/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S ) Problem 1: Valid CTRS Processor: -> Rules: pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S -> The system is a deterministic 3-CTRS. Problem 1: Dependency Pairs Processor: Conditional Termination Problem 1: -> Pairs: Empty -> QPairs: Empty -> Rules: pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S Conditional Termination Problem 2: -> Pairs: TC(x:S) -> PIN(x:S) TC(x:S) -> TC(z:S) | pin(x:S) ->* pout(z:S) -> QPairs: Empty -> Rules: pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S The problem is decomposed in 2 subproblems. Problem 1.1: SCC Processor: -> Pairs: Empty -> QPairs: Empty -> Rules: pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: SCC Processor: -> Pairs: TC(x:S) -> PIN(x:S) TC(x:S) -> TC(z:S) | pin(x:S) ->* pout(z:S) -> QPairs: Empty -> Rules: pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: TC(x:S) -> TC(z:S) | pin(x:S) ->* pout(z:S) -> QPairs: Empty ->->-> Rules: pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S Problem 1.2: Reduction Pair Processor: -> Pairs: TC(x:S) -> TC(z:S) | pin(x:S) ->* pout(z:S) -> Rules: pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S -> Needed rules: Empty -> Usable rules: pin(a) -> pout(b) pin(b) -> pout(c) ->Mace4 Output: ============================== Mace4 ================================= Mace4 (64) version 2009-11A, November 2009. Process 31075 was started by sandbox2 on n022.star.cs.uiowa.edu, Tue Jun 30 22:25:33 2020 The command was "./mace4 -c -f /tmp/mace41804289383846930886.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file /tmp/mace41804289383846930886.in assign(max_seconds,20). formulas(assumptions). arrowStar_s0(x,x) # label(reflexivity). arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility). gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence). arrow_s0(x1,y) -> arrow_s0(f13(x1,x2),f13(y,x2)) # label(congruence). arrow_s0(x2,y) -> arrow_s0(f13(x1,x2),f13(x1,y)) # label(congruence). arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence). arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence). arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence). arrowN_s0(x1,y) -> arrowN_s0(f11(x1),f11(y)) # label(congruence). arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence). arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence). arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence). arrow_s0(f2(f4),f8(f5)) # label(replacement). arrow_s0(f2(f5),f8(f6)) # label(replacement). arrow_s0(f13(x4,x5),x4) # label(replacement). arrow_s0(f13(x4,x5),x5) # label(replacement). arrowN_s0(f13(x4,x5),x4) # label(replacement). arrowN_s0(f13(x4,x5),x5) # label(replacement). arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). arrowStar_s0(f2(x1),f8(x3)) -> sqsupset_s0(f12(x1),f12(x3)) # label(replacement). sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). end_of_list. formulas(goals). (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 arrow_s0(x,y) & arrowStar_s0(y,z) -> arrowStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 2 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 3 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 4 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 5 arrow_s0(x1,y) -> arrow_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause). [assumption]. 6 arrow_s0(x1,y) -> arrow_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 7 arrow_s0(x1,y) -> arrow_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause). [assumption]. 8 arrow_s0(x1,y) -> arrow_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause). [assumption]. 9 arrow_s0(x2,y) -> arrow_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause). [assumption]. 10 arrowN_s0(x1,y) -> arrowN_s0(f2(x1),f2(y)) # label(congruence) # label(non_clause). [assumption]. 11 arrowN_s0(x1,y) -> arrowN_s0(f3(x1),f3(y)) # label(congruence) # label(non_clause). [assumption]. 12 arrowN_s0(x1,y) -> arrowN_s0(f8(x1),f8(y)) # label(congruence) # label(non_clause). [assumption]. 13 arrowN_s0(x1,y) -> arrowN_s0(f11(x1),f11(y)) # label(congruence) # label(non_clause). [assumption]. 