35.46/9.87 YES 35.67/9.92 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 35.67/9.92 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 35.67/9.92 35.67/9.92 35.67/9.92 Termination w.r.t. Q of the given QTRS could be proven: 35.67/9.92 35.67/9.92 (0) QTRS 35.67/9.92 (1) QTRS Reverse [EQUIVALENT, 0 ms] 35.67/9.92 (2) QTRS 35.67/9.92 (3) QTRSRRRProof [EQUIVALENT, 753 ms] 35.67/9.92 (4) QTRS 35.67/9.92 (5) DependencyPairsProof [EQUIVALENT, 72 ms] 35.67/9.92 (6) QDP 35.67/9.92 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 35.67/9.92 (8) QDP 35.67/9.92 (9) UsableRulesProof [EQUIVALENT, 0 ms] 35.67/9.92 (10) QDP 35.67/9.92 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 35.67/9.92 (12) YES 35.67/9.92 35.67/9.92 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (0) 35.67/9.92 Obligation: 35.67/9.92 Q restricted rewrite system: 35.67/9.92 The TRS R consists of the following rules: 35.67/9.92 35.67/9.92 0(0(1(0(2(1(3(4(0(4(5(5(3(4(5(1(x1)))))))))))))))) -> 0(0(1(5(1(4(4(4(4(1(4(5(0(2(1(2(x1)))))))))))))))) 35.67/9.92 0(0(1(0(2(1(3(4(0(4(5(5(3(4(5(1(x1)))))))))))))))) -> 0(2(5(3(4(2(5(4(0(1(4(2(2(3(4(0(x1)))))))))))))))) 35.67/9.92 0(0(1(0(2(1(3(4(0(4(5(5(3(4(5(1(x1)))))))))))))))) -> 0(4(5(2(0(5(0(2(3(2(2(0(5(5(4(2(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 0(0(1(5(1(4(4(4(4(1(4(5(0(2(1(2(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 0(1(2(5(5(1(3(4(5(4(4(5(1(5(0(3(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 0(2(5(3(4(2(5(4(0(1(4(2(2(3(4(0(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 0(4(5(2(0(5(0(2(3(2(2(0(5(5(4(2(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 0(4(5(4(3(5(0(5(3(2(5(3(0(0(5(2(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 0(5(3(1(3(1(3(5(3(2(5(5(4(2(5(3(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 0(5(3(4(2(1(4(3(5(5(2(0(5(4(2(3(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 4(5(2(5(4(1(4(2(1(1(3(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) -> 5(2(2(5(4(0(2(2(5(0(0(2(3(2(0(0(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(0(1(5(1(4(4(4(4(1(4(5(0(2(1(2(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(1(2(5(3(1(4(3(4(3(5(0(1(1(5(4(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(1(2(5(5(1(3(4(5(4(4(5(1(5(0(3(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(2(5(3(4(2(5(4(0(1(4(2(2(3(4(0(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(4(5(2(0(5(0(2(3(2(2(0(5(5(4(2(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(4(5(4(3(5(0(5(3(2(5(3(0(0(5(2(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(5(0(2(0(2(4(4(4(1(2(4(0(3(3(3(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(5(3(1(3(1(3(5(3(2(5(5(4(2(5(3(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 0(5(3(4(2(1(4(3(5(5(2(0(5(4(2(3(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 1(2(2(2(5(3(0(2(1(4(3(5(4(4(2(4(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 2(0(0(0(4(4(5(5(1(0(3(2(1(5(5(5(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 2(1(4(3(2(5(1(4(4(0(4(1(0(2(0(2(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 5(3(1(0(3(1(2(4(0(2(5(0(2(5(4(3(x1)))))))))))))))) 35.67/9.92 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) -> 5(5(2(1(2(2(1(0(2(3(4(0(4(0(2(4(x1)))))))))))))))) 35.67/9.92 0(3(0(4(4(4(2(3(2(4(5(0(3(0(1(1(x1)))))))))))))))) -> 0(0(1(5(1(4(4(4(4(1(4(5(0(2(1(2(x1)))))))))))))))) 35.67/9.92 0(3(0(4(4(4(2(3(2(4(5(0(3(0(1(1(x1)))))))))))))))) -> 0(2(5(3(4(2(5(4(0(1(4(2(2(3(4(0(x1)))))))))))))))) 35.67/9.92 0(3(0(4(4(4(2(3(2(4(5(0(3(0(1(1(x1)))))))))))))))) -> 0(4(5(2(0(5(0(2(3(2(2(0(5(5(4(2(x1)))))))))))))))) 35.67/9.92 0(3(0(4(4(4(2(3(2(4(5(0(3(0(1(1(x1)))))))))))))))) -> 