10.85/3.55 YES 11.25/3.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.25/3.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.25/3.61 11.25/3.61 11.25/3.61 Termination w.r.t. Q of the given QTRS could be proven: 11.25/3.61 11.25/3.61 (0) QTRS 11.25/3.61 (1) QTRS Reverse [EQUIVALENT, 0 ms] 11.25/3.61 (2) QTRS 11.25/3.61 (3) QTRSRRRProof [EQUIVALENT, 122 ms] 11.25/3.61 (4) QTRS 11.25/3.61 (5) DependencyPairsProof [EQUIVALENT, 11 ms] 11.25/3.61 (6) QDP 11.25/3.61 (7) DependencyGraphProof [EQUIVALENT, 1 ms] 11.25/3.61 (8) TRUE 11.25/3.61 11.25/3.61 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (0) 11.25/3.61 Obligation: 11.25/3.61 Q restricted rewrite system: 11.25/3.61 The TRS R consists of the following rules: 11.25/3.61 11.25/3.61 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 11.25/3.61 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 11.25/3.61 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 11.25/3.61 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 11.25/3.61 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 11.25/3.61 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 11.25/3.61 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 11.25/3.61 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 11.25/3.61 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 11.25/3.61 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 11.25/3.61 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 11.25/3.61 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 11.25/3.61 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 11.25/3.61 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 11.25/3.61 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 11.25/3.61 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 11.25/3.61 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) 11.25/3.61 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 11.25/3.61 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 11.25/3.61 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 11.25/3.61 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 11.25/3.61 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 11.25/3.61 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 11.25/3.61 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 11.25/3.61 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 11.25/3.61 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 11.25/3.61 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 11.25/3.61 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 