/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Outermost Termination of the given OTRS could be proven: (0) OTRS (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 71 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) AND (11) QDP (12) UsableRulesProof [EQUIVALENT, 0 ms] (13) QDP (14) QReductionProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QReductionProof [EQUIVALENT, 3 ms] (29) QDP (30) RFCMatchBoundsDPProof [EQUIVALENT, 5 ms] (31) YES ---------------------------------------- (0) Obligation: Term rewrite system R: The TRS R consists of the following rules: f(f(g(x))) -> x g(b) -> f(g(b)) Outermost Strategy. ---------------------------------------- (1) Raffelsieper-Zantema-Transformation (SOUND) We applied the Raffelsieper-Zantema transformation to transform the outermost TRS to a standard TRS. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: down(f(f(g(x)))) -> up(x) down(g(b)) -> up(f(g(b))) top(up(x)) -> top(down(x)) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(b) = 0 POL(down(x_1)) = 2 + 2*x_1 POL(f(x_1)) = x_1 POL(f_flat(x_1)) = x_1 POL(fresh_constant) = 0 POL(g(x_1)) = 1 + 2*x_1 POL(g_flat(x_1)) = 2*x_1 POL(top(x_1)) = 2*x_1 POL(up(x_1)) = 2 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: down(f(f(g(x)))) -> up(x) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: down(g(b)) -> up(f(g(b))) top(up(x)) -> top(down(x)) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) Q is empty. ---------------------------------------- (5) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) down(g(b)) -> up(f(g(b))) The TRS R 2 is top(up(x)) -> top(down(x)) The signature Sigma is {top_1} ---------------------------------------- (6) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: down(g(b)) -> up(f(g(b))) top(up(x)) -> top(down(x)) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) The set Q consists of the following terms: down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) ---------------------------------------- (7) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (8) Obligation: Q DP problem: The TRS P consists of the following rules: TOP(up(x)) -> TOP(down(x)) TOP(up(x)) -> DOWN(x) DOWN(f(g(y4))) -> F_FLAT(down(g(y4))) DOWN(f(g(y4))) -> DOWN(g(y4)) DOWN(f(b)) -> F_FLAT(down(b)) DOWN(f(b)) -> DOWN(b) DOWN(f(fresh_constant)) -> F_FLAT(down(fresh_constant)) DOWN(f(fresh_constant)) -> DOWN(fresh_constant) DOWN(g(f(y6))) -> G_FLAT(down(f(y6))) DOWN(g(f(y6))) -> DOWN(f(y6)) DOWN(g(g(y7))) -> G_FLAT(down(g(y7))) DOWN(g(g(y7))) -> DOWN(g(y7)) DOWN(g(fresh_constant)) -> G_FLAT(down(fresh_constant)) DOWN(g(fresh_constant)) -> DOWN(fresh_constant) DOWN(f(f(f(y9)))) -> F_FLAT(down(f(f(y9)))) DOWN(f(f(f(y9)))) -> DOWN(f(f(y9))) DOWN(f(f(b))) -> F_FLAT(down(f(b))) DOWN(f(f(b))) -> DOWN(f(b)) DOWN(f(f(fresh_constant))) -> F_FLAT(down(f(fresh_constant))) DOWN(f(f(fresh_constant))) -> DOWN(f(fresh_constant)) The TRS R consists of the following rules: down(g(b)) -> up(f(g(b))) top(up(x)) -> top(down(x)) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) The set Q consists of the following terms: down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (9) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 15 less nodes. ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: DOWN(f(f(f(y9)))) -> DOWN(f(f(y9))) The TRS R consists of the following rules: down(g(b)) -> up(f(g(b))) top(up(x)) -> top(down(x)) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) The set Q consists of the following terms: down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (12) 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. ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: DOWN(f(f(f(y9)))) -> DOWN(f(f(y9))) R is empty. The set Q consists of the following terms: down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) 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]. down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: DOWN(f(f(f(y9)))) -> DOWN(f(f(y9))) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (16) 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: *DOWN(f(f(f(y9)))) -> DOWN(f(f(y9))) The graph contains the following edges 1 > 1 ---------------------------------------- (17) YES ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: DOWN(g(f(y6))) -> DOWN(f(y6)) DOWN(f(g(y4))) -> DOWN(g(y4)) DOWN(g(g(y7))) -> DOWN(g(y7)) The TRS R consists of the following rules: down(g(b)) -> up(f(g(b))) top(up(x)) -> top(down(x)) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) The set Q consists of the following terms: down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (19) 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. ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: DOWN(g(f(y6))) -> DOWN(f(y6)) DOWN(f(g(y4))) -> DOWN(g(y4)) DOWN(g(g(y7))) -> DOWN(g(y7)) R is empty. The set Q consists of the following terms: down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) 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]. down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) ---------------------------------------- (22) Obligation: Q DP problem: The TRS P consists of the following rules: DOWN(g(f(y6))) -> DOWN(f(y6)) DOWN(f(g(y4))) -> DOWN(g(y4)) DOWN(g(g(y7))) -> DOWN(g(y7)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (23) 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: *DOWN(f(g(y4))) -> DOWN(g(y4)) The graph contains the following edges 1 > 1 *DOWN(g(g(y7))) -> DOWN(g(y7)) The graph contains the following edges 1 > 1 *DOWN(g(f(y6))) -> DOWN(f(y6)) The graph contains the following edges 1 > 1 ---------------------------------------- (24) YES ---------------------------------------- (25) Obligation: Q DP problem: The TRS P consists of the following rules: TOP(up(x)) -> TOP(down(x)) The TRS R consists of the following rules: down(g(b)) -> up(f(g(b))) top(up(x)) -> top(down(x)) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) The set Q consists of the following terms: down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (26) 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. ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: TOP(up(x)) -> TOP(down(x)) The TRS R consists of the following rules: down(g(b)) -> up(f(g(b))) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) The set Q consists of the following terms: down(g(b)) top(up(x0)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (28) 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]. top(up(x0)) ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: TOP(up(x)) -> TOP(down(x)) The TRS R consists of the following rules: down(g(b)) -> up(f(g(b))) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) The set Q consists of the following terms: down(g(b)) down(f(g(x0))) down(f(b)) down(f(fresh_constant)) down(g(f(x0))) down(g(g(x0))) down(g(fresh_constant)) down(f(f(f(x0)))) down(f(f(b))) down(f(f(fresh_constant))) f_flat(up(x0)) g_flat(up(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (30) RFCMatchBoundsDPProof (EQUIVALENT) Finiteness of the DP problem can be shown by a matchbound of 9. As the DP problem is minimal we only have to initialize the certificate graph by the rules of P: TOP(up(x)) -> TOP(down(x)) To find matches we regarded all rules of R and P: down(g(b)) -> up(f(g(b))) down(f(g(y4))) -> f_flat(down(g(y4))) down(f(b)) -> f_flat(down(b)) down(f(fresh_constant)) -> f_flat(down(fresh_constant)) down(g(f(y6))) -> g_flat(down(f(y6))) down(g(g(y7))) -> g_flat(down(g(y7))) down(g(fresh_constant)) -> g_flat(down(fresh_constant)) down(f(f(f(y9)))) -> f_flat(down(f(f(y9)))) down(f(f(b))) -> f_flat(down(f(b))) down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) f_flat(up(x_1)) -> up(f(x_1)) g_flat(up(x_1)) -> up(g(x_1)) TOP(up(x)) -> TOP(down(x)) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 600, 601, 602, 603, 608, 609, 610, 665, 666, 675, 676, 677, 678, 679, 680, 681, 682, 700, 701, 714, 715, 731, 732, 733 Node 520 is start node and node 521 is final node. Those nodes are connected through the following edges: * 520 to 522 labelled TOP_1(0)* 520 to 533 labelled TOP_1(1)* 520 to 545 labelled TOP_1(2)* 520 to 575 labelled TOP_1(3)* 521 to 521 labelled #_1(0)* 522 to 521 labelled down_1(0)* 522 to 523 labelled up_1(1)* 522 to 526 labelled f_flat_1(1), g_flat_1(1)* 522 to 528 labelled g_flat_1(1)* 522 to 530 labelled f_flat_1(1)* 522 to 536 labelled up_1(2)* 523 to 524 labelled f_1(1)* 524 to 525 labelled g_1(1)* 525 to 521 labelled b(1)* 526 to 527 labelled down_1(1)* 526 to 523 labelled up_1(1)* 526 to 528 labelled g_flat_1(1)* 526 to 526 labelled g_flat_1(1)* 526 to 536 labelled up_1(2)* 527 to 521 labelled g_1(1), b(1), fresh_constant(1)* 528 to 529 labelled down_1(1)* 528 to 526 labelled f_flat_1(1)* 528 to 530 labelled f_flat_1(1)* 528 to 536 labelled up_1(2)* 529 to 521 labelled f_1(1)* 530 to 531 labelled down_1(1)* 530 to 534 labelled f_flat_1(2)* 530 to 530 labelled f_flat_1(1)* 531 to 532 labelled f_1(1)* 532 to 521 labelled f_1(1), b(1), fresh_constant(1)* 533 to 523 labelled down_1(1)* 533 to 537 labelled f_flat_1(2), g_flat_1(2)* 533 to 536 labelled down_1(1)* 533 to 542 labelled up_1(3)* 533 to 543 labelled g_flat_1(2)* 534 to 535 labelled down_1(2)* 535 to 521 labelled b(2), fresh_constant(2)* 536 to 523 labelled f_1(2), g_1(2)* 536 to 536 labelled f_1(2), g_1(2)* 536 to 524 labelled f_1(2)* 537 to 538 labelled down_1(2)* 537 to 539 labelled up_1(2)* 537 to 543 labelled g_flat_1(2)* 537 to 546 labelled g_flat_1(3)* 537 to 548 labelled f_flat_1(3), g_flat_1(3)* 537 to 537 labelled