5(2(2(5(4(0(2(2(5(0(0(2(3(2(0(0(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(0(1(0(2(1(3(4(0(4(5(5(3(4(5(1(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(0(1(5(1(4(4(4(4(1(4(5(0(2(1(2(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(1(2(5(3(1(4(3(4(3(5(0(1(1(5(4(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(1(2(5(5(1(3(4(5(4(4(5(1(5(0(3(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(2(5(3(4(2(5(4(0(1(4(2(2(3(4(0(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(3(0(4(4(4(2(3(2(4(5(0(3(0(1(1(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(4(5(2(0(5(0(2(3(2(2(0(5(5(4(2(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(4(5(4(3(5(0(5(3(2(5(3(0(0(5(2(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(5(3(1(3(1(3(5(3(2(5(5(4(2(5(3(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(5(3(4(2(1(4(3(5(5(2(0(5(4(2(3(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 0(5(3(5(1(2(1(1(3(3(0(5(4(1(1(5(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 1(2(2(2(5(3(0(2(1(4(3(5(4(4(2(4(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 2(0(0(0(4(4(5(5(1(0(3(2(1(5(5(5(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 2(1(4(3(2(5(1(4(4(0(4(1(0(2(0(2(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 4(4(2(5(1(0(5(4(1(0(0(2(4(0(5(0(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 4(4(4(5(0(0(3(5(5(4(1(1(4(5(5(2(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 4(5(2(5(4(1(4(2(1(1(3(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 5(2(2(5(4(0(2(2(5(0(0(2(3(2(0(0(x1)))))))))))))))) 35.67/9.92 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) -> 5(5(2(1(2(2(1(0(2(3(4(0(4(0(2(4(x1)))))))))))))))) 35.67/9.92 0(5(0(2(0(2(4(4(4(1(2(4(0(3(3(3(x1)))))))))))))))) -> 0(1(2(5(5(1(3(4(5(4(4(5(1(5(0(3(x1)))))))))))))))) 35.67/9.92 0(5(0(2(0(2(4(4(4(1(2(4(0(3(3(3(x1)))))))))))))))) -> 0(5(3(1(3(1(3(5(3(2(5(5(4(2(5(3(x1)))))))))))))))) 35.67/9.92 0(5(0(2(0(2(4(4(4(1(2(4(0(3(3(3(x1)))))))))))))))) -> 0(5(3(4(2(1(4(3(5(5(2(0(5(4(2(3(x1)))))))))))))))) 35.67/9.92 1(0(2(3(5(3(2(4(2(4(3(3(2(5(2(2(x1)))))))))))))))) -> 0(0(1(5(1(4(4(4(4(1(4(5(0(2(1(2(x1)))))))))))))))) 35.67/9.92 1(0(2(3(5(3(2(4(2(4(3(3(2(5(2(2(x1)))))))))))))))) -> 0(4(5(2(0(5(0(2(3(2(2(0(5(5(4(2(x1)))))))))))))))) 35.67/9.92 1(0(2(3(5(3(2(4(2(4(3(3(2(5(2(2(x1)))))))))))))))) -> 0(4(5(4(3(5(0(5(3(2(5(3(0(0(5(2(x1)))))))))))))))) 35.67/9.92 1(0(2(3(5(3(2(4(2(4(3(3(2(5(2(2(x1)))))))))))))))) -> 4(4(4(5(0(0(3(5(5(4(1(1(4(5(5(2(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(0(1(0(2(1(3(4(0(4(5(5(3(4(5(1(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(0(1(5(1(4(4(4(4(1(4(5(0(2(1(2(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(1(2(5(3(1(4(3(4(3(5(0(1(1(5(4(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(1(2(5(5(1(3(4(5(4(4(5(1(5(0(3(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(1(5(3(2(5(2(2(4(0(3(0(2(3(2(0(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(2(3(0(0(1(3(1(4(4(3(5(1(5(1(3(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(2(5(3(4(2(5(4(0(1(4(2(2(3(4(0(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(3(0(4(4(4(2(3(2(4(5(0(3(0(1(1(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(3(1(0(4(1(0(2(4(5(3(4(2(3(4(1(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(4(5(2(0(5(0(2(3(2(2(0(5(5(4(2(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(4(5(4(3(5(0(5(3(2(5(3(0(0(5(2(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(5(0(2(0(2(4(4(4(1(2(4(0(3(3(3(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(5(3(1(3(1(3(5(3(2(5(5(4(2(5(3(x1)))))))))))))))) 35.67/9.92 1(3(1(0(3(3(0(0(1(3(5(2(3(1(0(3(x1)))))))))))))))) -> 0(5(3(4(2(1(4(3(5(5(2(0(5(4(2(3(x1)))))))))))))))) 35.67/9.92 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4(4(5(4(0(1(2(1(0(4(3(0(2(1(0(4(x1)))))))))))))))) 