14 arrowN_s0(x1,y) -> arrowN_s0(f12(x1),f12(y)) # label(congruence) # label(non_clause). [assumption]. 15 arrowN_s0(x1,y) -> arrowN_s0(f13(x1,x2),f13(y,x2)) # label(congruence) # label(non_clause). [assumption]. 16 arrowN_s0(x2,y) -> arrowN_s0(f13(x1,x2),f13(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17 arrowN_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 18 arrowStar_s0(f2(x1),f8(x3)) -> sqsupset_s0(f12(x1),f12(x3)) # label(replacement) # label(non_clause). [assumption]. 19 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 20 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 21 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. ============================== end of process non-clausal formulas === ============================== CLAUSES FOR SEARCH ==================== formulas(mace4_clauses). arrowStar_s0(x,x) # label(reflexivity). -arrow_s0(x,y) | -arrowStar_s0(y,z) | arrowStar_s0(x,z) # label(compatibility). -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). -arrow_s0(x,y) | arrow_s0(f2(x),f2(y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f3(x),f3(y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f8(x),f8(y)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f13(x,z),f13(y,z)) # label(congruence). -arrow_s0(x,y) | arrow_s0(f13(z,x),f13(z,y)) # label(congruence). -arrowN_s0(x,y) | arrowN_s0(f2(x),f2(y)) # label(congruence). -arrowN_s0(x,y) | arrowN_s0(f3(x),f3(y)) # label(congruence). -arrowN_s0(x,y) | arrowN_s0(f8(x),f8(y)) # label(congruence). -arrowN_s0(x,y) | arrowN_s0(f11(x),f11(y)) # label(congruence). -arrowN_s0(x,y) | arrowN_s0(f12(x),f12(y)) # label(congruence). -arrowN_s0(x,y) | arrowN_s0(f13(x,z),f13(y,z)) # label(congruence). -arrowN_s0(x,y) | arrowN_s0(f13(z,x),f13(z,y)) # label(congruence). arrow_s0(f2(f4),f8(f5)) # label(replacement). arrow_s0(f2(f5),f8(f6)) # label(replacement). arrow_s0(f13(x,y),x) # label(replacement). arrow_s0(f13(x,y),y) # label(replacement). arrowN_s0(f13(x,y),x) # label(replacement). arrowN_s0(f13(x,y),y) # label(replacement). -arrowN_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). -arrowStar_s0(f2(x),f8(y)) | sqsupset_s0(f12(x),f12(y)) # label(replacement). -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). -sqsupsetStar_s0(x,x) # label(wellfoundedness). end_of_list. ============================== end of clauses for search ============= % There are no natural numbers in the input. ============================== DOMAIN SIZE 2 ========================= ============================== STATISTICS ============================ For domain size 2. Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). Ground clauses: seen=138, kept=134. Selections=32, assignments=63, propagations=272, current_models=0. Rewrite_terms=1141, rewrite_bools=670, indexes=321. Rules_from_neg_clauses=122, cross_offs=122. ============================== end of statistics ===================== ============================== DOMAIN SIZE 3 ========================= ============================== STATISTICS ============================ For domain size 3. Current CPU time: 0.00 seconds (total CPU time: 0.02 seconds). Ground clauses: seen=386, kept=377. Selections=582, assignments=1738, propagations=13178, current_models=0. Rewrite_terms=61642, rewrite_bools=89397, indexes=9661. Rules_from_neg_clauses=2977, cross_offs=6832. ============================== end of statistics ===================== ============================== DOMAIN SIZE 4 ========================= ============================== MODEL ================================= interpretation( 4, [number=1, seconds=0], [ function(f4, [ 0 ]), function(f5, [ 1 ]), function(f6, [ 2 ]), function(f11(_), [ 0, 0, 0, 0 ]), function(f12(_), [ 0, 1, 2, 0 ]), function(f2(_), [ 0, 1, 2, 0 ]), function(f3(_), [ 0, 0, 0, 0 ]), function(f8(_), [ 3, 0, 1, 3 ]), function(f13(_,_), [ 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 3, 3, 3, 3 ]), relation(arrowN_s0(_,_), [ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ]), relation(arrowStar_s0(_,_), [ 