieve^#(cons(_0,n__from(_1))) -> sieve^#(from(_1)) is in U_IR^1. Let p1 = [0]. We unfold the rule of L1 forwards at position p1 with the rule from(_0) -> cons(_0,n__from(s(_0))). ==> L2 = sieve^#(cons(_0,n__from(_1))) -> sieve^#(cons(_1,n__from(s(_1)))) is in U_IR^2. ** END proof description ** Proof stopped at iteration 2 Number of unfolded rules generated by this proof = 20 Number of unfolded rules generated by all the parallel proofs = 20