/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- Graph construction failed Graph construction failed Graph construction failed YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern count(g,g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) UnifyTransformerProof [EQUIVALENT, 0 ms] (2) Prolog (3) UndefinedPredicateHandlerProof [SOUND, 0 ms] (4) Prolog (5) PrologToPiTRSProof [SOUND, 18 ms] (6) PiTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) PiDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) PiDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) PiDP (13) PiDPToQDPProof [SOUND, 11 ms] (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Clauses: count(Item, [], 0). count(Item, .(X, Xs), Result) :- ','(=(Item, X), ','(count(Item, Xs, TailCount), is(Result, +(TailCount, 1)))). count(Item, .(X, Xs), TailCount) :- ','(\=(Item, X), count(Item, Xs, TailCount)). Query: count(g,g,a) ---------------------------------------- (1) UnifyTransformerProof (EQUIVALENT) Added a fact for the built-in = predicate [PROLOG]. ---------------------------------------- (2) Obligation: Clauses: count(Item, [], 0). count(Item, .(X, Xs), Result) :- ','(=(Item, X), ','(count(Item, Xs, TailCount), is(Result, +(TailCount, 1)))). count(Item, .(X, Xs), TailCount) :- ','(\=(Item, X), count(Item, Xs, TailCount)). =(X, X). Query: count(g,g,a) ---------------------------------------- (3) UndefinedPredicateHandlerProof (SOUND) Added facts for all undefined predicates [PROLOG]. ---------------------------------------- (4) Obligation: Clauses: count(Item, [], 0). count(Item, .(X, Xs), Result) :- ','(=(Item, X), ','(count(Item, Xs, TailCount), is(Result, +(TailCount, 1)))). count(Item, .(X, Xs), TailCount) :- ','(\=(Item, X), count(Item, Xs, TailCount)). =(X, X). is(X0, X1). \=(X0, X1). Query: count(g,g,a) ---------------------------------------- (5) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: count_in_3: (b,b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: count_in_gga(Item, [], 0) -> count_out_gga(Item, [], 0) count_in_gga(Item, .(X, Xs), Result) -> U1_gga(Item, X, Xs, Result, =_in_gg(Item, X)) =_in_gg(X, X) -> =_out_gg(X, X) U1_gga(Item, X, Xs, Result, =_out_gg(Item, X)) -> U2_gga(Item, X, Xs, Result, count_in_gga(Item, Xs, TailCount)) count_in_gga(Item, .(X, Xs), TailCount) -> U4_gga(Item, X, Xs, TailCount, \=_in_gg(Item, X)) \=_in_gg(X0, X1) -> \=_out_gg(X0, X1) U4_gga(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> U5_gga(Item, X, Xs, TailCount, count_in_gga(Item, Xs, TailCount)) U5_gga(Item, X, Xs, TailCount, count_out_gga(Item, Xs, TailCount)) -> count_out_gga(Item, .(X, Xs), TailCount) U2_gga(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> U3_gga(Item, X, Xs, Result, TailCount, is_in_ag(Result, +(TailCount, 1))) is_in_ag(X0, X1) -> is_out_ag(X0, X1) U3_gga(Item, X, Xs, Result, TailCount, is_out_ag(Result, +(TailCount, 1))) -> count_out_gga(Item, .(X, Xs), Result) The argument filtering Pi contains the following mapping: count_in_gga(x1, x2, x3) = count_in_gga(x1, x2) [] = [] count_out_gga(x1, x2, x3) = count_out_gga .(x1, x2) = .