35.67/9.92 4(0(2(2(2(1(1(0(5(4(3(3(5(0(1(1(x1)))))))))))))))) -> 4(5(2(5(4(1(4(2(1(1(3(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 4(2(4(5(3(5(0(1(5(2(4(2(3(0(5(0(x1)))))))))))))))) -> 4(4(2(5(1(0(5(4(1(0(0(2(4(0(5(0(x1)))))))))))))))) 35.67/9.92 4(2(4(5(3(5(0(1(5(2(4(2(3(0(5(0(x1)))))))))))))))) -> 4(5(2(5(4(1(4(2(1(1(3(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 4(3(0(2(1(1(0(2(1(0(5(5(0(4(0(0(x1)))))))))))))))) -> 4(0(4(3(5(5(3(3(2(4(2(3(3(5(0(4(x1)))))))))))))))) 35.67/9.92 4(3(0(2(1(1(0(2(1(0(5(5(0(4(0(0(x1)))))))))))))))) -> 4(2(4(5(3(5(0(1(5(2(4(2(3(0(5(0(x1)))))))))))))))) 35.67/9.92 4(3(0(2(1(1(0(2(1(0(5(5(0(4(0(0(x1)))))))))))))))) -> 4(4(2(5(1(0(5(4(1(0(0(2(4(0(5(0(x1)))))))))))))))) 35.67/9.92 4(3(0(2(1(1(0(2(1(0(5(5(0(4(0(0(x1)))))))))))))))) -> 4(4(4(5(0(0(3(5(5(4(1(1(4(5(5(2(x1)))))))))))))))) 35.67/9.92 4(3(0(2(1(1(0(2(1(0(5(5(0(4(0(0(x1)))))))))))))))) -> 4(5(2(5(4(1(4(2(1(1(3(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 5(4(3(5(1(0(3(5(1(2(0(3(1(1(3(5(x1)))))))))))))))) -> 0(0(1(5(1(4(4(4(4(1(4(5(0(2(1(2(x1)))))))))))))))) 35.67/9.92 5(4(3(5(1(0(3(5(1(2(0(3(1(1(3(5(x1)))))))))))))))) -> 0(2(5(3(4(2(5(4(0(1(4(2(2(3(4(0(x1)))))))))))))))) 35.67/9.92 5(4(3(5(1(0(3(5(1(2(0(3(1(1(3(5(x1)))))))))))))))) -> 0(4(5(2(0(5(0(2(3(2(2(0(5(5(4(2(x1)))))))))))))))) 35.67/9.92 5(4(3(5(1(0(3(5(1(2(0(3(1(1(3(5(x1)))))))))))))))) -> 0(5(3(4(2(1(4(3(5(5(2(0(5(4(2(3(x1)))))))))))))))) 35.67/9.92 5(4(3(5(1(0(3(5(1(2(0(3(1(1(3(5(x1)))))))))))))))) -> 1(2(2(2(5(3(0(2(1(4(3(5(4(4(2(4(x1)))))))))))))))) 35.67/9.92 5(4(3(5(1(0(3(5(1(2(0(3(1(1(3(5(x1)))))))))))))))) -> 2(0(0(0(4(4(5(5(1(0(3(2(1(5(5(5(x1)))))))))))))))) 35.67/9.92 5(4(3(5(1(0(3(5(1(2(0(3(1(1(3(5(x1)))))))))))))))) -> 5(2(2(5(4(0(2(2(5(0(0(2(3(2(0(0(x1)))))))))))))))) 35.67/9.92 5(5(2(1(2(2(1(0(2(3(4(0(4(0(2(4(x1)))))))))))))))) -> 1(2(2(2(5(3(0(2(1(4(3(5(4(4(2(4(x1)))))))))))))))) 35.67/9.92 35.67/9.92 Q is empty. 35.67/9.92 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (1) QTRS Reverse (EQUIVALENT) 35.67/9.92 We applied the QTRS Reverse Processor [REVERSE]. 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (2) 35.67/9.92 Obligation: 35.67/9.92 Q restricted rewrite system: 35.67/9.92 The TRS R consists of the following rules: 35.67/9.92 35.67/9.92 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 3(0(5(1(5(4(4(5(4(3(1(5(5(2(1(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 3(2(4(5(0(2(5(5(3(4(1(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 4(5(1(1(0(5(3(4(3(4(1(3(5(2(1(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 3(0(5(1(5(4(4(5(4(3(1(5(5(2(1(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 3(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 3(2(4(5(0(2(5(5(3(4(1(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 5(5(5(1(2(3(0(1(5(5(4(4(0(0(0(2(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 2(0(2(0(1(4(0(4(4(1(5(2(3(4(1(2(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 3(4(5(2(0(5(2(0(4(2(1(3(0(1(3(5(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 4(2(0(4(0(4(3(2(0(1(2(2(1(2(5(5(x1)))))))))))))))) 35.67/9.92 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 4(5(1(1(0(5(3(4(3(4(1(3(5(2(1(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3(0(5(1(5(4(4(5(4(3(1(5(5(2(1(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 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2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 2(2(5(2(3(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 5(5(5(1(2(3(0(1(5(5(4(4(0(0(0(2(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 2(0(2(0(1(4(0(4(4(1(5(2(3(4(1(2(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 