11.25/3.61 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 11.25/3.61 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 11.25/3.61 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 11.25/3.61 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 11.25/3.61 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 11.25/3.61 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 11.25/3.61 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 11.25/3.61 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 11.25/3.61 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 11.25/3.61 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 11.25/3.61 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 11.25/3.61 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 11.25/3.61 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 11.25/3.61 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 11.25/3.61 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 11.25/3.61 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 11.25/3.61 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 11.25/3.61 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 11.25/3.61 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 11.25/3.61 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 11.25/3.61 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 11.25/3.61 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 11.25/3.61 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 11.25/3.61 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 11.25/3.61 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 11.25/3.61 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 11.25/3.61 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 11.25/3.61 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 11.25/3.61 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 11.25/3.61 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 11.25/3.61 11.25/3.61 Q is empty. 11.25/3.61 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (1) QTRS Reverse (EQUIVALENT) 11.25/3.61 We applied the QTRS Reverse Processor [REVERSE]. 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (2) 11.25/3.61 Obligation: 11.25/3.61 Q restricted rewrite system: 11.25/3.61 The TRS R consists of the following rules: 11.25/3.61 11.25/3.61 0(1(0(x1))) -> 4(2(4(2(3(2(2(3(3(2(x1)))))))))) 11.25/3.61 0(4(0(0(0(x1))))) -> 4(3(0(2(2(1(4(4(4(3(x1)))))))))) 11.25/3.61 1(1(4(4(0(x1))))) -> 2(2(2(2(2(2(3(2(4(0(x1)))))))))) 11.25/3.61 2(1(4(5(0(x1))))) -> 