/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern p() w.r.t. the given Prolog program could not be shown: (0) Prolog (1) PrologToTRSTransformerProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 57 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 6 ms] (10) QTRS (11) QTRSRRRProof [EQUIVALENT, 0 ms] (12) QTRS (13) PrologToDTProblemTransformerProof [SOUND, 0 ms] (14) TRIPLES (15) TriplesToPiDPProof [SOUND, 13 ms] (16) PiDP (17) DependencyGraphProof [EQUIVALENT, 0 ms] (18) PiDP (19) PiDPToQDPProof [EQUIVALENT, 0 ms] (20) QDP (21) PrologToIRSwTTransformerProof [SOUND, 0 ms] (22) IRSwT (23) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (24) IRSwT (25) IntTRSCompressionProof [EQUIVALENT, 14 ms] (26) IRSwT (27) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (28) IRSwT (29) IRSwTTerminationDigraphProof [EQUIVALENT, 6 ms] (30) IRSwT (31) FilterProof [EQUIVALENT, 0 ms] (32) IntTRS (33) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (34) NO ---------------------------------------- (0) Obligation: Clauses: p :- q(and(r, !)). q(X) :- X. r. r :- r. and(X, Y) :- ','(X, Y). Query: p() ---------------------------------------- (1) PrologToTRSTransformerProof (SOUND) Transformed Prolog program to TRS. { "root": 1, "program": { "directives": [], "clauses": [ [ "(p)", "(q (and (r) (!)))" ], [ "(q X)", "X" ], [ "(r)", null ], [ "(r)", "(r)" ], [ "(and X Y)", "(',' X Y)" ] ] }, "graph": { "nodes": { "22": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (call (r)) (call (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "23": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (r) (call (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "13": { "goal": [{ "clause": -1, "scope": -1, "term": "(call (and (r) (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "35": { "goal": [{ "clause": -1, "scope": -1, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "46": { "goal": [{ "clause": -1, "scope": -1, "term": "(!_7)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "15": { "goal": [{ "clause": -1, "scope": -1, "term": "(and (r) (!))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "37": { "goal": [{ "clause": -1, "scope": -1, "term": "(call (!))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "48": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "38": { "goal": [ { "clause": 2, "scope": 6, "term": "(r)" }, { "clause": 3, "scope": 6, "term": "(r)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "49": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "39": { "goal": [{ "clause": 2, "scope": 6, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "18": { "goal": [{ "clause": 4, "scope": 4, "term": "(and (r) (!))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "type": "Nodes", "1": { "goal": [{ "clause": -1, "scope": -1, "term": "(p)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "6": { "goal": [{ "clause": 0, "scope": 1, "term": "(p)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "7": { "goal": [{ "clause": -1, "scope": -1, "term": "(q (and (r) (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "40": { "goal": [{ "clause": 3, "scope": 6, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "41": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "42": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "10": { "goal": [{ "clause": 1, "scope": 2, "term": "(q (and (r) (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "43": { "goal": [{ "clause": -1, "scope": -1, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 1, "to": 6, "label": "CASE" }, { "from": 6, "to": 7, "label": "ONLY EVAL with clause\np :- q(and(r, !)).\nand substitution" }, { "from": 7, "to": 10, "label": "CASE" }, { "from": 10, "to": 13, "label": "ONLY EVAL with clause\nq(X3) :- call(X3).\nand substitutionX3 -> and(r, !)" }, { "from": 13, "to": 15, "label": "CALL" }, { "from": 15, "to": 18, "label": "CASE" }, { "from": 18, "to": 22, "label": "ONLY EVAL with clause\nand(X8, X9) :- ','(call(X8), call(X9)).\nand substitutionX8 -> r,\nX9 -> !" }, { "from": 22, "to": 23, "label": "CALL" }, { "from": 23, "to": 35, "label": "SPLIT 1" }, { "from": 23, "to": 37, "label": "SPLIT 2" }, { "from": 35, "to": 38, "label": "CASE" }, { "from": 37, "to": 46, "label": "CALL" }, { "from": 38, "to": 39, "label": "PARALLEL" }, { "from": 38, "to": 40, "label": "PARALLEL" }, { "from": 39, "to": 41, "label": "ONLY EVAL with clause\nr.