/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern p2(a) w.r.t. the given Prolog program could not be shown: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) PiDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) PiDP (9) PiDPToQDPProof [SOUND, 0 ms] (10) QDP (11) PrologToPiTRSProof [SOUND, 0 ms] (12) PiTRS (13) DependencyPairsProof [EQUIVALENT, 0 ms] (14) PiDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) PiDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) PiDP (19) PiDPToQDPProof [SOUND, 0 ms] (20) QDP (21) PrologToDTProblemTransformerProof [SOUND, 0 ms] (22) TRIPLES (23) TriplesToPiDPProof [SOUND, 0 ms] (24) PiDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) PiDP (27) PiDPToQDPProof [SOUND, 1 ms] (28) QDP (29) PrologToTRSTransformerProof [SOUND, 0 ms] (30) QTRS (31) QTRSRRRProof [EQUIVALENT, 17 ms] (32) QTRS (33) Overlay + Local Confluence [EQUIVALENT, 0 ms] (34) QTRS (35) DependencyPairsProof [EQUIVALENT, 0 ms] (36) QDP (37) UsableRulesProof [EQUIVALENT, 2 ms] (38) QDP (39) QReductionProof [EQUIVALENT, 0 ms] (40) QDP (41) PrologToIRSwTTransformerProof [SOUND, 0 ms] (42) IRSwT (43) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (44) IRSwT (45) IntTRSCompressionProof [EQUIVALENT, 18 ms] (46) IRSwT (47) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (48) IRSwT (49) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (50) IRSwT (51) FilterProof [EQUIVALENT, 0 ms] (52) IntTRS (53) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (54) NO ---------------------------------------- (0) Obligation: Clauses: p1(f(X)) :- p1(X). p2(f(X)) :- p2(X). Query: p2(a) ---------------------------------------- (1) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: p2_in_1: (f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: Pi DP problem: The TRS P consists of the following rules: P2_IN_A(f(X)) -> U2_A(X, p2_in_a(X)) P2_IN_A(f(X)) -> P2_IN_A(X) The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) P2_IN_A(x1) = P2_IN_A U2_A(x1, x2) = U2_A(x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (4) Obligation: Pi DP problem: The TRS P consists of the following rules: P2_IN_A(f(X)) -> U2_A(X, p2_in_a(X)) P2_IN_A(f(X)) -> P2_IN_A(X) The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) P2_IN_A(x1) = P2_IN_A U2_A(x1, x2) = U2_A(x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 1 less node. ---------------------------------------- (6) Obligation: Pi DP problem: The TRS P consists of the following rules: P2_IN_A(f(X)) -> P2_IN_A(X) The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) P2_IN_A(x1) = P2_IN_A We have to consider all (P,R,Pi)-chains ---------------------------------------- (7) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (8) Obligation: Pi DP problem: The TRS P consists of the following rules: P2_IN_A(f(X)) -> P2_IN_A(X) R is empty. The argument filtering Pi contains the following mapping: f(x1) = f(x1) P2_IN_A(x1) = P2_IN_A We have to consider all (P,R,Pi)-chains ---------------------------------------- (9) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: P2_IN_A -> P2_IN_A R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (11) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: p2_in_1: (f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (12) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) ---------------------------------------- (13) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: Pi DP problem: The TRS P consists of the following rules: P2_IN_A(f(X)) -> U2_A(X, p2_in_a(X)) P2_IN_A(f(X)) -> P2_IN_A(X) The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) P2_IN_A(x1) = P2_IN_A U2_A(x1, x2) = U2_A(x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (14) Obligation: Pi DP problem: The TRS P consists of the following rules: P2_IN_A(f(X)) -> U2_A(X, p2_in_a(X)) P2_IN_A(f(X)) -> P2_IN_A(X) The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) P2_IN_A(x1) = P2_IN_A U2_A(x1, x2) = U2_A(x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (15) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 1 less node. ---------------------------------------- (16) Obligation: Pi DP problem: The TRS P consists of the following rules: P2_IN_A(f(X)) -> P2_IN_A(X) The TRS R consists of the following rules: p2_in_a(f(X)) -> U2_a(X, p2_in_a(X)) U2_a(X, p2_out_a(X)) -> p2_out_a(f(X)) The argument filtering Pi contains the following mapping: p2_in_a(x1) = p2_in_a U2_a(x1, x2) = U2_a(x2) p2_out_a(x1) = p2_out_a(x1) f(x1) = f(x1) P2_IN_A(x1) = P2_IN_A