1(2(3(2(4(3(3(1(2(3(x1)))))))))) 11.25/3.61 0(3(0(0(1(x1))))) -> 0(3(4(2(3(2(3(2(1(1(x1)))))))))) 11.25/3.61 5(4(0(0(0(0(x1)))))) -> 5(3(2(5(1(4(2(3(2(0(x1)))))))))) 11.25/3.61 4(0(2(0(0(0(x1)))))) -> 4(0(1(1(4(2(1(2(2(3(x1)))))))))) 11.25/3.61 0(3(5(4(0(0(x1)))))) -> 4(1(1(2(2(5(3(2(2(1(x1)))))))))) 11.25/3.61 1(1(3(5(1(0(x1)))))) -> 3(5(5(2(1(2(3(1(2(3(x1)))))))))) 11.25/3.61 1(1(0(0(2(0(x1)))))) -> 3(3(2(3(2(1(3(2(4(3(x1)))))))))) 11.25/3.61 2(0(0(0(5(0(x1)))))) -> 1(2(1(3(4(5(0(2(3(2(x1)))))))))) 11.25/3.61 4(0(3(0(4(1(x1)))))) -> 4(4(1(2(3(3(5(2(2(3(x1)))))))))) 11.25/3.61 5(3(1(0(0(3(x1)))))) -> 5(1(3(5(0(2(3(3(1(2(x1)))))))))) 11.25/3.61 2(1(0(4(1(3(x1)))))) -> 2(1(1(3(0(1(2(2(3(2(x1)))))))))) 11.25/3.61 1(3(1(0(0(4(x1)))))) -> 1(4(4(5(0(2(1(2(2(3(x1)))))))))) 11.25/3.61 1(4(2(0(5(4(x1)))))) -> 1(4(3(2(2(3(2(4(1(2(x1)))))))))) 11.25/3.61 5(1(0(3(4(5(x1)))))) -> 2(3(5(1(2(3(3(3(2(5(x1)))))))))) 11.25/3.61 5(0(3(2(1(0(0(x1))))))) -> 5(5(3(4(1(2(3(1(2(3(x1)))))))))) 11.25/3.61 3(1(5(1(5(0(0(x1))))))) -> 2(2(3(0(5(3(3(1(3(3(x1)))))))))) 11.25/3.61 1(2(5(2(5(0(0(x1))))))) -> 0(2(1(2(2(4(3(5(3(2(x1)))))))))) 11.25/3.61 2(0(2(4(5(0(0(x1))))))) -> 3(1(3(0(0(2(2(3(2(3(x1)))))))))) 11.25/3.61 0(2(5(5(0(1(0(x1))))))) -> 0(2(0(3(3(3(4(2(2(3(x1)))))))))) 11.25/3.61 2(0(0(3(0(2(0(x1))))))) -> 3(2(5(4(4(3(1(3(2(3(x1)))))))))) 11.25/3.61 3(4(0(5(2(2(0(x1))))))) -> 3(5(2(3(2(2(1(1(4(0(x1)))))))))) 11.25/3.61 4(5(1(0(4(2(0(x1))))))) -> 4(3(5(1(2(3(1(0(2(3(x1)))))))))) 11.25/3.61 0(0(0(0(0(3(0(x1))))))) -> 4(4(2(0(1(3(2(5(0(2(x1)))))))))) 11.25/3.61 3(4(0(0(0(4(0(x1))))))) -> 3(3(3(2(3(1(2(5(5(0(x1)))))))))) 11.25/3.61 4(0(5(5(5(4(0(x1))))))) -> 4(4(2(0(3(2(1(5(3(2(x1)))))))))) 11.25/3.61 0(0(5(1(1(5(0(x1))))))) -> 4(3(3(0(2(5(0(1(2(3(x1)))))))))) 11.25/3.61 0(1(4(2(2(5(0(x1))))))) -> 4(0(3(2(3(2(1(3(3(2(x1)))))))))) 11.25/3.61 1(3(4(1(3(5(0(x1))))))) -> 1(0(1(4(4(3(1(2(3(2(x1)))))))))) 11.25/3.61 0(0(0(1(3(0(1(x1))))))) -> 4(4(4(2(3(5(2(2(4(2(x1)))))))))) 11.25/3.61 2(0(4(4(2(1(1(x1))))))) -> 2(2(5(1(2(3(2(2(1(1(x1)))))))))) 11.25/3.61 1(5(0(4(4(2(1(x1))))))) -> 3(0(1(5(3(2(2(3(3(1(x1)))))))))) 11.25/3.61 5(3(3(0(0(3(1(x1))))))) -> 5(3(4(5(4(2(1(2(2(3(x1)))))))))) 11.25/3.61 3(4(0(3(1(4(1(x1))))))) -> 1(5(2(2(3(2(1(5(3(1(x1)))))))))) 11.25/3.61 0(0(0(0(4(4(1(x1))))))) -> 0(1(3(5(3(3(4(2(1(2(x1)))))))))) 11.25/3.61 3(3(5(0(0(5(1(x1))))))) -> 1(2(3(1(1(2(3(4(5(1(x1)))))))))) 11.25/3.61 2(0(4(0(0(0(4(x1))))))) -> 2(2(1(4(2(3(2(2(4(4(x1)))))))))) 11.25/3.61 4(1(4(0(0(0(4(x1))))))) -> 0(0(1(2(1(1(2(3(4(4(x1)))))))))) 11.25/3.61 2(0(0(4(0(0(4(x1))))))) -> 