\nand substitution" }, { "from": 40, "to": 43, "label": "ONLY EVAL with clause\nr :- r.\nand substitution" }, { "from": 41, "to": 42, "label": "SUCCESS" }, { "from": 43, "to": 35, "label": "INSTANCE" }, { "from": 46, "to": 48, "label": "CUT" }, { "from": 48, "to": 49, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f1_in -> U1(f23_in) U1(f23_out1) -> f1_out1 f35_in -> f35_out1 f35_in -> U2(f35_in) U2(f35_out1) -> f35_out1 f37_in -> f37_out1 f23_in -> U3(f35_in) U3(f35_out1) -> U4(f37_in) U4(f37_out1) -> f23_out1 Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U1(x_1)) = 2*x_1 POL(U2(x_1)) = 2*x_1 POL(U3(x_1)) = 2*x_1 POL(U4(x_1)) = x_1 POL(f1_in) = 2 POL(f1_out1) = 0 POL(f23_in) = 0 POL(f23_out1) = 0 POL(f35_in) = 0 POL(f35_out1) = 0 POL(f37_in) = 0 POL(f37_out1) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f1_in -> U1(f23_in) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U1(f23_out1) -> f1_out1 f35_in -> f35_out1 f35_in -> U2(f35_in) U2(f35_out1) -> f35_out1 f37_in -> f37_out1 f23_in -> U3(f35_in) U3(f35_out1) -> U4(f37_in) U4(f37_out1) -> f23_out1 Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U1(x_1)) = 1 + 2*x_1 POL(U2(x_1)) = 2*x_1 POL(U3(x_1)) = 2*x_1 POL(U4(x_1)) = 2*x_1 POL(f1_out1) = 0 POL(f23_in) = 1 POL(f23_out1) = 0 POL(f35_in) = 0 POL(f35_out1) = 0 POL(f37_in) = 0 POL(f37_out1) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U1(f23_out1) -> f1_out1 f23_in -> U3(f35_in) ---------------------------------------- (6) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f35_in -> f35_out1 f35_in -> U2(f35_in) U2(f35_out1) -> f35_out1 f37_in -> f37_out1 U3(f35_out1) -> U4(f37_in) U4(f37_out1) -> f23_out1 Q is empty. ---------------------------------------- (7) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U2(x_1)) = 2*x_1 POL(U3(x_1)) = 2 + 2*x_1 POL(U4(x_1)) = 1 + 2*x_1 POL(f23_out1) = 1 POL(f35_in) = 0 POL(f35_out1) = 0 POL(f37_in) = 0 POL(f37_out1) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U3(f35_out1) -> U4(f37_in) ---------------------------------------- (8) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f35_in -> f35_out1 f35_in -> U2(f35_in) U2(f35_out1) -> f35_out1 f37_in -> f37_out1 U4(f37_out1) -> f23_out1 Q is empty. ---------------------------------------- (9) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U2(x_1)) = 2*x_1 POL(U4(x_1)) = 2 + 2*x_1 POL(f23_out1) = 0 POL(f35_in) = 0 POL(f35_out1) = 0 POL(f37_in) = 1 POL(f37_out1) = 1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U4(f37_out1) -> f23_out1 ---------------------------------------- (10) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f35_in -> f35_out1 f35_in -> U2(f35_in) U2(f35_out1) -> f35_out1 f37_in -> f37_out1 Q is empty. ---------------------------------------- (11) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U2(x_1)) = 2*x_1 POL(f35_in) = 0 POL(f35_out1) = 0 POL(f37_in) = 1 POL(f37_out1) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f37_in -> f37_out1 ---------------------------------------- (12) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f35_in -> f35_out1 f35_in -> U2(f35_in) U2(f35_out1) -> f35_out1 Q is empty. ---------------------------------------- (13) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 2, "program": { "directives": [], "clauses": [ [ "(p)", "(q (and (r) (!)))" ], [ "(q X)", "X" ], [ "(r)", null ], [ "(r)", "(r)" ], [ "(and X Y)", "(',' X Y)" ] ] }, "graph": { "nodes": { "55": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "12": { "goal": [{ "clause": 1, "scope": 2, "term": "(q (and (r) (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "56": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "24": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (call (r)) (call (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "57": { "goal": [{ "clause": -1, "scope": -1, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "14": { "goal": [{ "clause": -1, "scope": -1, "term": "(call (and (r) (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "25": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (r) (call (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "58": { "goal": [{ "clause": -1, "scope": -1, "term": "(!