We have to consider all (P,R,Pi)-chains ---------------------------------------- (17) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (18) Obligation: Pi DP problem: The TRS P consists of the following rules: P2_IN_A(f(X)) -> P2_IN_A(X) R is empty. The argument filtering Pi contains the following mapping: f(x1) = f(x1) P2_IN_A(x1) = P2_IN_A We have to consider all (P,R,Pi)-chains ---------------------------------------- (19) PiDPToQDPProof (SOUND) 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: P2_IN_A -> P2_IN_A R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (21) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 1, "program": { "directives": [], "clauses": [ [ "(p1 (f X))", "(p1 X)" ], [ "(p2 (f X))", "(p2 X)" ] ] }, "graph": { "nodes": { "1": { "goal": [{ "clause": -1, "scope": -1, "term": "(p2 T1)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "56": { "goal": [{ "clause": 1, "scope": 2, "term": "(p2 T4)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "57": { "goal": [{ "clause": -1, "scope": -1, "term": "(p2 T8)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "58": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "7": { "goal": [{ "clause": 1, "scope": 1, "term": "(p2 T1)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "type": "Nodes", "52": { "goal": [{ "clause": -1, "scope": -1, "term": "(p2 T4)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "54": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 1, "to": 7, "label": "CASE" }, { "from": 7, "to": 52, "label": "EVAL with clause\np2(f(X2)) :- p2(X2).\nand substitutionX2 -> T4,\nT1 -> f(T4),\nT3 -> T4" }, { "from": 7, "to": 54, "label": "EVAL-BACKTRACK" }, { "from": 52, "to": 56, "label": "CASE" }, { "from": 56, "to": 57, "label": "EVAL with clause\np2(f(X5)) :- p2(X5).\nand substitutionX5 -> T8,\nT4 -> f(T8),\nT7 -> T8" }, { "from": 56, "to": 58, "label": "EVAL-BACKTRACK" }, { "from": 57, "to": 1, "label": "INSTANCE with matching:\nT1 -> T8" } ], "type": "Graph" } } ---------------------------------------- (22) Obligation: Triples: p2A(f(f(X1))) :- p2A(X1). Clauses: p2cA(f(f(X1))) :- p2cA(X1). Afs: p2A(x1) = p2A ---------------------------------------- (23) TriplesToPiDPProof (SOUND) We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes: p2A_in_1: (f) Transforming TRIPLES into the following Term Rewriting System: Pi DP problem: The TRS P consists of the following rules: P2A_IN_A(f(f(X1))) -> U1_A(X1, p2A_in_a(X1)) P2A_IN_A(f(f(X1))) -> P2A_IN_A(X1) R is empty. The argument filtering Pi contains the following mapping: p2A_in_a(x1) = p2A_in_a f(x1) = f(x1) P2A_IN_A(x1) = P2A_IN_A U1_A(x1, x2) = U1_A(x2) We have to consider all (P,R,Pi)-chains Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES ---------------------------------------- (24) Obligation: Pi DP problem: The TRS P consists of the following rules: P2A_IN_A(f(f(X1))) -> U1_A(X1, p2A_in_a(X1)) P2A_IN_A(f(f(X1))) -> P2A_IN_A(X1) R is empty. The argument filtering Pi contains the following mapping: p2A_in_a(x1) = p2A_in_a f(x1) = f(x1) P2A_IN_A(x1) = P2A_IN_A U1_A(x1, x2) = U1_A(x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (25) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 1 less node. ---------------------------------------- (26) Obligation: Pi DP problem: The TRS P consists of the following rules: P2A_IN_A(f(f(X1))) -> P2A_IN_A(X1) R is empty. The argument filtering Pi contains the following mapping: f(x1) = f(x1) P2A_IN_A(x1) = P2A_IN_A We have to consider all (P,R,Pi)-chains ---------------------------------------- (27) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (28) Obligation: Q DP problem: The TRS P consists of the following rules: P2A_IN_A -> P2A_IN_A R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (29) PrologToTRSTransformerProof (SOUND) Transformed Prolog program to TRS. { "root": 2, "program": { "directives": [], "clauses": [ [ "(p1 (f X))", "(p1 X)" ], [ "(p2 (f X))", "(p2 X)" ] ] }, "graph": { "nodes": { "2": { "goal": [{ "clause": -1, "scope": -1, "term": "(p2 T1)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "59": { "goal": [{ "clause": -1, "scope": -1, "term": "(p2 T5)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "60": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "type": "Nodes", "10": { "goal": [{ "clause": 1, "scope": 1, "term": "(p2 T1)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 2, "to": 10, "label": "CASE" }, { "from": 10, "to": 59, "label": "EVAL with clause\np2(f(X3)) :- p2(X3).