5(1(4(5(3(3(2(3(0(3(x1)))))))))) 11.25/3.61 4(2(5(4(0(0(4(x1))))))) -> 0(4(4(3(2(2(2(5(3(3(x1)))))))))) 11.25/3.61 1(5(2(0(3(0(4(x1))))))) -> 3(0(1(3(4(3(2(3(3(4(x1)))))))))) 11.25/3.61 2(1(1(0(4(0(4(x1))))))) -> 2(2(2(3(4(1(3(0(2(2(x1)))))))))) 11.25/3.61 0(0(4(1(4(0(4(x1))))))) -> 4(1(1(2(0(0(2(2(1(3(x1)))))))))) 11.25/3.61 4(1(4(5(0(1(4(x1))))))) -> 4(3(4(2(3(1(2(1(5(2(x1)))))))))) 11.25/3.61 0(0(4(5(2(1(4(x1))))))) -> 4(0(2(3(0(3(1(5(4(2(x1)))))))))) 11.25/3.61 0(1(3(0(4(1(4(x1))))))) -> 4(1(5(2(2(2(0(2(3(5(x1)))))))))) 11.25/3.61 2(0(5(5(0(3(4(x1))))))) -> 2(5(4(2(2(3(2(3(0(3(x1)))))))))) 11.25/3.61 0(1(4(5(5(3(4(x1))))))) -> 4(3(3(2(5(4(3(1(5(3(x1)))))))))) 11.25/3.61 0(4(1(0(0(0(5(x1))))))) -> 4(5(0(3(2(2(3(5(2(5(x1)))))))))) 11.25/3.61 5(1(5(1(2(0(5(x1))))))) -> 2(3(3(4(3(3(3(2(3(5(x1)))))))))) 11.25/3.61 0(4(4(5(2(0(5(x1))))))) -> 4(3(1(1(2(2(3(0(4(5(x1)))))))))) 11.25/3.61 2(5(1(0(5(0(5(x1))))))) -> 2(0(2(3(4(2(3(2(3(5(x1)))))))))) 11.25/3.61 5(4(5(5(5(0(5(x1))))))) -> 2(3(0(3(3(2(3(3(2(5(x1)))))))))) 11.25/3.61 1(3(4(1(0(3(5(x1))))))) -> 1(3(0(0(1(2(1(2(2(3(x1)))))))))) 11.25/3.61 1(0(1(0(5(3(5(x1))))))) -> 1(5(3(5(5(1(2(2(3(5(x1)))))))))) 11.25/3.61 3(0(1(4(0(4(5(x1))))))) -> 3(4(2(3(4(4(2(2(3(5(x1)))))))))) 11.25/3.61 11.25/3.61 Q is empty. 11.25/3.61 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (3) QTRSRRRProof (EQUIVALENT) 11.25/3.61 Used ordering: 11.25/3.61 Polynomial interpretation [POLO]: 11.25/3.61 11.25/3.61 POL(0(x_1)) = 5 + x_1 11.25/3.61 POL(1(x_1)) = x_1 11.25/3.61 POL(2(x_1)) = x_1 11.25/3.61 POL(3(x_1)) = x_1 11.25/3.61 POL(4(x_1)) = 2 + x_1 11.25/3.61 POL(5(x_1)) = 3 + x_1 11.25/3.61 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 11.25/3.61 11.25/3.61 0(1(0(x1))) -> 4(2(4(2(3(2(2(3(3(2(x1)))))))))) 11.25/3.61 0(4(0(0(0(x1))))) -> 4(3(0(2(2(1(4(4(4(3(x1)))))))))) 11.25/3.61 1(1(4(4(0(x1))))) -> 2(2(2(2(2(2(3(2(4(0(x1)))))))))) 11.25/3.61 2(1(4(5(0(x1))))) -> 1(2(3(2(4(3(3(1(2(3(x1)))))))))) 11.25/3.61 0(3(0(0(1(x1))))) -> 0(3(4(2(3(2(3(2(1(1(x1)))))))))) 11.25/3.61 5(4(0(0(0(0(x1)))))) -> 5(3(2(5(1(4(2(3(2(0(x1)))))))))) 11.25/3.61 4(0(2(0(0(0(x1)))))) -> 4(0(1(1(4(2(1(2(2(3(x1)))))))))) 11.25/3.61 0(3(5(4(0(0(x1)))))) -> 4(1(1(2(2(5(3(2(2(1(x1)))))))))) 11.25/3.61 1(1(3(5(1(0(x1)))))) -> 3(5(5(2(1(2(3(1(2(3(x1)))))))))) 11.25/3.61 1(1(0(0(2(0(x1)))))) -> 3(3(2(3(2(1(3(2(4(3(x1)))))))))) 11.25/3.61 2(0(0(0(5(0(x1)))))) -> 1(2(1(3(4(5(0(2(3(2(x1)))))))))) 11.25/3.61 4(0(3(0(4(1(x1)))))) -> 4(4(1(2(3(3(5(2(2(3(x1)))))))))) 11.25/3.61 5(3(1(0(0(3(x1)))))) -> 