/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 = 8] active(f(mark(c),g(mark(c)),mark(g(active(b))))) -> active(f(mark(c),g(mark(c)),mark(g(active(b))))) 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 = active(f(mark(c),g(mark(c)),mark(g(active(b))))) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = active(f(mark(c),g(mark(c)),mark(g(active(b))))) 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... ## 3 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [3 DP problems]: ## DP problem: Dependency pairs = [active^#(f(_0,g(_0),_1)) -> mark^#(f(_1,_1,_1)), mark^#(g(_0)) -> active^#(g(mark(_0))), mark^#(f(_0,_1,_2)) -> active^#(f(_0,_1,_2)), mark^#(g(_0)) -> mark^#(_0)] TRS = {active(f(_0,g(_0),_1)) -> mark(f(_1,_1,_1)), active(g(b)) -> mark(c), active(b) -> mark(c), mark(f(_0,_1,_2)) -> active(f(_0,_1,_2)), mark(g(_0)) -> active(g(mark(_0))), mark(b) -> active(b), mark(c) -> active(c), f(mark(_0),_1,_2) -> f(_0,_1,_2), f(_0,mark(_1),_2) -> f(_0,_1,_2), f(_0,_1,mark(_2)) -> f(_0,_1,_2), f(active(_0),_1,_2) -> f(_0,_1,_2), f(_0,active(_1),_2) -> f(_0,_1,_2), f(_0,_1,active(_2)) -> f(_0,_1,_2), g(mark(_0)) -> g(_0), g(active(_0)) -> g(_0)} ## 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. ## DP problem: Dependency pairs = [g^#(mark(_0)) -> g^#(_0), g^#(active(_0)) -> g^#(_0)] TRS = {active(f(_0,g(_0),_1)) -> mark(f(_1,_1,_1)), active(g(b)) -> mark(c), active(b) -> mark(c), mark(f(_0,_1,_2)) -> active(f(_0,_1,_2)), mark(g(_0)) -> active(g(mark(_0))), mark(b) -> active(b), mark(c) -> active(c), f(mark(_0),_1,_2) -> f(_0,_1,_2), f(_0,mark(_1),_2) -> f(_0,_1,_2), f(_0,_1,mark(_2)) -> f(_0,_1,_2), f(active(_0),_1,_2) -> f(_0,_1,_2), f(_0,active(_1),_2) -> f(_0,_1,_2), f(_0,_1,active(_2)) -> f(_0,_1,_2), g(mark(_0)) -> g(_0), g(active(_0)) -> g(_0)} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## DP problem: Dependency pairs = [f^#(mark(_0),_1,_2) -> f^#(_0,_1,_2), f^#(_0,mark(_1),_2) -> f^#(_0,_1,_2), f^#(_0,_1,mark(_2)) -> f^#(_0,_1,_2), f^#(active(_0),_1,_2) -> f^#(_0,_1,_2), f^#(_0,active(_1),_2) -> f^#(_0,_1,_2), f^#(_0,_1,active(_2)) -> f^#(_0,_1,_2)] TRS = {active(f(_0,g(_0),_1)) -> mark(f(_1,_1,_1)), active(g(b)) -> mark(c), active(b) -> mark(c), mark(f(_0,_1,_2)) -> active(f(_0,_1,_2)), mark(g(_0)) -> active(g(mark(_0))), mark(b) -> active(b), mark(c) -> active(c), f(mark(_0),_1,_2) -> f(_0,_1,_2), f(_0,mark(_1),_2) -> f(_0,_1,_2), f(_0,_1,mark(_2)) -> f(_0,_1,_2), f(active(_0),_1,_2) -> f(_0,_1,_2), f(_0,active(_1),_2) -> f(_0,_1,_2), f(_0,_1,active(_2)) -> f(_0,_1,_2), g(mark(_0)) -> g(_0), g(active(_0)) -> g(_0)} ## Trying with homeomorphic embeddings... Success! 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=false, max=-1) # max_depth=3, unfold_variables=false: # Iteration 0: no loop found, 4 unfolded rules generated. # Iteration 1: no loop found, 11 unfolded rules generated. # Iteration 2: no loop found, 20 unfolded rules generated. # Iteration 3: no loop found, 58 unfolded rules generated. # Iteration 4: no loop found, 90 unfolded rules generated. # Iteration 5: no loop found, 34 unfolded rules generated. # Iteration 6: no loop found, 40 unfolded rules generated. # Iteration 7: no loop found, 38 unfolded rules generated. # Iteration 8: no loop found, 32 unfolded rules generated. # Iteration 9: no loop found, 12 unfolded rules generated. # Iteration 10: no loop found, 0 unfolded rule generated. No loop found at all! # max_depth=3, unfold_variables=true: # Iteration 0: no loop found, 4 unfolded rules generated. # Iteration 1: no loop found, 11 unfolded rules generated. # Iteration 2: no loop found, 20 unfolded rules generated. # Iteration 3: no loop found, 55 unfolded rules generated. # Iteration 4: no loop found, 83 unfolded rules generated. # Iteration 5: no loop found, 32 unfolded rules generated. # Iteration 6: no loop found, 63 unfolded rules generated. # Iteration 7: no loop found, 73 unfolded rules generated. # Iteration 8: no loop found, 70 unfolded rules generated. # Iteration 9: no loop found, 30 unfolded rules generated. # Iteration 10: no loop found, 0 unfolded rule generated. No loop found at all! # max_depth=4, unfold_variables=false: # Iteration 0: no loop found, 4 unfolded rules generated. # Iteration 1: no loop found, 11 unfolded rules generated. # Iteration 2: no loop found, 25 unfolded rules generated. # Iteration 