(x1, x2) U1_gga(x1, x2, x3, x4, x5) = U1_gga(x1, x3, x5) =_in_gg(x1, x2) = =_in_gg(x1, x2) =_out_gg(x1, x2) = =_out_gg U2_gga(x1, x2, x3, x4, x5) = U2_gga(x5) U4_gga(x1, x2, x3, x4, x5) = U4_gga(x1, x3, x5) \=_in_gg(x1, x2) = \=_in_gg(x1, x2) \=_out_gg(x1, x2) = \=_out_gg U5_gga(x1, x2, x3, x4, x5) = U5_gga(x5) U3_gga(x1, x2, x3, x4, x5, x6) = U3_gga(x6) is_in_ag(x1, x2) = is_in_ag(x2) is_out_ag(x1, x2) = is_out_ag +(x1, x2) = +(x2) 1 = 1 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (6) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: count_in_gga(Item, [], 0) -> count_out_gga(Item, [], 0) count_in_gga(Item, .(X, Xs), Result) -> U1_gga(Item, X, Xs, Result, =_in_gg(Item, X)) =_in_gg(X, X) -> =_out_gg(X, X) U1_gga(Item, X, Xs, Result, =_out_gg(Item, X)) -> U2_gga(Item, X, Xs, Result, count_in_gga(Item, Xs, TailCount)) count_in_gga(Item, .(X, Xs), TailCount) -> U4_gga(Item, X, Xs, TailCount, \=_in_gg(Item, X)) \=_in_gg(X0, X1) -> \=_out_gg(X0, X1) U4_gga(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> U5_gga(Item, X, Xs, TailCount, count_in_gga(Item, Xs, TailCount)) U5_gga(Item, X, Xs, TailCount, count_out_gga(Item, Xs, TailCount)) -> count_out_gga(Item, .(X, Xs), TailCount) U2_gga(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> U3_gga(Item, X, Xs, Result, TailCount, is_in_ag(Result, +(TailCount, 1))) is_in_ag(X0, X1) -> is_out_ag(X0, X1) U3_gga(Item, X, Xs, Result, TailCount, is_out_ag(Result, +(TailCount, 1))) -> count_out_gga(Item, .(X, Xs), Result) The argument filtering Pi contains the following mapping: count_in_gga(x1, x2, x3) = count_in_gga(x1, x2) [] = [] count_out_gga(x1, x2, x3) = count_out_gga .(x1, x2) = .(x1, x2) U1_gga(x1, x2, x3, x4, x5) = U1_gga(x1, x3, x5) =_in_gg(x1, x2) = =_in_gg(x1, x2) =_out_gg(x1, x2) = =_out_gg U2_gga(x1, x2, x3, x4, x5) = U2_gga(x5) U4_gga(x1, x2, x3, x4, x5) = U4_gga(x1, x3, x5) \=_in_gg(x1, x2) = \=_in_gg(x1, x2) \=_out_gg(x1, x2) = \=_out_gg U5_gga(x1, x2, x3, x4, x5) = U5_gga(x5) U3_gga(x1, x2, x3, x4, x5, x6) = U3_gga(x6) is_in_ag(x1, x2) = is_in_ag(x2) is_out_ag(x1, x2) = is_out_ag +(x1, x2) = +(x2) 1 = 1 ---------------------------------------- (7) 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: COUNT_IN_GGA(Item, .(X, Xs), Result) -> U1_GGA(Item, X, Xs, Result, =_in_gg(Item, X)) COUNT_IN_GGA(Item, .(X, Xs), Result) -> =_IN_GG(Item, X) U1_GGA(Item, X, Xs, Result, =_out_gg(Item, X)) -> U2_GGA(Item, X, Xs, Result, count_in_gga(Item, Xs, TailCount)) U1_GGA(Item, X, Xs, Result, =_out_gg(Item, X)) -> COUNT_IN_GGA(Item, Xs, TailCount) COUNT_IN_GGA(Item, .(X, Xs), TailCount) -> U4_GGA(Item, X, Xs, TailCount, \=_in_gg(Item, X)) COUNT_IN_GGA(Item, .(X, Xs), TailCount) -> \=_IN_GG(Item, X) U4_GGA(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> U5_GGA(Item, X, Xs, TailCount, count_in_gga(Item, Xs, TailCount)) U4_GGA(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> COUNT_IN_GGA(Item, Xs, TailCount) U2_GGA(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> U3_GGA(Item, X, Xs, Result, TailCount, is_in_ag(Result, +(TailCount, 1))) U2_GGA(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> IS_IN_AG(Result, +(TailCount, 1)) The TRS R consists of the following rules: count_in_gga(Item, [], 0) -> count_out_gga(Item, [], 0) count_in_gga(Item, .