_7)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "59": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "16": { "goal": [{ "clause": -1, "scope": -1, "term": "(and (r) (!))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "type": "Nodes", "2": { "goal": [{ "clause": -1, "scope": -1, "term": "(p)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5": { "goal": [{ "clause": 0, "scope": 1, "term": "(p)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "9": { "goal": [{ "clause": -1, "scope": -1, "term": "(q (and (r) (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "60": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "50": { "goal": [{ "clause": -1, "scope": -1, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "51": { "goal": [{ "clause": -1, "scope": -1, "term": "(call (!))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "52": { "goal": [ { "clause": 2, "scope": 6, "term": "(r)" }, { "clause": 3, "scope": 6, "term": "(r)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "53": { "goal": [{ "clause": 2, "scope": 6, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "21": { "goal": [{ "clause": 4, "scope": 4, "term": "(and (r) (!))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "54": { "goal": [{ "clause": 3, "scope": 6, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 2, "to": 5, "label": "CASE" }, { "from": 5, "to": 9, "label": "ONLY EVAL with clause\np :- q(and(r, !)).\nand substitution" }, { "from": 9, "to": 12, "label": "CASE" }, { "from": 12, "to": 14, "label": "ONLY EVAL with clause\nq(X3) :- call(X3).\nand substitutionX3 -> and(r, !)" }, { "from": 14, "to": 16, "label": "CALL" }, { "from": 16, "to": 21, "label": "CASE" }, { "from": 21, "to": 24, "label": "ONLY EVAL with clause\nand(X8, X9) :- ','(call(X8), call(X9)).\nand substitutionX8 -> r,\nX9 -> !" }, { "from": 24, "to": 25, "label": "CALL" }, { "from": 25, "to": 50, "label": "SPLIT 1" }, { "from": 25, "to": 51, "label": "SPLIT 2" }, { "from": 50, "to": 52, "label": "CASE" }, { "from": 51, "to": 58, "label": "CALL" }, { "from": 52, "to": 53, "label": "PARALLEL" }, { "from": 52, "to": 54, "label": "PARALLEL" }, { "from": 53, "to": 55, "label": "ONLY EVAL with clause\nr.\nand substitution" }, { "from": 54, "to": 57, "label": "ONLY EVAL with clause\nr :- r.\nand substitution" }, { "from": 55, "to": 56, "label": "SUCCESS" }, { "from": 57, "to": 50, "label": "INSTANCE" }, { "from": 58, "to": 59, "label": "CUT" }, { "from": 59, "to": 60, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (14) Obligation: Triples: rA :- rA. pB :- rA. Clauses: rcA. rcA :- rcA. Afs: pB = pB ---------------------------------------- (15) TriplesToPiDPProof (SOUND) We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes: Transforming TRIPLES into the following Term Rewriting System: Pi DP problem: The TRS P consists of the following rules: PB_IN_ -> U2_^1(rA_in_) PB_IN_ -> RA_IN_ RA_IN_ -> U1_^1(rA_in_) RA_IN_ -> RA_IN_ R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES ---------------------------------------- (16) Obligation: Pi DP problem: The TRS P consists of the following rules: PB_IN_ -> U2_^1(rA_in_) PB_IN_ -> RA_IN_ RA_IN_ -> U1_^1(rA_in_) RA_IN_ -> RA_IN_ R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (17) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 3 less nodes. ---------------------------------------- (18) Obligation: Pi DP problem: The TRS P consists of the following rules: RA_IN_ -> RA_IN_ R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (19) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: RA_IN_ -> RA_IN_ R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (21) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 3, "program": { "directives": [], "clauses": [ [ "(p)", "(q (and (r) (!)))" ], [ "(q X)", "X" ], [ "(r)", null ], [ "(r)", "(r)" ], [ "(and X Y)", "(',' X Y)" ] ] }, "graph": { "nodes": { "11": { "goal": [{ "clause": 1, "scope": 2, "term": "(q (and (r) (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "33": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "44": { "goal": [{ "clause": -1, "scope": -1, "term": "(!