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1 ]), relation(arrow_s0(_,_), [ 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ]), relation(gtrsim_s0(_,_), [ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 ]), relation(sqsupsetStar_s0(_,_), [ 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0 ]), relation(sqsupset_s0(_,_), [ 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0 ]), relation(succeq_s0(_,_), [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) ]). ============================== end of model ========================== ============================== STATISTICS ============================ For domain size 4. Current CPU time: 0.00 seconds (total CPU time: 0.96 seconds). Ground clauses: seen=826, kept=810. Selections=44683, assignments=178483, propagations=476301, current_models=1. Rewrite_terms=3194403, rewrite_bools=4688761, indexes=312025. Rules_from_neg_clauses=40104, cross_offs=237067. ============================== end of statistics ===================== User_CPU=0.96, System_CPU=0.04, Wall_clock=1. Exiting with 1 model. Process 31075 exit (max_models) Tue Jun 30 22:25:34 2020 The process finished Tue Jun 30 22:25:34 2020 Mace4 cooked interpretation: % number = 1 % seconds = 0 % Interpretation of size 4 f4 = 0. f5 = 1. f6 = 2. f11(0) = 0. f11(1) = 0. f11(2) = 0. f11(3) = 0. f12(0) = 0. f12(1) = 1. f12(2) = 2. f12(3) = 0. f2(0) = 0. f2(1) = 1. f2(2) = 2. f2(3) = 0. f3(0) = 0. f3(1) = 0. f3(2) = 0. f3(3) = 0. f8(0) = 3. f8(1) = 0. f8(2) = 1. f8(3) = 3. f13(0,0) = 0. f13(0,1) = 0. f13(0,2) = 0. f13(0,3) = 3. f13(1,0) = 0. f13(1,1) = 0. f13(1,2) = 0. f13(1,3) = 3. f13(2,0) = 0. f13(2,1) = 0. f13(2,2) = 0. f13(2,3) = 3. f13(3,0) = 3. f13(3,1) = 3. f13(3,2) = 3. f13(3,3) = 3. arrowN_s0(0,0). arrowN_s0(0,1). arrowN_s0(0,2). - arrowN_s0(0,3). - arrowN_s0(1,0). - arrowN_s0(1,1). - arrowN_s0(1,2). - arrowN_s0(1,3). - arrowN_s0(2,0). - arrowN_s0(2,1). - arrowN_s0(2,2). - arrowN_s0(2,3). arrowN_s0(3,0). arrowN_s0(3,1). arrowN_s0(3,2). arrowN_s0(3,3). arrowStar_s0(0,0). arrowStar_s0(0,1). arrowStar_s0(0,2). - arrowStar_s0(0,3). - arrowStar_s0(1,0). arrowStar_s0(1,1). - arrowStar_s0(1,2). - arrowStar_s0(1,3). - arrowStar_s0(2,0). - arrowStar_s0(2,1). arrowStar_s0(2,2). - arrowStar_s0(2,3). arrowStar_s0(3,0). arrowStar_s0(3,1). arrowStar_s0(3,2). arrowStar_s0(3,3). arrow_s0(0,0). arrow_s0(0,1). arrow_s0(0,2). - arrow_s0(0,3). - arrow_s0(1,0). arrow_s0(1,1). - arrow_s0(1,2). - arrow_s0(1,3). - arrow_s0(2,0). - arrow_s0(2,1). - arrow_s0(2,2). - arrow_s0(2,3). arrow_s0(3,0). arrow_s0(3,1). arrow_s0(3,2). arrow_s0(3,3). gtrsim_s0(0,0). gtrsim_s0(0,1). gtrsim_s0(0,2). - gtrsim_s0(0,3). - gtrsim_s0(1,0). - gtrsim_s0(1,1). - gtrsim_s0(1,2). - gtrsim_s0(1,3). - gtrsim_s0(2,0). - gtrsim_s0(2,1). - gtrsim_s0(2,2). - gtrsim_s0(2,3). gtrsim_s0(3,0). gtrsim_s0(3,1). gtrsim_s0(3,2). gtrsim_s0(3,3). - sqsupsetStar_s0(0,0). sqsupsetStar_s0(0,1). sqsupsetStar_s0(0,2). - sqsupsetStar_s0(0,3). - sqsupsetStar_s0(1,0). - sqsupsetStar_s0(1,1). sqsupsetStar_s0(1,2). - sqsupsetStar_s0(1,3). - sqsupsetStar_s0(2,0). - sqsupsetStar_s0(2,1). - sqsupsetStar_s0(2,2). - sqsupsetStar_s0(2,3). - sqsupsetStar_s0(3,0). sqsupsetStar_s0(3,1). sqsupsetStar_s0(3,2). - sqsupsetStar_s0(3,3). - sqsupset_s0(0,0). sqsupset_s0(0,1). sqsupset_s0(0,2). - sqsupset_s0(0,3). - sqsupset_s0(1,0). - sqsupset_s0(1,1). sqsupset_s0(1,2). - sqsupset_s0(1,3). - sqsupset_s0(2,0). - sqsupset_s0(2,1). - sqsupset_s0(2,2). - sqsupset_s0(2,3). - sqsupset_s0(3,0). sqsupset_s0(3,1). sqsupset_s0(3,2). - sqsupset_s0(3,3). - succeq_s0(0,0). - succeq_s0(0,1). - succeq_s0(0,2). - succeq_s0(0,3). - succeq_s0(1,0). - succeq_s0(1,1). - succeq_s0(1,2). - succeq_s0(1,3). - succeq_s0(2,0). - succeq_s0(2,1). - succeq_s0(2,2). - succeq_s0(2,3). - succeq_s0(3,0). - succeq_s0(3,1). - succeq_s0(3,2). - succeq_s0(3,3). Problem 1.2: SCC Processor: -> Pairs: Empty -> QPairs: Empty -> Rules: pin(a) -> pout(b) pin(b) -> pout(c) tc(x:S) -> x:S tc(x:S) -> y:S | pin(x:S) ->* pout(z:S), tc(z:S) ->* y:S ->Strongly Connected Components: There is no strongly connected component The problem is finite.