\nand substitutionX3 -> T5,\nT1 -> f(T5),\nT4 -> T5" }, { "from": 10, "to": 60, "label": "EVAL-BACKTRACK" }, { "from": 59, "to": 2, "label": "INSTANCE with matching:\nT1 -> T5" } ], "type": "Graph" } } ---------------------------------------- (30) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f2_in -> U1(f2_in) U1(f2_out1(T5)) -> f2_out1(f(T5)) Q is empty. ---------------------------------------- (31) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U1(x_1)) = 2*x_1 POL(f(x_1)) = x_1 POL(f2_in) = 0 POL(f2_out1(x_1)) = 2 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U1(f2_out1(T5)) -> f2_out1(f(T5)) ---------------------------------------- (32) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f2_in -> U1(f2_in) Q is empty. ---------------------------------------- (33) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (34) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f2_in -> U1(f2_in) The set Q consists of the following terms: f2_in ---------------------------------------- (35) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (36) Obligation: Q DP problem: The TRS P consists of the following rules: F2_IN -> F2_IN The TRS R consists of the following rules: f2_in -> U1(f2_in) The set Q consists of the following terms: f2_in We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (37) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (38) Obligation: Q DP problem: The TRS P consists of the following rules: F2_IN -> F2_IN R is empty. The set Q consists of the following terms: f2_in We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (39) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. f2_in ---------------------------------------- (40) Obligation: Q DP problem: The TRS P consists of the following rules: F2_IN -> F2_IN R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (41) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 3, "program": { "directives": [], "clauses": [ [ "(p1 (f X))", "(p1 X)" ], [ "(p2 (f X))", "(p2 X)" ] ] }, "graph": { "nodes": { "3": { "goal": [{ "clause": -1, "scope": -1, "term": "(p2 T1)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "type": "Nodes", "62": { "goal": [{ "clause": 1, "scope": 1, "term": "(p2 T1)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "64": { "goal": [{ "clause": -1, "scope": -1, "term": "(p2 T5)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "65": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 3, "to": 62, "label": "CASE" }, { "from": 62, "to": 64, "label": "EVAL with clause\np2(f(X3)) :- p2(X3).\nand substitutionX3 -> T5,\nT1 -> f(T5),\nT4 -> T5" }, { "from": 62, "to": 65, "label": "EVAL-BACKTRACK" }, { "from": 64, "to": 3, "label": "INSTANCE with matching:\nT1 -> T5" } ], "type": "Graph" } } ---------------------------------------- (42) Obligation: Rules: f3_in -> f62_in :|: TRUE f62_out -> f3_out :|: TRUE f3_out -> f64_out :|: TRUE f64_in -> f3_in :|: TRUE f62_in -> f65_in :|: TRUE f64_out -> f62_out :|: TRUE f65_out -> f62_out :|: TRUE f62_in -> f64_in :|: TRUE Start term: f3_in ---------------------------------------- (43) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: intTRSProblem: f3_in -> f62_in :|: TRUE f64_in -> f3_in :|: TRUE f62_in -> f64_in :|: TRUE ---------------------------------------- (44) Obligation: Rules: f3_in -> f62_in :|: TRUE f64_in -> f3_in :|: TRUE f62_in -> f64_in :|: TRUE ---------------------------------------- (45) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (46) Obligation: Rules: f64_in -> f64_in :|: TRUE ---------------------------------------- (47) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (48) Obligation: Rules: f64_in -> f64_in :|: TRUE ---------------------------------------- (49) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f64_in -> f64_in :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (50) Obligation: Termination digraph: Nodes: (1) f64_in -> f64_in :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (51) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f64_in() Replaced non-predefined constructor symbols by 0. ---------------------------------------- (52) Obligation: Rules: f64_in -> f64_in :|: TRUE ---------------------------------------- (53) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc) -> f(1) :|: pc = 1 && TRUE Witness term starting non-terminating reduction: f(1) ---------------------------------------- (54) NO