5(1(3(5(0(2(3(3(1(2(x1)))))))))) 11.25/3.61 2(1(0(4(1(3(x1)))))) -> 2(1(1(3(0(1(2(2(3(2(x1)))))))))) 11.25/3.61 1(4(2(0(5(4(x1)))))) -> 1(4(3(2(2(3(2(4(1(2(x1)))))))))) 11.25/3.61 5(1(0(3(4(5(x1)))))) -> 2(3(5(1(2(3(3(3(2(5(x1)))))))))) 11.25/3.61 5(0(3(2(1(0(0(x1))))))) -> 5(5(3(4(1(2(3(1(2(3(x1)))))))))) 11.25/3.61 3(1(5(1(5(0(0(x1))))))) -> 2(2(3(0(5(3(3(1(3(3(x1)))))))))) 11.25/3.61 1(2(5(2(5(0(0(x1))))))) -> 0(2(1(2(2(4(3(5(3(2(x1)))))))))) 11.25/3.61 2(0(2(4(5(0(0(x1))))))) -> 3(1(3(0(0(2(2(3(2(3(x1)))))))))) 11.25/3.61 0(2(5(5(0(1(0(x1))))))) -> 0(2(0(3(3(3(4(2(2(3(x1)))))))))) 11.25/3.61 2(0(0(3(0(2(0(x1))))))) -> 3(2(5(4(4(3(1(3(2(3(x1)))))))))) 11.25/3.61 3(4(0(5(2(2(0(x1))))))) -> 3(5(2(3(2(2(1(1(4(0(x1)))))))))) 11.25/3.61 4(5(1(0(4(2(0(x1))))))) -> 4(3(5(1(2(3(1(0(2(3(x1)))))))))) 11.25/3.61 0(0(0(0(0(3(0(x1))))))) -> 4(4(2(0(1(3(2(5(0(2(x1)))))))))) 11.25/3.61 3(4(0(0(0(4(0(x1))))))) -> 3(3(3(2(3(1(2(5(5(0(x1)))))))))) 11.25/3.61 4(0(5(5(5(4(0(x1))))))) -> 4(4(2(0(3(2(1(5(3(2(x1)))))))))) 11.25/3.61 0(0(5(1(1(5(0(x1))))))) -> 4(3(3(0(2(5(0(1(2(3(x1)))))))))) 11.25/3.61 0(1(4(2(2(5(0(x1))))))) -> 4(0(3(2(3(2(1(3(3(2(x1)))))))))) 11.25/3.61 1(3(4(1(3(5(0(x1))))))) -> 1(0(1(4(4(3(1(2(3(2(x1)))))))))) 11.25/3.61 0(0(0(1(3(0(1(x1))))))) -> 4(4(4(2(3(5(2(2(4(2(x1)))))))))) 11.25/3.61 2(0(4(4(2(1(1(x1))))))) -> 2(2(5(1(2(3(2(2(1(1(x1)))))))))) 11.25/3.61 1(5(0(4(4(2(1(x1))))))) -> 3(0(1(5(3(2(2(3(3(1(x1)))))))))) 11.25/3.61 5(3(3(0(0(3(1(x1))))))) -> 5(3(4(5(4(2(1(2(2(3(x1)))))))))) 11.25/3.61 3(4(0(3(1(4(1(x1))))))) -> 1(5(2(2(3(2(1(5(3(1(x1)))))))))) 11.25/3.61 0(0(0(0(4(4(1(x1))))))) -> 0(1(3(5(3(3(4(2(1(2(x1)))))))))) 11.25/3.61 3(3(5(0(0(5(1(x1))))))) -> 1(2(3(1(1(2(3(4(5(1(x1)))))))))) 11.25/3.61 2(0(4(0(0(0(4(x1))))))) -> 2(2(1(4(2(3(2(2(4(4(x1)))))))))) 11.25/3.61 4(1(4(0(0(0(4(x1))))))) -> 0(0(1(2(1(1(2(3(4(4(x1)))))))))) 11.25/3.61 2(0(0(4(0(0(4(x1))))))) -> 5(1(4(5(3(3(2(3(0(3(x1)))))))))) 11.25/3.61 4(2(5(4(0(0(4(x1))))))) -> 0(4(4(3(2(2(2(5(3(3(x1)))))))))) 11.25/3.61 1(5(2(0(3(0(4(x1))))))) -> 3(0(1(3(4(3(2(3(3(4(x1)))))))))) 11.25/3.61 2(1(1(0(4(0(4(x1))))))) -> 2(2(2(3(4(1(3(0(2(2(x1)))))))))) 11.25/3.61 0(0(4(1(4(0(4(x1))))))) -> 4(1(1(2(0(0(2(2(1(3(x1)))))))))) 11.25/3.61 4(1(4(5(0(1(4(x1))))))) -> 4(3(4(2(3(1(2(1(5(2(x1)))))))))) 11.25/3.61 0(1(3(0(4(1(4(x1))))))) -> 4(1(5(2(2(2(0(2(3(5(x1)))))))))) 11.25/3.61 2(0(5(5(0(3(4(x1))))))) -> 2(5(4(2(2(3(2(3(0(3(x1)))))))))) 11.25/3.61 0(1(4(5(5(3(4(x1))))))) -> 4(3(3(2(5(4(3(1(5(3(x1)))))))))) 11.25/3.61 0(4(1(0(0(0(5(x1))))))) -> 4(5(0(3(2(2(3(5(2(5(x1)))))))))) 