(X, Xs), Result) -> U1_gga(Item, X, Xs, Result, =_in_gg(Item, X)) =_in_gg(X, X) -> =_out_gg(X, X) U1_gga(Item, X, Xs, Result, =_out_gg(Item, X)) -> U2_gga(Item, X, Xs, Result, count_in_gga(Item, Xs, TailCount)) count_in_gga(Item, .(X, Xs), TailCount) -> U4_gga(Item, X, Xs, TailCount, \=_in_gg(Item, X)) \=_in_gg(X0, X1) -> \=_out_gg(X0, X1) U4_gga(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> U5_gga(Item, X, Xs, TailCount, count_in_gga(Item, Xs, TailCount)) U5_gga(Item, X, Xs, TailCount, count_out_gga(Item, Xs, TailCount)) -> count_out_gga(Item, .(X, Xs), TailCount) U2_gga(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> U3_gga(Item, X, Xs, Result, TailCount, is_in_ag(Result, +(TailCount, 1))) is_in_ag(X0, X1) -> is_out_ag(X0, X1) U3_gga(Item, X, Xs, Result, TailCount, is_out_ag(Result, +(TailCount, 1))) -> count_out_gga(Item, .(X, Xs), Result) The argument filtering Pi contains the following mapping: count_in_gga(x1, x2, x3) = count_in_gga(x1, x2) [] = [] count_out_gga(x1, x2, x3) = count_out_gga .(x1, x2) = .(x1, x2) U1_gga(x1, x2, x3, x4, x5) = U1_gga(x1, x3, x5) =_in_gg(x1, x2) = =_in_gg(x1, x2) =_out_gg(x1, x2) = =_out_gg U2_gga(x1, x2, x3, x4, x5) = U2_gga(x5) U4_gga(x1, x2, x3, x4, x5) = U4_gga(x1, x3, x5) \=_in_gg(x1, x2) = \=_in_gg(x1, x2) \=_out_gg(x1, x2) = \=_out_gg U5_gga(x1, x2, x3, x4, x5) = U5_gga(x5) U3_gga(x1, x2, x3, x4, x5, x6) = U3_gga(x6) is_in_ag(x1, x2) = is_in_ag(x2) is_out_ag(x1, x2) = is_out_ag +(x1, x2) = +(x2) 1 = 1 COUNT_IN_GGA(x1, x2, x3) = COUNT_IN_GGA(x1, x2) U1_GGA(x1, x2, x3, x4, x5) = U1_GGA(x1, x3, x5) =_IN_GG(x1, x2) = =_IN_GG(x1, x2) U2_GGA(x1, x2, x3, x4, x5) = U2_GGA(x5) U4_GGA(x1, x2, x3, x4, x5) = U4_GGA(x1, x3, x5) \=_IN_GG(x1, x2) = \=_IN_GG(x1, x2) U5_GGA(x1, x2, x3, x4, x5) = U5_GGA(x5) U3_GGA(x1, x2, x3, x4, x5, x6) = U3_GGA(x6) IS_IN_AG(x1, x2) = IS_IN_AG(x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (8) Obligation: Pi DP problem: The TRS P consists of the following rules: COUNT_IN_GGA(Item, .(X, Xs), Result) -> U1_GGA(Item, X, Xs, Result, =_in_gg(Item, X)) COUNT_IN_GGA(Item, .(X, Xs), Result) -> =_IN_GG(Item, X) U1_GGA(Item, X, Xs, Result, =_out_gg(Item, X)) -> U2_GGA(Item, X, Xs, Result, count_in_gga(Item, Xs, TailCount)) U1_GGA(Item, X, Xs, Result, =_out_gg(Item, X)) -> COUNT_IN_GGA(Item, Xs, TailCount) COUNT_IN_GGA(Item, .(X, Xs), TailCount) -> U4_GGA(Item, X, Xs, TailCount, \=_in_gg(Item, X)) COUNT_IN_GGA(Item, .(X, Xs), TailCount) -> \=_IN_GG(Item, X) U4_GGA(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> U5_GGA(Item, X, Xs, TailCount, count_in_gga(Item, Xs, TailCount)) U4_GGA(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> COUNT_IN_GGA(Item, Xs, TailCount) U2_GGA(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> U3_GGA(Item, X, Xs, Result, TailCount, is_in_ag(Result, +(TailCount, 1))) U2_GGA(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> IS_IN_AG(Result, +(TailCount, 1)) The TRS R consists of the following rules: count_in_gga(Item, [], 0) -> count_out_gga(Item, [], 0) count_in_gga(Item, .