5(2(0(2(1(2(5(1(1(3(1(4(0(0(5(2(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 2(4(3(4(5(1(0(5(2(2(2(1(4(1(3(2(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 2(4(3(4(5(1(0(5(2(2(2(1(4(1(3(2(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 5(5(5(1(2(3(0(1(5(5(4(4(0(0(0(2(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 4(0(5(3(3(2(4(2(3(3(5(5(3(4(0(4(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 4(0(1(2(0(3(4(0(1(2(1(0(4(5(4(4(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 5(2(0(2(1(2(5(1(1(3(1(4(0(0(5(2(x1)))))))))))))))) -> 5(5(5(1(2(3(0(1(5(5(4(4(0(0(0(2(x1)))))))))))))))) 35.67/9.92 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) -> 3(2(4(5(0(2(5(5(3(4(1(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3(0(5(1(5(4(4(5(4(3(1(5(5(2(1(0(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3(2(4(5(0(2(5(5(3(4(1(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 4(3(4(4(4(3(0(2(5(5(1(0(1(3(5(3(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 4(0(5(3(3(2(4(2(3(3(5(5(3(4(0(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 4(0(1(2(0(3(4(0(1(2(1(0(4(5(4(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3(4(5(2(0(5(2(0(4(2(1(3(0(1(3(5(x1)))))))))))))))) 35.67/9.92 0(4(3(2(3(2(0(2(2(3(3(0(2(0(0(4(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 0(4(3(2(3(2(0(2(2(3(3(0(2(0(0(4(x1)))))))))))))))) -> 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) 35.67/9.92 0(4(3(2(3(2(0(2(2(3(3(0(2(0(0(4(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 0(4(3(2(3(2(0(2(2(3(3(0(2(0(0(4(x1)))))))))))))))) -> 4(0(1(2(0(3(4(0(1(2(1(0(4(5(4(4(x1)))))))))))))))) 35.67/9.92 0(4(3(2(3(2(0(2(2(3(3(0(2(0(0(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 4(0(5(3(3(2(4(2(3(3(5(5(3(4(0(4(x1)))))))))))))))) 35.67/9.92 1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) 35.67/9.92 1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 4(0(1(2(0(3(4(0(1(2(1(0(4(5(4(4(x1)))))))))))))))) 35.67/9.92 1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 4(0(5(3(3(2(4(2(3(3(5(5(3(4(0(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 3(2(4(5(0(2(5(5(3(4(1(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 5(5(5(1(2(3(0(1(5(5(4(4(0(0(0(2(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 4(2(0(4(0(4(3(2(0(1(2(2(1(2(5(5(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 35.67/9.92 Q is empty. 35.67/9.92 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (3) QTRSRRRProof (EQUIVALENT) 35.67/9.92 Used ordering: 35.67/9.92 Polynomial interpretation [POLO]: 35.67/9.92 35.67/9.92 POL(0(x_1)) = 2 + x_1 35.67/9.92 POL(1(x_1)) = 2 + x_1 35.67/9.92 POL(2(x_1)) = 2 + x_1 35.67/9.92 POL(3(x_1)) = 3 + x_1 35.67/9.92 POL(4(x_1)) = x_1 35.67/9.92 POL(5(x_1)) = x_1 35.67/9.92 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 35.67/9.92 35.67/9.92 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 3(0(5(1(5(4(4(5(4(3(1(5(5(2(1(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 3(2(4(5(0(2(5(5(3(4(1(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 0(2(3(2(0(3(0(4(2(2(5(2(3(5(1(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 4(5(1(1(0(5(3(4(3(4(1(3(5(2(1(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 3(0(5(1(5(4(4(5(4(3(1(5(5(2(1(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 3(1(5(1(5(3(4(4(1(3(1(0(0(3(2(0(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 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3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3(4(5(2(0(5(2(0(4(2(1(3(0(1(3(5(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 4(2(0(4(0(4(3(2(0(1(2(2(1(2(5(5(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 2(2(5(2(3(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))))))) 35.67/9.92 