f_flat_1(2)* 537 to 550 labelled f_flat_1(3)* 537 to 542 labelled up_1(3)* 537 to 557 labelled up_1(4)* 538 to 525 labelled g_1(2)* 538 to 523 labelled g_1(2)* 538 to 536 labelled f_1(2), g_1(2)* 539 to 540 labelled f_1(2)* 540 to 541 labelled g_1(2)* 541 to 521 labelled b(2)* 542 to 539 labelled f_1(3), g_1(3)* 542 to 542 labelled f_1(3), g_1(3), f_1(5)* 542 to 557 labelled f_1(3), g_1(3), f_1(5)* 543 to 544 labelled down_1(2)* 543 to 537 labelled f_flat_1(2)* 543 to 542 labelled up_1(3)* 544 to 524 labelled f_1(2)* 544 to 523 labelled f_1(2)* 545 to 542 labelled down_1(2)* 545 to 553 labelled g_flat_1(3), f_flat_1(3)* 545 to 558 labelled f_flat_1(3), g_flat_1(3)* 545 to 563 labelled f_flat_1(3)* 545 to 574 labelled up_1(4)* 546 to 547 labelled down_1(3)* 546 to 537 labelled f_flat_1(2)* 546 to 548 labelled f_flat_1(3)* 546 to 550 labelled f_flat_1(3)* 546 to 542 labelled up_1(3)* 546 to 557 labelled up_1(4)* 547 to 523 labelled f_1(3)* 547 to 536 labelled f_1(3)* 547 to 524 labelled f_1(3)* 548 to 549 labelled down_1(3)* 548 to 543 labelled g_flat_1(2)* 548 to 546 labelled g_flat_1(3)* 548 to 548 labelled g_flat_1(3)* 548 to 542 labelled up_1(3)* 548 to 557 labelled up_1(4)* 549 to 523 labelled g_1(3)* 549 to 536 labelled g_1(3)* 550 to 551 labelled down_1(3)* 550 to 537 labelled f_flat_1(2)* 550 to 550 labelled f_flat_1(3)* 550 to 542 labelled up_1(3)* 550 to 557 labelled up_1(4)* 551 to 552 labelled f_1(3)* 552 to 523 labelled f_1(3)* 552 to 536 labelled f_1(3)* 552 to 524 labelled f_1(3)* 553 to 554 labelled down_1(3)* 553 to 555 labelled f_flat_1(3)* 553 to 566 labelled up_1(4)* 553 to 569 labelled f_flat_1(4), g_flat_1(4)* 553 to 563 labelled f_flat_1(3)* 553 to 571 labelled f_flat_1(4)* 553 to 567 labelled f_flat_1(4), g_flat_1(4)* 553 to 578 labelled up_1(5)* 554 to 540 labelled f_1(3)* 554 to 539 labelled f_1(3)* 554 to 542 labelled f_1(3)* 554 to 557 labelled f_1(3), g_1(3)* 555 to 556 labelled down_1(3)* 555 to 560 labelled up_1(3)* 556 to 541 labelled g_1(3)* 557 to 542 labelled g_1(4), f_1(4)* 557 to 557 labelled g_1(4), f_1(4)* 558 to 559 labelled down_1(3)* 558 to 553 labelled g_flat_1(3)* 558 to 567 labelled g_flat_1(4)* 558 to 569 labelled g_flat_1(4)* 558 to 574 labelled up_1(4)* 558 to 578 labelled up_1(5)* 559 to 539 labelled g_1(3)* 559 to 542 labelled g_1(3)* 560 to 561 labelled f_1(3)* 560 to 666 labelled f_1(4)* 560 to 665 labelled f_1(4)* 560 to 675 labelled f_1(4)* 561 to 562 labelled g_1(3)* 562 to 521 labelled b(3)* 563 to 564 labelled down_1(3)* 564 to 565 labelled f_1(3)* 565 to 540 labelled f_1(3)* 566 to 560 labelled f_1(4)* 567 to 568 labelled down_1(4)* 567 to 569 labelled f_flat_1(4)* 567 to 563 labelled f_flat_1(3)* 567 to 571 labelled f_flat_1(4)* 567 to 567 labelled f_flat_1(4)* 567 to 576 labelled f_flat_1(5)* 567 to 578 labelled up_1(5)* 567 to 665 labelled up_1(6)* 568 to 539 labelled f_1(4)* 568 to 542 labelled f_1(4)* 568 to 557 labelled f_1(4)* 569 to 570 labelled down_1(4)* 569 to 553 labelled g_flat_1(3)* 569 to 567 labelled g_flat_1(4)* 569 to 569 labelled g_flat_1(4)* 569 to 574 labelled up_1(4)* 569 to 576 labelled g_flat_1(5)* 569 to 578 labelled up_1(5)* 569 to 666 labelled up_1(6)* 