(X, Xs), Result) -> U1_gga(Item, X, Xs, Result, =_in_gg(Item, X)) =_in_gg(X, X) -> =_out_gg(X, X) U1_gga(Item, X, Xs, Result, =_out_gg(Item, X)) -> U2_gga(Item, X, Xs, Result, count_in_gga(Item, Xs, TailCount)) count_in_gga(Item, .(X, Xs), TailCount) -> U4_gga(Item, X, Xs, TailCount, \=_in_gg(Item, X)) \=_in_gg(X0, X1) -> \=_out_gg(X0, X1) U4_gga(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> U5_gga(Item, X, Xs, TailCount, count_in_gga(Item, Xs, TailCount)) U5_gga(Item, X, Xs, TailCount, count_out_gga(Item, Xs, TailCount)) -> count_out_gga(Item, .(X, Xs), TailCount) U2_gga(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> U3_gga(Item, X, Xs, Result, TailCount, is_in_ag(Result, +(TailCount, 1))) is_in_ag(X0, X1) -> is_out_ag(X0, X1) U3_gga(Item, X, Xs, Result, TailCount, is_out_ag(Result, +(TailCount, 1))) -> count_out_gga(Item, .(X, Xs), Result) The argument filtering Pi contains the following mapping: count_in_gga(x1, x2, x3) = count_in_gga(x1, x2) [] = [] count_out_gga(x1, x2, x3) = count_out_gga .(x1, x2) = .(x1, x2) U1_gga(x1, x2, x3, x4, x5) = U1_gga(x1, x3, x5) =_in_gg(x1, x2) = =_in_gg(x1, x2) =_out_gg(x1, x2) = =_out_gg U2_gga(x1, x2, x3, x4, x5) = U2_gga(x5) U4_gga(x1, x2, x3, x4, x5) = U4_gga(x1, x3, x5) \=_in_gg(x1, x2) = \=_in_gg(x1, x2) \=_out_gg(x1, x2) = \=_out_gg U5_gga(x1, x2, x3, x4, x5) = U5_gga(x5) U3_gga(x1, x2, x3, x4, x5, x6) = U3_gga(x6) is_in_ag(x1, x2) = is_in_ag(x2) is_out_ag(x1, x2) = is_out_ag +(x1, x2) = +(x2) 1 = 1 COUNT_IN_GGA(x1, x2, x3) = COUNT_IN_GGA(x1, x2) U1_GGA(x1, x2, x3, x4, x5) = U1_GGA(x1, x3, x5) =_IN_GG(x1, x2) = =_IN_GG(x1, x2) U2_GGA(x1, x2, x3, x4, x5) = U2_GGA(x5) U4_GGA(x1, x2, x3, x4, x5) = U4_GGA(x1, x3, x5) \=_IN_GG(x1, x2) = \=_IN_GG(x1, x2) U5_GGA(x1, x2, x3, x4, x5) = U5_GGA(x5) U3_GGA(x1, x2, x3, x4, x5, x6) = U3_GGA(x6) IS_IN_AG(x1, x2) = IS_IN_AG(x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (9) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 6 less nodes. ---------------------------------------- (10) Obligation: Pi DP problem: The TRS P consists of the following rules: U1_GGA(Item, X, Xs, Result, =_out_gg(Item, X)) -> COUNT_IN_GGA(Item, Xs, TailCount) COUNT_IN_GGA(Item, .(X, Xs), Result) -> U1_GGA(Item, X, Xs, Result, =_in_gg(Item, X)) COUNT_IN_GGA(Item, .(X, Xs), TailCount) -> U4_GGA(Item, X, Xs, TailCount, \=_in_gg(Item, X)) U4_GGA(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> COUNT_IN_GGA(Item, Xs, TailCount) The TRS R consists of the following rules: count_in_gga(Item, [], 0) -> count_out_gga(Item, [], 0) count_in_gga(Item, .(X, Xs), Result) -> U1_gga(Item, X, Xs, Result, =_in_gg(Item, X)) =_in_gg(X, X) -> =_out_gg(X, X) U1_gga(Item, X, Xs, Result, =_out_gg(Item, X)) -> U2_gga(Item, X, Xs, Result, count_in_gga(Item, Xs, TailCount)) count_in_gga(Item, .(X, Xs), TailCount) -> U4_gga(Item, X, Xs, TailCount, \=_in_gg(Item, X)) \=_in_gg(X0, X1) -> \=_out_gg(X0, X1) U4_gga(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> U5_gga(Item, X, Xs, TailCount, count_in_gga(Item, Xs, TailCount)) U5_gga(Item, X, Xs, TailCount, count_out_gga(Item, Xs, TailCount)) -> count_out_gga(Item, .