2(2(2(3(5(2(1(3(0(0(2(0(1(0(0(2(x1)))))))))))))))) -> 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1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 2(5(0(0(3(5(2(3(5(0(5(3(4(5(4(0(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 5(5(5(1(2(3(0(1(5(5(4(4(0(0(0(2(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 4(0(5(3(3(2(4(2(3(3(5(5(3(4(0(4(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 4(0(1(2(0(3(4(0(1(2(1(0(4(5(4(4(x1)))))))))))))))) 35.67/9.92 1(2(0(3(0(2(3(2(2(1(1(4(2(1(4(2(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 5(2(0(2(1(2(5(1(1(3(1(4(0(0(5(2(x1)))))))))))))))) -> 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3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 4(3(4(4(4(3(0(2(5(5(1(0(1(3(5(3(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 4(0(5(3(3(2(4(2(3(3(5(5(3(4(0(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 4(0(1(2(0(3(4(0(1(2(1(0(4(5(4(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 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1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 4(0(1(2(0(3(4(0(1(2(1(0(4(5(4(4(x1)))))))))))))))) 35.67/9.92 1(1(0(5(3(3(4(5(0(1(1(2(2(2(0(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 4(0(5(3(3(2(4(2(3(3(5(5(3(4(0(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 0(5(0(4(2(0(0(1(4(5(0(1(5(2(4(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 2(5(5(4(1(1(4(5(5(3(0(0(5(4(4(4(x1)))))))))))))))) 35.67/9.92 0(0(4(0(5(5(0(1(2(0(1(1(2(0(3(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 2(1(2(0(5(4(1(4(4(4(4(1(5(1(0(0(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 2(4(5(5(0(2(2(3(2(0(5(0(2(5(4(0(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 3(2(4(5(0(2(5(5(3(4(1(2(4(3(5(0(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 5(5(5(1(2(3(0(1(5(5(4(4(0(0(0(2(x1)))))))))))))))) 35.67/9.92 5(3(1(1(3(0(2(1(5(3(0(1(5(3(4(5(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 4(2(0(4(0(4(3(2(0(1(2(2(1(2(5(5(x1)))))))))))))))) -> 4(2(4(4(5(3(4(1(2(0(3(5(2(2(2(1(x1)))))))))))))))) 35.67/9.92 35.67/9.92 35.67/9.92 35.67/9.92 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (4) 35.67/9.92 Obligation: 35.67/9.92 Q restricted rewrite system: 35.67/9.92 The TRS R consists of the following rules: 35.67/9.92 35.67/9.92 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 5(1(1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 3(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 2(2(5(2(3(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 35.67/9.92 Q is empty. 35.67/9.92 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (5) DependencyPairsProof (EQUIVALENT) 35.67/9.92 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (6) 35.67/9.92 Obligation: 35.67/9.92 Q DP problem: 35.67/9.92 The TRS P consists of the following rules: 35.67/9.92 35.67/9.92 1^1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 0^1(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 1^1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 3^1(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))) 35.67/9.92 1^1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 1^1(0(4(5(2(4(3(5(2(0(x1)))))))))) 35.67/9.92 1^1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 0^1(4(5(2(4(3(5(2(0(x1))))))))) 35.67/9.92 1^1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 3^1(5(2(0(x1)))) 35.67/9.92 1^1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0^1(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 1^1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0^1(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))))) 35.67/9.92 1^1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 3^1(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))) 