570 to 539 labelled g_1(4)* 570 to 542 labelled g_1(4)* 570 to 557 labelled g_1(4)* 571 to 572 labelled down_1(4)* 571 to 563 labelled f_flat_1(3)* 571 to 571 labelled f_flat_1(4)* 571 to 567 labelled f_flat_1(4)* 571 to 576 labelled f_flat_1(5)* 571 to 578 labelled up_1(5)* 571 to 665 labelled up_1(6)* 572 to 573 labelled f_1(4)* 573 to 539 labelled f_1(4)* 573 to 542 labelled f_1(4)* 574 to 566 labelled g_1(4), f_1(4)* 574 to 574 labelled f_1(4), g_1(4)* 574 to 578 labelled g_1(4), f_1(4)* 575 to 574 labelled down_1(3)* 575 to 581 labelled g_flat_1(4), f_flat_1(4)* 575 to 583 labelled f_flat_1(4), g_flat_1(4)* 575 to 588 labelled f_flat_1(4)* 576 to 577 labelled down_1(5)* 576 to 567 labelled g_flat_1(4), f_flat_1(4)* 576 to 569 labelled g_flat_1(4), f_flat_1(4)* 576 to 579 labelled g_flat_1(6)* 576 to 576 labelled g_flat_1(5), f_flat_1(5)* 576 to 563 labelled f_flat_1(3)* 576 to 571 labelled f_flat_1(4)* 576 to 585 labelled f_flat_1(6)* 576 to 578 labelled up_1(5)* 576 to 666 labelled up_1(6)* 576 to 665 labelled up_1(6)* 576 to 675 labelled up_1(7)* 577 to 542 labelled g_1(5), f_1(5)* 577 to 557 labelled g_1(5), f_1(5)* 578 to 574 labelled f_1(5), g_1(5)* 578 to 578 labelled f_1(5), g_1(5), f_1(7), f_1(8)* 578 to 666 labelled f_1(5), g_1(5), f_1(7), f_1(8)* 578 to 665 labelled f_1(5), g_1(5), f_1(8)* 578 to 675 labelled f_1(8)* 579 to 580 labelled down_1(6)* 579 to 569 labelled f_flat_1(4)* 579 to 576 labelled f_flat_1(5)* 579 to 563 labelled f_flat_1(3)* 579 to 571 labelled f_flat_1(4)* 579 to 567 labelled f_flat_1(4)* 579 to 585 labelled f_flat_1(6)* 579 to 578 labelled up_1(5)* 579 to 665 labelled up_1(6)* 579 to 675 labelled up_1(7)* 580 to 542 labelled f_1(6)* 580 to 557 labelled f_1(6)* 581 to 582 labelled down_1(4)* 581 to 602 labelled f_flat_1(5), g_flat_1(5)* 581 to 588 labelled f_flat_1(4)* 581 to 608 labelled f_flat_1(5)* 581 to 600 labelled f_flat_1(5), g_flat_1(5)* 582 to 560 labelled f_1(4)* 582 to 566 labelled f_1(4)* 582 to 574 labelled f_1(4)* 582 to 578 labelled g_1(4), f_1(4)* 582 to 666 labelled f_1(4), g_1(4)* 582 to 665 labelled f_1(4), g_1(4)* 582 to 675 labelled f_1(4)* 583 to 584 labelled down_1(4)* 583 to 600 labelled g_flat_1(5)* 583 to 602 labelled g_flat_1(5)* 584 to 566 labelled g_1(4)* 584 to 574 labelled g_1(4)* 585 to 586 labelled down_1(6)* 585 to 571 labelled f_flat_1(4)* 585 to 567 labelled f_flat_1(4)* 585 to 585 labelled f_flat_1(6)* 585 to 576 labelled f_flat_1(5)* 585 to 578 labelled up_1(5)* 585 to 665 labelled up_1(6)* 585 to 675 labelled up_1(7)* 586 to 587 labelled f_1(6)* 587 to 542 labelled f_1(6)* 587 to 557 labelled f_1(6)* 588 to 589 labelled down_1(4)* 589 to 590 labelled f_1(4)* 590 to 561 labelled f_1(4)* 600 to 601 labelled down_1(5)* 600 to 602 labelled f_flat_1(5)* 600 to 588 labelled f_flat_1(4)* 600 to 608 labelled f_flat_1(5)* 600 to 600 labelled f_flat_1(5)* 600 to 678 labelled f_flat_1(6)* 600 to 680 labelled f_flat_1(6)* 600 to 676 labelled f_flat_1(6)* 601 to 560 labelled f_1(5)* 601 to 566 labelled f_1(5)* 601 to 574 labelled f_1(5)* 601 to 578 labelled f_1(5)* 602 to 603 labelled down_1(5)* 602 to 600 labelled g_flat_1(5)* 602 to 602 labelled g_flat_1(5)* 602 to 676 