_7)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "34": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "45": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "36": { "goal": [{ "clause": -1, "scope": -1, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "47": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "26": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (call (r)) (call (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "27": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (r) (call (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "17": { "goal": [{ "clause": -1, "scope": -1, "term": "(call (and (r) (!)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "28": { "goal": [{ "clause": -1, "scope": -1, "term": "(r)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "29": { "goal": [{ "clause": -1, "scope": -1, "term": "(call (!))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "19": { "goal": [{ "clause": -1, "scope": -1, "term": "(and (r) (!))" }], "kb": { 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"to": 17, "label": "ONLY EVAL with clause\nq(X3) :- call(X3).\nand substitutionX3 -> and(r, !)" }, { "from": 17, "to": 19, "label": "CALL" }, { "from": 19, "to": 20, "label": "CASE" }, { "from": 20, "to": 26, "label": "ONLY EVAL with clause\nand(X8, X9) :- ','(call(X8), call(X9)).\nand substitutionX8 -> r,\nX9 -> !" }, { "from": 26, "to": 27, "label": "CALL" }, { "from": 27, "to": 28, "label": "SPLIT 1" }, { "from": 27, "to": 29, "label": "SPLIT 2" }, { "from": 28, "to": 30, "label": "CASE" }, { "from": 29, "to": 44, "label": "CALL" }, { "from": 30, "to": 31, "label": "PARALLEL" }, { "from": 30, "to": 32, "label": "PARALLEL" }, { "from": 31, "to": 33, "label": "ONLY EVAL with clause\nr.\nand substitution" }, { "from": 32, "to": 36, "label": "ONLY EVAL with clause\nr :- r.\nand substitution" }, { "from": 33, "to": 34, "label": "SUCCESS" }, { "from": 36, "to": 28, "label": "INSTANCE" }, { "from": 44, "to": 45, "label": "CUT" }, { "from": 45, "to": 47, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (22) Obligation: Rules: f36_out -> f32_out :|: TRUE f32_in -> f36_in :|: TRUE f36_in -> f28_in :|: TRUE f28_out -> f36_out :|: TRUE f28_in -> f30_in :|: TRUE f30_out -> f28_out :|: TRUE f30_in -> f32_in :|: TRUE f31_out -> f30_out :|: TRUE f32_out -> f30_out :|: TRUE f30_in -> f31_in :|: TRUE f4_out -> f3_out :|: TRUE f3_in -> f4_in :|: TRUE f4_in -> f8_in :|: TRUE f8_out -> f4_out :|: TRUE f8_in -> f11_in :|: TRUE f11_out -> f8_out :|: TRUE f17_out -> f11_out :|: TRUE f11_in -> f17_in :|: TRUE f17_in -> f19_in :|: TRUE f19_out -> f17_out :|: TRUE f19_in -> f20_in :|: TRUE f20_out -> f19_out :|: TRUE f20_in -> f26_in :|: TRUE f26_out -> f20_out :|: TRUE f26_in -> f27_in :|: TRUE f27_out -> f26_out :|: TRUE f29_out -> f27_out :|: TRUE f28_out -> f29_in :|: TRUE f27_in -> f28_in :|: TRUE Start term: f3_in ---------------------------------------- (23) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: intTRSProblem: f32_in -> f36_in :|: TRUE f36_in -> f28_in :|: TRUE f28_in -> f30_in :|: TRUE f30_in -> f32_in :|: TRUE ---------------------------------------- (24) Obligation: Rules: f32_in -> f36_in :|: TRUE f36_in -> f28_in :|: TRUE f28_in -> f30_in :|: TRUE f30_in -> f32_in :|: TRUE ---------------------------------------- (25) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (26) Obligation: Rules: f32_in -> f32_in :|: TRUE ---------------------------------------- (27) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (28) Obligation: Rules: f32_in -> f32_in :|: TRUE ---------------------------------------- (29) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f32_in -> f32_in :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (30) Obligation: Termination digraph: Nodes: (1) f32_in -> f32_in :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (31) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f32_in() Replaced non-predefined constructor symbols by 0. ---------------------------------------- (32) Obligation: Rules: f32_in -> f32_in :|: TRUE ---------------------------------------- (33) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc) -> f(1) :|: pc = 1 && TRUE Witness term starting non-terminating reduction: f(1) ---------------------------------------- (34) NO