35.67/9.92 1^1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0^1(0(5(2(2(0(4(5(2(2(5(x1))))))))))) 35.67/9.92 1^1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0^1(5(2(2(0(4(5(2(2(5(x1)))))))))) 35.67/9.92 1^1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0^1(4(5(2(2(5(x1)))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1))))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(0(5(4(2(3(2(4(4(4(0(3(0(x1))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(2(4(4(4(0(3(0(x1)))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(3(0(x1))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(5(3(1(3(1(3(5(0(x1))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(1(3(1(3(5(0(x1))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(3(1(3(5(0(x1)))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(1(3(5(0(x1))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(3(5(0(x1)))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(5(0(x1))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1))))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1)))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(3(3(1(1(2(1(5(3(5(0(x1))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(3(1(1(2(1(5(3(5(0(x1)))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(1(1(2(1(5(3(5(0(x1))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(1(2(1(5(3(5(0(x1)))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(2(1(5(3(5(0(x1))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1^1(5(3(5(0(x1))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3^1(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(0(5(2(2(0(4(5(2(2(5(x1))))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(5(2(2(0(4(5(2(2(5(x1)))))))))) 35.67/9.92 1^1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0^1(4(5(2(2(5(x1)))))) 35.67/9.92 3^1(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 3^1(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 3^1(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 3^1(5(3(1(3(1(3(5(0(x1))))))))) 35.67/9.92 3^1(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 3^1(1(3(1(3(5(0(x1))))))) 35.67/9.92 3^1(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 1^1(3(1(3(5(0(x1)))))) 35.67/9.92 3^1(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 3^1(1(3(5(0(x1))))) 35.67/9.92 3^1(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 1^1(3(5(0(x1)))) 35.67/9.92 3^1(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 3^1(5(0(x1))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(4(2(4(2(3(5(3(2(0(1(x1))))))))))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(5(3(2(0(1(x1)))))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(2(0(1(x1)))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 0^1(1(x1)) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 1^1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1))))))))))))))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(4(1(1(3(1(2(3(x1)))))))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 1^1(1(3(1(2(3(x1)))))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 1^1(3(1(2(3(x1))))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(1(2(3(x1)))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 1^1(2(3(x1))) 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(x1) 35.67/9.92 3^1(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3^1(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 3^1(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 1^1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1))))))))))))))) 35.67/9.92 3^1(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3^1(4(1(1(3(1(2(3(x1)))))))) 35.67/9.92 3^1(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 