labelled g_flat_1(6), f_flat_1(6)* 602 to 678 labelled g_flat_1(6), f_flat_1(6)* 602 to 680 labelled f_flat_1(6)* 603 to 566 labelled g_1(5)* 603 to 574 labelled g_1(5)* 603 to 578 labelled g_1(5)* 603 to 666 labelled f_1(5), g_1(5)* 603 to 665 labelled f_1(5), g_1(5)* 603 to 675 labelled g_1(5), f_1(5)* 608 to 609 labelled down_1(5)* 608 to 588 labelled f_flat_1(4)* 608 to 608 labelled f_flat_1(5)* 608 to 600 labelled f_flat_1(5)* 608 to 602 labelled f_flat_1(5)* 609 to 610 labelled f_1(5)* 610 to 560 labelled f_1(5)* 610 to 566 labelled f_1(5)* 610 to 574 labelled f_1(5)* 665 to 578 labelled f_1(6)* 665 to 666 labelled f_1(6)* 665 to 665 labelled f_1(6)* 665 to 675 labelled f_1(6)* 666 to 578 labelled g_1(6)* 666 to 666 labelled g_1(6)* 666 to 665 labelled g_1(6)* 666 to 675 labelled g_1(6), f_1(5)* 675 to 665 labelled g_1(7), f_1(7)* 675 to 675 labelled g_1(7), f_1(7)* 676 to 677 labelled down_1(6)* 676 to 602 labelled f_flat_1(5)* 676 to 678 labelled f_flat_1(6)* 676 to 608 labelled f_flat_1(5)* 676 to 600 labelled f_flat_1(5)* 676 to 680 labelled f_flat_1(6)* 676 to 676 labelled f_flat_1(6)* 676 to 700 labelled f_flat_1(7)* 677 to 574 labelled f_1(6)* 677 to 578 labelled f_1(6)* 677 to 666 labelled f_1(6)* 677 to 665 labelled f_1(6)* 677 to 675 labelled f_1(6)* 678 to 679 labelled down_1(6)* 678 to 602 labelled g_flat_1(5)* 678 to 600 labelled g_flat_1(5)* 678 to 676 labelled g_flat_1(6)* 678 to 678 labelled g_flat_1(6)* 678 to 700 labelled g_flat_1(7)* 679 to 574 labelled g_1(6)* 679 to 578 labelled g_1(6)* 679 to 666 labelled g_1(6)* 679 to 665 labelled g_1(6)* 679 to 675 labelled g_1(6)* 680 to 681 labelled down_1(6)* 680 to 608 labelled f_flat_1(5)* 680 to 600 labelled f_flat_1(5)* 680 to 680 labelled f_flat_1(6)* 680 to 676 labelled f_flat_1(6)* 680 to 700 labelled f_flat_1(7)* 681 to 682 labelled f_1(6)* 682 to 574 labelled f_1(6)* 682 to 578 labelled f_1(6)* 700 to 701 labelled down_1(7)* 700 to 676 labelled g_flat_1(6), f_flat_1(6)* 700 to 678 labelled g_flat_1(6), f_flat_1(6)* 700 to 714 labelled g_flat_1(8), f_flat_1(8)* 700 to 700 labelled g_flat_1(7), f_flat_1(7)* 700 to 608 labelled f_flat_1(5)* 700 to 600 labelled f_flat_1(5)* 700 to 680 labelled f_flat_1(6)* 701 to 578 labelled g_1(7), f_1(7)* 701 to 666 labelled g_1(7), f_1(7)* 701 to 665 labelled g_1(7), f_1(7)* 701 to 675 labelled g_1(7), f_1(7)* 714 to 715 labelled down_1(8)* 714 to 678 labelled f_flat_1(6)* 714 to 700 labelled f_flat_1(7), g_flat_1(7)* 714 to 714 labelled g_flat_1(8), f_flat_1(8)* 714 to 608 labelled f_flat_1(5)* 714 to 600 labelled f_flat_1(5)* 714 to 680 labelled f_flat_1(6)* 714 to 676 labelled f_flat_1(6)* 714 to 731 labelled f_flat_1(9)* 715 to 578 labelled f_1(8)* 715 to 666 labelled f_1(8)* 715 to 665 labelled g_1(8), f_1(8)* 715 to 675 labelled g_1(8), f_1(8)* 731 to 732 labelled down_1(9)* 731 to 680 labelled f_flat_1(6)* 731 to 676 labelled f_flat_1(6)* 731 to 714 labelled f_flat_1(8)* 731 to 731 labelled f_flat_1(9)* 731 to 700 labelled f_flat_1(7)* 732 to 733 labelled f_1(9)* 733 to 578 labelled f_1(9)* 733 to 666 labelled f_1(9)* 733 to 665 labelled f_1(9)* 733 to 675 labelled f_1(9) ---------------------------------------- (31) YES