11.25/3.61 5(1(5(1(2(0(5(x1))))))) -> 2(3(3(4(3(3(3(2(3(5(x1)))))))))) 11.25/3.61 0(4(4(5(2(0(5(x1))))))) -> 4(3(1(1(2(2(3(0(4(5(x1)))))))))) 11.25/3.61 2(5(1(0(5(0(5(x1))))))) -> 2(0(2(3(4(2(3(2(3(5(x1)))))))))) 11.25/3.61 5(4(5(5(5(0(5(x1))))))) -> 2(3(0(3(3(2(3(3(2(5(x1)))))))))) 11.25/3.61 1(0(1(0(5(3(5(x1))))))) -> 1(5(3(5(5(1(2(2(3(5(x1)))))))))) 11.25/3.61 3(0(1(4(0(4(5(x1))))))) -> 3(4(2(3(4(4(2(2(3(5(x1)))))))))) 11.25/3.61 11.25/3.61 11.25/3.61 11.25/3.61 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (4) 11.25/3.61 Obligation: 11.25/3.61 Q restricted rewrite system: 11.25/3.61 The TRS R consists of the following rules: 11.25/3.61 11.25/3.61 1(3(1(0(0(4(x1)))))) -> 1(4(4(5(0(2(1(2(2(3(x1)))))))))) 11.25/3.61 0(0(4(5(2(1(4(x1))))))) -> 4(0(2(3(0(3(1(5(4(2(x1)))))))))) 11.25/3.61 1(3(4(1(0(3(5(x1))))))) -> 1(3(0(0(1(2(1(2(2(3(x1)))))))))) 11.25/3.61 11.25/3.61 Q is empty. 11.25/3.61 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (5) DependencyPairsProof (EQUIVALENT) 11.25/3.61 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (6) 11.25/3.61 Obligation: 11.25/3.61 Q DP problem: 11.25/3.61 The TRS P consists of the following rules: 11.25/3.61 11.25/3.61 1^1(3(1(0(0(4(x1)))))) -> 1^1(4(4(5(0(2(1(2(2(3(x1)))))))))) 11.25/3.61 1^1(3(1(0(0(4(x1)))))) -> 0^1(2(1(2(2(3(x1)))))) 11.25/3.61 1^1(3(1(0(0(4(x1)))))) -> 1^1(2(2(3(x1)))) 11.25/3.61 0^1(0(4(5(2(1(4(x1))))))) -> 0^1(2(3(0(3(1(5(4(2(x1))))))))) 11.25/3.61 0^1(0(4(5(2(1(4(x1))))))) -> 0^1(3(1(5(4(2(x1)))))) 11.25/3.61 0^1(0(4(5(2(1(4(x1))))))) -> 1^1(5(4(2(x1)))) 11.25/3.61 1^1(3(4(1(0(3(5(x1))))))) -> 1^1(3(0(0(1(2(1(2(2(3(x1)))))))))) 11.25/3.61 1^1(3(4(1(0(3(5(x1))))))) -> 0^1(0(1(2(1(2(2(3(x1)))))))) 11.25/3.61 1^1(3(4(1(0(3(5(x1))))))) -> 0^1(1(2(1(2(2(3(x1))))))) 11.25/3.61 1^1(3(4(1(0(3(5(x1))))))) -> 1^1(2(1(2(2(3(x1)))))) 11.25/3.61 1^1(3(4(1(0(3(5(x1))))))) -> 1^1(2(2(3(x1)))) 11.25/3.61 11.25/3.61 The TRS R consists of the following rules: 11.25/3.61 11.25/3.61 1(3(1(0(0(4(x1)))))) -> 1(4(4(5(0(2(1(2(2(3(x1)))))))))) 11.25/3.61 0(0(4(5(2(1(4(x1))))))) -> 4(0(2(3(0(3(1(5(4(2(x1)))))))))) 11.25/3.61 1(3(4(1(0(3(5(x1))))))) -> 1(3(0(0(1(2(1(2(2(3(x1)))))))))) 11.25/3.61 11.25/3.61 Q is empty. 11.25/3.61 We have to consider all minimal (P,Q,R)-chains. 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (7) DependencyGraphProof (EQUIVALENT) 11.25/3.61 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 11 less nodes. 11.25/3.61 ---------------------------------------- 11.25/3.61 11.25/3.61 (8) 11.25/3.61 TRUE 11.25/3.68 EOF