/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- NO ** BEGIN proof argument ** The following rule was generated while unfolding the analyzed TRS: [iteration = 5] a__f(a__c,b,a__c) -> a__f(a__c,b,a__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 = a__f(a__c,b,a__c) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = a__f(a__c,b,a__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 = [a__f^#(a,b,_0) -> a__f^#(_0,_0,mark(_0)), mark^#(f(_0,_1,_2)) -> a__f^#(_0,_1,mark(_2)), mark^#(f(_0,_1,_2)) -> mark^#(_2), a__f^#(a,b,_0) -> mark^#(_0)] TRS = {a__f(a,b,_0) -> a__f(_0,_0,mark(_0)), a__c -> a, a__c -> b, mark(f(_0,_1,_2)) -> a__f(_0,_1,mark(_2)), mark(c) -> a__c, mark(a) -> a, mark(b) -> b, a__f(_0,_1,_2) -> f(_0,_1,_2), a__c -> c} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... This DP problem is too complex! Aborting! ## 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, 4 unfolded rules generated. # Iteration 1: no loop found, 12 unfolded rules generated. # Iteration 2: no loop found, 36 unfolded rules generated. # Iteration 3: no loop found, 111 unfolded rules generated. # Iteration 4: no loop found, 402 unfolded rules generated. # Iteration 5: success, found a loop, 98 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = a__f^#(a,b,_0) -> a__f^#(_0,_0,mark(_0)) [trans] is in U_IR^0. We build a unit triple from L0. ==> L1 = a__f^#(a,b,_0) -> a__f^#(_0,_0,mark(_0)) [unit] is in U_IR^1. Let p1 = [0]. We unfold the rule of L1 backwards at position p1 with the rule a__c -> a. ==> L2 = a__f^#(a__c,b,a__c) -> a__f^#(a__c,a__c,mark(a__c)) [unit] is in U_IR^2. Let p2 = [1]. We unfold the rule of L2 forwards at position p2 with the rule a__c -> b. ==> L3 = a__f^#(a__c,b,a__c) -> a__f^#(a__c,b,mark(a__c)) [unit] is in U_IR^3. Let p3 = [2, 0]. We unfold the rule of L3 forwards at position p3 with the rule a__c -> c. ==> L4 = a__f^#(a__c,b,a__c) -> a__f^#(a__c,b,mark(c)) [unit] is in U_IR^4. Let p4 = [2]. We unfold the rule of L4 forwards at position p4 with the rule mark(c) -> a__c. ==> L5 = a__f^#(a__c,b,a__c) -> a__f^#(a__c,b,a__c) [unit] is in U_IR^5. 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 = 1260