(X, Xs), TailCount) U2_gga(Item, X, Xs, Result, count_out_gga(Item, Xs, TailCount)) -> U3_gga(Item, X, Xs, Result, TailCount, is_in_ag(Result, +(TailCount, 1))) is_in_ag(X0, X1) -> is_out_ag(X0, X1) U3_gga(Item, X, Xs, Result, TailCount, is_out_ag(Result, +(TailCount, 1))) -> count_out_gga(Item, .(X, Xs), Result) The argument filtering Pi contains the following mapping: count_in_gga(x1, x2, x3) = count_in_gga(x1, x2) [] = [] count_out_gga(x1, x2, x3) = count_out_gga .(x1, x2) = .(x1, x2) U1_gga(x1, x2, x3, x4, x5) = U1_gga(x1, x3, x5) =_in_gg(x1, x2) = =_in_gg(x1, x2) =_out_gg(x1, x2) = =_out_gg U2_gga(x1, x2, x3, x4, x5) = U2_gga(x5) U4_gga(x1, x2, x3, x4, x5) = U4_gga(x1, x3, x5) \=_in_gg(x1, x2) = \=_in_gg(x1, x2) \=_out_gg(x1, x2) = \=_out_gg U5_gga(x1, x2, x3, x4, x5) = U5_gga(x5) U3_gga(x1, x2, x3, x4, x5, x6) = U3_gga(x6) is_in_ag(x1, x2) = is_in_ag(x2) is_out_ag(x1, x2) = is_out_ag +(x1, x2) = +(x2) 1 = 1 COUNT_IN_GGA(x1, x2, x3) = COUNT_IN_GGA(x1, x2) U1_GGA(x1, x2, x3, x4, x5) = U1_GGA(x1, x3, x5) U4_GGA(x1, x2, x3, x4, x5) = U4_GGA(x1, x3, x5) We have to consider all (P,R,Pi)-chains ---------------------------------------- (11) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (12) Obligation: Pi DP problem: The TRS P consists of the following rules: U1_GGA(Item, X, Xs, Result, =_out_gg(Item, X)) -> COUNT_IN_GGA(Item, Xs, TailCount) COUNT_IN_GGA(Item, .(X, Xs), Result) -> U1_GGA(Item, X, Xs, Result, =_in_gg(Item, X)) COUNT_IN_GGA(Item, .(X, Xs), TailCount) -> U4_GGA(Item, X, Xs, TailCount, \=_in_gg(Item, X)) U4_GGA(Item, X, Xs, TailCount, \=_out_gg(Item, X)) -> COUNT_IN_GGA(Item, Xs, TailCount) The TRS R consists of the following rules: =_in_gg(X, X) -> =_out_gg(X, X) \=_in_gg(X0, X1) -> \=_out_gg(X0, X1) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) =_in_gg(x1, x2) = =_in_gg(x1, x2) =_out_gg(x1, x2) = =_out_gg \=_in_gg(x1, x2) = \=_in_gg(x1, x2) \=_out_gg(x1, x2) = \=_out_gg COUNT_IN_GGA(x1, x2, x3) = COUNT_IN_GGA(x1, x2) U1_GGA(x1, x2, x3, x4, x5) = U1_GGA(x1, x3, x5) U4_GGA(x1, x2, x3, x4, x5) = U4_GGA(x1, x3, x5) We have to consider all (P,R,Pi)-chains ---------------------------------------- (13) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: U1_GGA(Item, Xs, =_out_gg) -> COUNT_IN_GGA(Item, Xs) COUNT_IN_GGA(Item, .(X, Xs)) -> U1_GGA(Item, Xs, =_in_gg(Item, X)) COUNT_IN_GGA(Item, .(X, Xs)) -> U4_GGA(Item, Xs, \=_in_gg(Item, X)) U4_GGA(Item, Xs, \=_out_gg) -> COUNT_IN_GGA(Item, Xs) The TRS R consists of the following rules: =_in_gg(X, X) -> =_out_gg \=_in_gg(X0, X1) -> \=_out_gg The set Q consists of the following terms: =_in_gg(x0, x1) \=_in_gg(x0, x1) We have to consider all (P,Q,R)-chains. ---------------------------------------- (15) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *COUNT_IN_GGA(Item, .(X, Xs)) -> U1_GGA(Item, Xs, =_in_gg(Item, X)) The graph contains the following edges 1 >= 1, 2 > 2 *COUNT_IN_GGA(Item, .(X, Xs)) -> U4_GGA(Item, Xs, \=_in_gg(Item, X)) The graph contains the following edges 1 >= 1, 2 > 2 *U1_GGA(Item, Xs, =_out_gg) -> COUNT_IN_GGA(Item, Xs) The graph contains the following edges 1 >= 1, 2 >= 2 *U4_GGA(Item, Xs, \=_out_gg) -> COUNT_IN_GGA(Item, Xs) The graph contains the following edges 1 >= 1, 2 >= 2 ---------------------------------------- (16) YES