1^1(1(3(1(2(3(x1)))))) 35.67/9.92 3^1(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 1^1(3(1(2(3(x1))))) 35.67/9.92 3^1(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3^1(1(2(3(x1)))) 35.67/9.92 3^1(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 1^1(2(3(x1))) 35.67/9.92 0^1(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 0^1(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 0^1(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 3^1(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))) 35.67/9.92 0^1(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 3^1(1(1(2(4(1(4(5(2(5(4(x1))))))))))) 35.67/9.92 0^1(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 1^1(1(2(4(1(4(5(2(5(4(x1)))))))))) 35.67/9.92 0^1(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 1^1(2(4(1(4(5(2(5(4(x1))))))))) 35.67/9.92 0^1(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 1^1(4(5(2(5(4(x1)))))) 35.67/9.92 35.67/9.92 The TRS R consists of the following rules: 35.67/9.92 35.67/9.92 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 5(1(1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 3(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 2(2(5(2(3(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 35.67/9.92 Q is empty. 35.67/9.92 We have to consider all minimal (P,Q,R)-chains. 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (7) DependencyGraphProof (EQUIVALENT) 35.67/9.92 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 71 less nodes. 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (8) 35.67/9.92 Obligation: 35.67/9.92 Q DP problem: 35.67/9.92 The TRS P consists of the following rules: 35.67/9.92 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(x1) 35.67/9.92 35.67/9.92 The TRS R consists of the following rules: 35.67/9.92 35.67/9.92 1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) -> 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) 35.67/9.92 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 5(1(1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1)))))))))))))))) 35.67/9.92 1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) -> 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) 35.67/9.92 3(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) -> 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 2(2(5(2(3(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))))))) 35.67/9.92 3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) -> 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) 35.67/9.92 0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) -> 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) 35.67/9.92 35.67/9.92 Q is empty. 35.67/9.92 We have to consider all minimal (P,Q,R)-chains. 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (9) UsableRulesProof (EQUIVALENT) 35.67/9.92 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (10) 35.67/9.92 Obligation: 35.67/9.92 Q DP problem: 35.67/9.92 The TRS P consists of the following rules: 35.67/9.92 35.67/9.92 3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(x1) 35.67/9.92 35.67/9.92 R is empty. 35.67/9.92 Q is empty. 35.67/9.92 We have to consider all minimal (P,Q,R)-chains. 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (11) QDPSizeChangeProof (EQUIVALENT) 35.67/9.92 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. 35.67/9.92 35.67/9.92 From the DPs we obtained the following set of size-change graphs: 35.67/9.92 *3^1(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) -> 3^1(x1) 35.67/9.92 The graph contains the following edges 1 > 1 35.67/9.92 35.67/9.92 35.67/9.92 ---------------------------------------- 35.67/9.92 35.67/9.92 (12) 35.67/9.92 YES 35.91/10.01 EOF