/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO ** BEGIN proof argument ** The following rule was generated while unfolding the analyzed TRS: [iteration = 4] f(c,n__b,c) -> f(c,n__b,c) Let l be the left-hand side and r be the right-hand side of this rule. Let p = epsilon, theta1 = {} and theta2 = {}. We have r|p = f(c,n__b,c) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = f(c,n__b,c) 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! ## Applying the DP framework... ## 1 initial DP problem to solve. ## First, we try to decompose this problem into smaller problems. ## Round 1 [1 DP problem]: ## DP problem: Dependency pairs = [f^#(a,n__b,_0) -> f^#(_0,_0,_0)] TRS = {f(a,n__b,_0) -> f(_0,_0,_0), c -> a, c -> b, b -> n__b, activate(n__b) -> b, activate(_0) -> _0} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... Failed! ## Trying with lexicographic path orders... Failed! ## Trying with Knuth-Bendix orders... Failed! Don't know whether this DP problem is finite. ## A DP problem could not be proved finite. ## Now, we try to prove that this problem is infinite. ## Trying to find a loop (forward=true, backward=true, max=20) # max_depth=20, unfold_variables=false: # Iteration 0: no loop found, 1 unfolded rule generated. # Iteration 1: no loop found, 1 unfolded rule generated. # Iteration 2: no loop found, 4 unfolded rules generated. # Iteration 3: no loop found, 13 unfolded rules generated. # Iteration 4: success, found a loop, 13 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = f^#(a,n__b,_0) -> f^#(_0,_0,_0) [trans] is in U_IR^0. We build a unit triple from L0. ==> L1 = f^#(a,n__b,_0) -> f^#(_0,_0,_0) [unit] is in U_IR^1. Let p1 = [0]. We unfold the rule of L1 backwards at position p1 with the rule c -> a. ==> L2 = f^#(c,n__b,c) -> f^#(c,c,c) [unit] is in U_IR^2. Let p2 = [1]. We unfold the rule of L2 forwards at position p2 with the rule c -> b. ==> L3 = f^#(c,n__b,c) -> f^#(c,b,c) [unit] is in U_IR^3. Let p3 = [1]. We unfold the rule of L3 forwards at position p3 with the rule b -> n__b. ==> L4 = f^#(c,n__b,c) -> f^#(c,n__b,c) [unit] is in U_IR^4. This DP problem is infinite. Proof run on Linux version 3.10.0-1160.25.1.el7.x86_64 for amd64 using Java version 1.8.0_292 ** END proof description ** Total number of generated unfolded rules = 41