3.73/1.55 YES 3.73/1.55 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.73/1.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.73/1.55 3.73/1.55 3.73/1.55 Outermost Termination of the given OTRS could be proven: 3.73/1.55 3.73/1.55 (0) OTRS 3.73/1.55 (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] 3.73/1.55 (2) QTRS 3.73/1.55 (3) QTRSRRRProof [EQUIVALENT, 36 ms] 3.73/1.55 (4) QTRS 3.73/1.55 (5) QTRSRRRProof [EQUIVALENT, 14 ms] 3.73/1.55 (6) QTRS 3.73/1.55 (7) AAECC Innermost [EQUIVALENT, 0 ms] 3.73/1.55 (8) QTRS 3.73/1.55 (9) DependencyPairsProof [EQUIVALENT, 0 ms] 3.73/1.55 (10) QDP 3.73/1.55 (11) DependencyGraphProof [EQUIVALENT, 0 ms] 3.73/1.55 (12) AND 3.73/1.55 (13) QDP 3.73/1.55 (14) UsableRulesProof [EQUIVALENT, 0 ms] 3.73/1.55 (15) QDP 3.73/1.55 (16) QReductionProof [EQUIVALENT, 0 ms] 3.73/1.55 (17) QDP 3.73/1.55 (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] 3.73/1.55 (19) YES 3.73/1.55 (20) QDP 3.73/1.55 (21) UsableRulesProof [EQUIVALENT, 0 ms] 3.73/1.55 (22) QDP 3.73/1.55 (23) QReductionProof [EQUIVALENT, 0 ms] 3.73/1.55 (24) QDP 3.73/1.55 (25) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] 3.73/1.55 (26) YES 3.73/1.55 3.73/1.55 3.73/1.55 ---------------------------------------- 3.73/1.55 3.73/1.55 (0) 3.73/1.55 Obligation: 3.73/1.55 Term rewrite system R: 3.73/1.55 The TRS R consists of the following rules: 3.73/1.55 3.73/1.55 f(x) -> g(f(x)) 3.73/1.55 g(g(f(x))) -> x 3.73/1.55 3.73/1.55 3.73/1.55 3.73/1.55 Outermost Strategy. 3.73/1.55 3.73/1.55 ---------------------------------------- 3.73/1.55 3.73/1.55 (1) Raffelsieper-Zantema-Transformation (SOUND) 3.73/1.55 We applied the Raffelsieper-Zantema transformation to transform the outermost TRS to a standard TRS. 3.73/1.55 ---------------------------------------- 3.73/1.55 3.73/1.55 (2) 3.73/1.55 Obligation: 3.73/1.55 Q restricted rewrite system: 3.73/1.55 The TRS R consists of the following rules: 3.73/1.55 3.73/1.55 down(f(x)) -> up(g(f(x))) 3.73/1.55 down(g(g(f(x)))) -> up(x) 3.73/1.55 top(up(x)) -> top(down(x)) 3.73/1.55 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.55 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.55 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.55 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.55 f_flat(up(x_1)) -> up(f(x_1)) 3.73/1.55 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.55 3.73/1.55 Q is empty. 3.73/1.55 3.73/1.55 ---------------------------------------- 3.73/1.55 3.73/1.55 (3) QTRSRRRProof (EQUIVALENT) 3.73/1.55 Used ordering: 3.73/1.55 Polynomial interpretation [POLO]: 3.73/1.55 3.73/1.55 POL(down(x_1)) = 2*x_1 3.73/1.55 POL(f(x_1)) = 2*x_1 3.73/1.55 POL(f_flat(x_1)) = 1 + 2*x_1 3.73/1.56 POL(fresh_constant) = 0 3.73/1.56 POL(g(x_1)) = x_1 3.73/1.56 POL(g_flat(x_1)) = x_1 3.73/1.56 POL(top(x_1)) = 2*x_1 3.73/1.56 POL(up(x_1)) = 2*x_1 3.73/1.56 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 3.73/1.56 3.73/1.56 f_flat(up(x_1)) -> up(f(x_1)) 3.73/1.56 3.73/1.56 3.73/1.56 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (4) 3.73/1.56 Obligation: 3.73/1.56 Q restricted rewrite system: 3.73/1.56 The TRS R consists of the following rules: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 down(g(g(f(x)))) -> up(x) 3.73/1.56 top(up(x)) -> top(down(x)) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 3.73/1.56 Q is empty. 