3: no loop found, 141 unfolded rules generated. # Iteration 4: no loop found, 664 unfolded rules generated. # Iteration 5: no loop found, 2484 unfolded rules generated. # Iteration 6: no loop found, 6757 unfolded rules generated. # Iteration 7: no loop found, 9992 unfolded rules generated. # Iteration 8: no loop found, 2934 unfolded rules generated. # Iteration 9: no loop found, 5058 unfolded rules generated. # Iteration 10: no loop found, 6486 unfolded rules generated. # Iteration 11: no loop found, 5850 unfolded rules generated. # Iteration 12: no loop found, 2446 unfolded rules generated. # Iteration 13: no loop found, 180 unfolded rules generated. # Iteration 14: no loop found, 12 unfolded rules generated. # Iteration 15: no loop found, 0 unfolded rule generated. No loop found at all! # max_depth=4, unfold_variables=true: # Iteration 0: no loop found, 4 unfolded rules generated. # Iteration 1: no loop found, 11 unfolded rules generated. # Iteration 2: no loop found, 25 unfolded rules generated. # Iteration 3: no loop found, 148 unfolded rules generated. # Iteration 4: no loop found, 705 unfolded rules generated. # Iteration 5: no loop found, 2607 unfolded rules generated. # Iteration 6: no loop found, 6930 unfolded rules generated. # Iteration 7: no loop found, 10301 unfolded rules generated. # Iteration 8: no loop found, 3860 unfolded rules generated. # Iteration 9: no loop found, 8544 unfolded rules generated. # Iteration 10: no loop found, 17136 unfolded rules generated. # Iteration 11: no loop found, 29280 unfolded rules generated. # Iteration 12: no loop found, 40680 unfolded rules generated. # Iteration 13: no loop found, 42840 unfolded rules generated. # Iteration 14: no loop found, 30240 unfolded rules generated. # Iteration 15: no loop found, 10080 unfolded rules generated. # Iteration 16: no loop found, 0 unfolded rule generated. No loop found at all! # max_depth=5, unfold_variables=false: # Iteration 0: no loop found, 4 unfolded rules generated. # Iteration 1: no loop found, 11 unfolded rules generated. # Iteration 2: no loop found, 25 unfolded rules generated. # Iteration 3: no loop found, 153 unfolded rules generated. # Iteration 4: no loop found, 899 unfolded rules generated. # Iteration 5: no loop found, 4916 unfolded rules generated. # Iteration 6: no loop found, 24385 unfolded rules generated. # Iteration 7: no loop found, 105707 unfolded rules generated. # Iteration 8: success, found a loop, 4546 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = active^#(f(_0,g(_0),_1)) -> mark^#(f(_1,_1,_1)) [trans] is in U_IR^0. D = mark^#(f(_0,_1,_2)) -> active^#(f(_0,_1,_2)) is a dependency pair of IR. We build a composed triple from L0 and D. ==> L1 = active^#(f(_0,g(_0),_1)) -> active^#(f(_1,_1,_1)) [trans] is in U_IR^1. We build a unit triple from L1. ==> L2 = active^#(f(_0,g(_0),_1)) -> active^#(f(_1,_1,_1)) [unit] is in U_IR^2. Let p2 = [0]. We unfold the rule of L2 forwards at position p2 with the rule f(_0,mark(_1),_2) -> f(_0,_1,_2). ==> L3 = active^#(f(_0,g(_0),mark(_1))) -> active^#(f(mark(_1),_1,mark(_1))) [unit] is in U_IR^3. Let p3 = [0, 0]. We unfold the rule of L3 forwards at position p3 with the rule mark(g(_0)) -> active(g(mark(_0))). ==> L4 = active^#(f(_0,g(_0),mark(g(_1)))) -> active^#(f(active(g(mark(_1))),g(_1),mark(g(_1)))) [unit] is in U_IR^4. Let p4 = [0, 0, 0]. We unfold the rule of L4 forwards at position p4 with the rule g(mark(_0)) -> g(_0). ==> L5 = active^#(f(_0,g(_0),mark(g(_1)))) -> active^#(f(active(g(_1)),g(_1),mark(g(_1)))) [unit] is in U_IR^5. Let p5 = [0, 0, 0]. We unfold the rule of L5 forwards at position p5 with the rule g(active(_0)) -> g(_0). ==> L6 = active^#(f(_0,g(_0),mark(g(active(_1))))) -> active^#(f(active(g(_1)),g(active(_1)),mark(g(active(_1))))) [unit] is in U_IR^6. Let p6 = [0, 0]. We unfold the rule of L6 forwards at position p6 with the rule active(g(b)) -> mark(c). ==> L7 = active^#(f(mark(c),g(mark(c)),mark(g(active(b))))) -> active^#(f(mark(c),g(active(b)),mark(g(active(b))))) [unit] is in U_IR^7. Let p7 = [0, 1, 0]. We unfold the rule of L7 forwards at position p7 with the rule active(b) -> mark(c). ==> L8 = active^#(f(mark(c),g(mark(c)),mark(g(active(b))))) -> active^#(f(mark(c),g(mark(c)),mark(g(active(b))))) [unit] is in U_IR^8. 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 = 4684356