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (5) QTRSRRRProof (EQUIVALENT) 3.73/1.56 Used ordering: 3.73/1.56 Polynomial interpretation [POLO]: 3.73/1.56 3.73/1.56 POL(down(x_1)) = 2*x_1 3.73/1.56 POL(f(x_1)) = 2 + x_1 3.73/1.56 POL(fresh_constant) = 0 3.73/1.56 POL(g(x_1)) = x_1 3.73/1.56 POL(g_flat(x_1)) = x_1 3.73/1.56 POL(top(x_1)) = x_1 3.73/1.56 POL(up(x_1)) = 2*x_1 3.73/1.56 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 3.73/1.56 3.73/1.56 down(g(g(f(x)))) -> up(x) 3.73/1.56 3.73/1.56 3.73/1.56 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (6) 3.73/1.56 Obligation: 3.73/1.56 Q restricted rewrite system: 3.73/1.56 The TRS R consists of the following rules: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 top(up(x)) -> top(down(x)) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 3.73/1.56 Q is empty. 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (7) AAECC Innermost (EQUIVALENT) 3.73/1.56 We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 3.73/1.56 The TRS R 2 is 3.73/1.56 top(up(x)) -> top(down(x)) 3.73/1.56 3.73/1.56 The signature Sigma is {top_1} 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (8) 3.73/1.56 Obligation: 3.73/1.56 Q restricted rewrite system: 3.73/1.56 The TRS R consists of the following rules: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 top(up(x)) -> top(down(x)) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 3.73/1.56 The set Q consists of the following terms: 3.73/1.56 3.73/1.56 down(f(x0)) 3.73/1.56 top(up(x0)) 3.73/1.56 down(g(f(x0))) 3.73/1.56 down(g(fresh_constant)) 3.73/1.56 down(g(g(g(x0)))) 3.73/1.56 down(g(g(fresh_constant))) 3.73/1.56 g_flat(up(x0)) 3.73/1.56 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (9) DependencyPairsProof (EQUIVALENT) 3.73/1.56 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (10) 3.73/1.56 Obligation: 3.73/1.56 Q DP problem: 3.73/1.56 The TRS P consists of the following rules: 3.73/1.56 3.73/1.56 TOP(up(x)) -> TOP(down(x)) 3.73/1.56 TOP(up(x)) -> DOWN(x) 3.73/1.56 DOWN(g(f(y3))) -> G_FLAT(down(f(y3))) 3.73/1.56 DOWN(g(f(y3))) -> DOWN(f(y3)) 3.73/1.56 DOWN(g(fresh_constant)) -> G_FLAT(down(fresh_constant)) 3.73/1.56 DOWN(g(fresh_constant)) -> DOWN(fresh_constant) 3.73/1.56 DOWN(g(g(g(y7)))) -> G_FLAT(down(g(g(y7)))) 3.73/1.56 DOWN(g(g(g(y7)))) -> DOWN(g(g(y7))) 3.73/1.56 DOWN(g(g(fresh_constant))) -> G_FLAT(down(g(fresh_constant))) 3.73/1.56 DOWN(g(g(fresh_constant))) -> DOWN(g(fresh_constant)) 3.73/1.56 3.73/1.56 The TRS R consists of the following rules: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 top(up(x)) -> top(down(x)) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 3.73/1.56 The set Q consists of the following terms: 3.73/1.56 3.73/1.56 down(f(x0)) 3.73/1.56 top(up(x0)) 3.73/1.56 down(g(f(x0))) 3.73/1.56 down(g(fresh_constant)) 3.73/1.56 down(g(g(g(x0)))) 3.73/1.56 down(g(g(fresh_constant))) 3.73/1.56 g_flat(up(x0)) 3.73/1.56 3.73/1.56 We have to consider all minimal (P,Q,R)-chains. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (11) DependencyGraphProof (EQUIVALENT) 3.73/1.56 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 8 less nodes. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (12) 3.73/1.56 Complex Obligation (AND) 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (13) 3.73/1.56 Obligation: 3.73/1.56 Q DP problem: 3.73/1.56 The TRS P consists of the following rules: 3.73/1.56 3.73/1.56 DOWN(g(g(g(y7)))) -> DOWN(g(g(y7))) 3.73/1.56 3.73/1.56 The TRS R consists of the following rules: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 top(up(x)) -> top(down(x)) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 3.73/1.56 The set Q consists of the following terms: 3.73/1.56 3.73/1.56 down(f(x0)) 3.73/1.56 top(up(x0)) 3.73/1.56 down(g(f(x0))) 3.73/1.56 down(g(fresh_constant)) 3.73/1.56 down(g(g(g(x0)))) 3.73/1.56 down(g(g(fresh_constant))) 3.73/1.56 g_flat(up(x0)) 3.73/1.56 3.73/1.56 We have to consider all minimal (P,Q,R)-chains. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (14) UsableRulesProof (EQUIVALENT) 3.73/1.56 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. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (15) 3.73/1.56 Obligation: 3.73/1.56 Q DP problem: 3.73/1.56 The TRS P consists of the following rules: 3.73/1.56 3.73/1.56 DOWN(g(g(g(y7)))) -> DOWN(g(g(y7))) 3.73/1.56 3.73/1.56 R is empty. 3.73/1.56 The set Q consists of the following terms: 3.73/1.56 3.73/1.56 down(f(x0)) 3.73/1.56 top(up(x0)) 3.73/1.56 down(g(f(x0))) 3.73/1.56 down(g(fresh_constant)) 3.73/1.56 down(g(g(g(x0)))) 3.73/1.56 down(g(g(fresh_constant))) 3.73/1.56 g_flat(up(x0)) 3.73/1.56 3.73/1.56 We have to consider all minimal (P,Q,R)-chains. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (16) QReductionProof (EQUIVALENT) 3.73/1.56 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 3.73/1.56 3.73/1.56 down(f(x0)) 3.73/1.56 top(up(x0)) 3.73/1.56 down(g(f(x0))) 3.73/1.56 down(g(fresh_constant)) 3.73/1.56 down(g(g(g(x0)))) 3.73/1.56 down(g(g(fresh_constant))) 3.73/1.56 g_flat(up(x0)) 3.73/1.56 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (17) 3.73/1.56 Obligation: 3.73/1.56 Q DP problem: 3.73/1.56 The TRS P consists of the following rules: 3.73/1.56 3.73/1.56 DOWN(g(g(g(y7)))) -> DOWN(g(g(y7))) 3.73/1.56 3.73/1.56 R is empty. 3.73/1.56 Q is empty. 3.73/1.56 We have to consider all minimal (P,Q,R)-chains. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (18) QDPSizeChangeProof (EQUIVALENT) 3.73/1.56 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. 3.73/1.56 3.73/1.56 From the DPs we obtained the following set of size-change graphs: 3.73/1.56 *DOWN(g(g(g(y7)))) -> DOWN(g(g(y7))) 3.73/1.56 The graph contains the following edges 1 > 1 3.73/1.56 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (19) 3.73/1.56 YES 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (20) 3.73/1.56 Obligation: 3.73/1.56 Q DP problem: 3.73/1.56 The TRS P consists of the following rules: 3.73/1.56 3.73/1.56 TOP(up(x)) -> TOP(down(x)) 3.73/1.56 3.73/1.56 The TRS R consists of the following rules: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 top(up(x)) -> top(down(x)) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 3.73/1.56 The set Q consists of the following terms: 3.73/1.56 3.73/1.56 down(f(x0)) 3.73/1.56 top(up(x0)) 3.73/1.56 down(g(f(x0))) 3.73/1.56 down(g(fresh_constant)) 3.73/1.56 down(g(g(g(x0)))) 3.73/1.56 down(g(g(fresh_constant))) 3.73/1.56 g_flat(up(x0)) 3.73/1.56 3.73/1.56 We have to consider all minimal (P,Q,R)-chains. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (21) UsableRulesProof (EQUIVALENT) 3.73/1.56 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. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (22) 3.73/1.56 Obligation: 3.73/1.56 Q DP problem: 3.73/1.56 The TRS P consists of the following rules: 3.73/1.56 3.73/1.56 TOP(up(x)) -> TOP(down(x)) 3.73/1.56 3.73/1.56 The TRS R consists of the following rules: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 3.73/1.56 The set Q consists of the following terms: 3.73/1.56 3.73/1.56 down(f(x0)) 3.73/1.56 top(up(x0)) 3.73/1.56 down(g(f(x0))) 3.73/1.56 down(g(fresh_constant)) 3.73/1.56 down(g(g(g(x0)))) 3.73/1.56 down(g(g(fresh_constant))) 3.73/1.56 g_flat(up(x0)) 3.73/1.56 3.73/1.56 We have to consider all minimal (P,Q,R)-chains. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (23) QReductionProof (EQUIVALENT) 3.73/1.56 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 3.73/1.56 3.73/1.56 top(up(x0)) 3.73/1.56 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (24) 3.73/1.56 Obligation: 3.73/1.56 Q DP problem: 3.73/1.56 The TRS P consists of the following rules: 3.73/1.56 3.73/1.56 TOP(up(x)) -> TOP(down(x)) 3.73/1.56 3.73/1.56 The TRS R consists of the following rules: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 3.73/1.56 The set Q consists of the following terms: 3.73/1.56 3.73/1.56 down(f(x0)) 3.73/1.56 down(g(f(x0))) 3.73/1.56 down(g(fresh_constant)) 3.73/1.56 down(g(g(g(x0)))) 3.73/1.56 down(g(g(fresh_constant))) 3.73/1.56 g_flat(up(x0)) 3.73/1.56 3.73/1.56 We have to consider all minimal (P,Q,R)-chains. 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (25) RFCMatchBoundsDPProof (EQUIVALENT) 3.73/1.56 Finiteness of the DP problem can be shown by a matchbound of 3. 3.73/1.56 As the DP problem is minimal we only have to initialize the certificate graph by the rules of P: 3.73/1.56 3.73/1.56 TOP(up(x)) -> TOP(down(x)) 3.73/1.56 3.73/1.56 To find matches we regarded all rules of R and P: 3.73/1.56 3.73/1.56 down(f(x)) -> up(g(f(x))) 3.73/1.56 down(g(f(y3))) -> g_flat(down(f(y3))) 3.73/1.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 3.73/1.56 down(g(g(g(y7)))) -> g_flat(down(g(g(y7)))) 3.73/1.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 3.73/1.56 g_flat(up(x_1)) -> up(g(x_1)) 3.73/1.56 TOP(up(x)) -> TOP(down(x)) 3.73/1.56 3.73/1.56 The certificate found is represented by the following graph. 3.73/1.56 The certificate consists of the following enumerated nodes: 3.73/1.56 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283 3.73/1.56 3.73/1.56 Node 262 is start node and node 263 is final node. 3.73/1.56 3.73/1.56 Those nodes are connected through the following edges: 3.73/1.56 3.73/1.56 * 262 to 264 labelled TOP_1(0)* 262 to 272 labelled TOP_1(1)* 262 to 283 labelled TOP_1(2)* 263 to 263 labelled #_1(0)* 264 to 263 labelled down_1(0)* 264 to 265 labelled up_1(1)* 264 to 267 labelled g_flat_1(1)* 264 to 269 labelled g_flat_1(1)* 264 to 277 labelled up_1(2)* 265 to 266 labelled g_1(1)* 266 to 263 labelled f_1(1)* 267 to 268 labelled down_1(1)* 267 to 273 labelled up_1(2)* 268 to 263 labelled f_1(1), fresh_constant(1)* 269 to 270 labelled down_1(1)* 269 to 275 labelled g_flat_1(2)* 269 to 269 labelled g_flat_1(1)* 270 to 271 labelled g_1(1)* 271 to 263 labelled g_1(1), fresh_constant(1)* 272 to 265 labelled down_1(1)* 272 to 278 labelled g_flat_1(2)* 272 to 277 labelled down_1(1)* 272 to 282 labelled up_1(3)* 273 to 274 labelled g_1(2)* 274 to 263 labelled f_1(2)* 275 to 276 labelled down_1(2)* 276 to 263 labelled fresh_constant(2)* 277 to 273 labelled g_1(2)* 278 to 279 labelled down_1(2)* 278 to 280 labelled up_1(3)* 279 to 263 labelled f_1(2)* 280 to 281 labelled g_1(3)* 281 to 263 labelled f_1(3)* 282 to 280 labelled g_1(3)* 283 to 282 labelled down_1(2) 3.73/1.56 3.73/1.56 3.73/1.56 ---------------------------------------- 3.73/1.56 3.73/1.56 (26) 3.73/1.56 YES 3.73/1.61 EOF