60.88/16.54 YES 68.76/18.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 68.76/18.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 68.76/18.52 68.76/18.52 68.76/18.52 Termination w.r.t. Q of the given QTRS could be proven: 68.76/18.52 68.76/18.52 (0) QTRS 68.76/18.52 (1) QTRSRRRProof [EQUIVALENT, 597 ms] 68.76/18.52 (2) QTRS 68.76/18.52 (3) DependencyPairsProof [EQUIVALENT, 920 ms] 68.76/18.52 (4) QDP 68.76/18.52 (5) DependencyGraphProof [EQUIVALENT, 2 ms] 68.76/18.52 (6) QDP 68.76/18.52 (7) QDPOrderProof [EQUIVALENT, 638 ms] 68.76/18.52 (8) QDP 68.76/18.52 (9) PisEmptyProof [EQUIVALENT, 0 ms] 68.76/18.52 (10) YES 68.76/18.52 68.76/18.52 68.76/18.52 ---------------------------------------- 68.76/18.52 68.76/18.52 (0) 68.76/18.52 Obligation: 68.76/18.52 Q restricted rewrite system: 68.76/18.52 The TRS R consists of the following rules: 68.76/18.52 68.76/18.52 0(1(2(1(x1)))) -> 0(2(2(2(1(x1))))) 68.76/18.52 0(2(1(1(2(0(2(x1))))))) -> 2(2(2(0(2(1(2(2(x1)))))))) 68.76/18.52 2(0(0(0(0(1(0(x1))))))) -> 1(2(2(2(1(2(1(0(1(x1))))))))) 68.76/18.52 0(0(0(1(1(0(0(1(0(1(1(0(0(x1))))))))))))) -> 2(2(1(2(0(2(2(1(1(1(2(2(1(0(x1)))))))))))))) 68.76/18.52 0(1(1(0(0(1(1(2(1(2(0(0(2(x1))))))))))))) -> 1(2(2(2(1(2(1(0(2(2(0(0(1(2(2(2(2(x1))))))))))))))))) 68.76/18.52 1(0(0(0(1(0(1(1(0(1(1(0(1(2(0(1(x1)))))))))))))))) -> 2(2(1(1(2(1(2(0(0(1(2(0(0(1(1(0(0(0(x1)))))))))))))))))) 68.76/18.52 1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0(0(2(1(2(0(2(0(0(2(0(1(2(0(2(2(x1)))))))))))))))) 68.76/18.52 1(1(0(1(1(2(0(0(0(0(0(0(1(2(0(0(x1)))))))))))))))) -> 2(0(1(1(0(0(2(0(0(2(2(2(0(2(1(2(2(x1))))))))))))))))) 68.76/18.52 2(0(0(2(2(2(0(1(2(1(2(0(1(1(0(0(x1)))))))))))))))) -> 2(2(2(2(2(2(2(1(2(0(0(2(1(0(1(0(1(2(1(2(x1)))))))))))))))))))) 68.76/18.52 1(1(1(1(1(1(2(1(0(1(2(1(0(2(2(0(1(x1))))))))))))))))) -> 1(1(2(2(0(2(2(2(2(1(0(1(2(0(2(1(0(0(0(x1))))))))))))))))))) 68.76/18.52 0(2(0(0(2(1(0(0(0(0(1(0(2(1(1(1(0(1(x1)))))))))))))))))) -> 0(1(2(2(1(0(0(2(2(1(1(1(1(2(1(1(2(1(0(x1))))))))))))))))))) 68.76/18.52 1(1(2(1(2(1(1(1(1(1(1(2(2(1(0(1(2(1(x1)))))))))))))))))) -> 2(0(2(2(2(2(2(1(1(1(2(0(1(0(2(1(2(2(1(2(2(2(1(2(2(2(x1)))))))))))))))))))))))))) 68.76/18.52 0(0(1(0(2(0(1(0(1(1(2(0(0(1(0(0(0(1(1(x1))))))))))))))))))) -> 0(2(2(2(0(2(0(1(2(1(1(0(1(2(2(0(1(0(0(2(2(2(2(x1))))))))))))))))))))))) 68.76/18.52 0(2(0(2(1(0(2(2(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) -> 2(2(0(0(1(2(1(2(1(2(2(2(2(1(0(2(1(1(2(0(x1)))))))))))))))))))) 68.76/18.52 1(0(0(2(2(0(2(0(2(0(0(2(1(1(0(0(0(1(2(x1))))))))))))))))))) -> 2(2(1(0(2(1(0(2(1(2(1(2(1(0(2(2(2(1(2(2(1(2(x1)))))))))))))))))))))) 68.76/18.52 0(1(0(0(1(2(2(0(1(0(1(1(1(2(1(1(1(1(0(2(0(x1))))))))))))))))))))) -> 1(0(1(1(1(1(2(2(1(1(2(1(0(0(0(2(2(0(2(0(0(2(x1)))))))))))))))))))))) 68.76/18.52 1(1(0(1(0(1(1(2(1(0(0(0(1(0(2(0(1(0(0(1(0(1(x1)))))))))))))))))))))) -> 0(1(1(1(1(1(0(0(2(1(0(0(2(1(2(0(2(2(1(2(2(1(1(x1))))))))))))))))))))))) 68.76/18.52 0(2(0(2(2(1(0(1(2(1(0(0(1(0(2(0(0(0(0(0(2(2(0(x1))))))))))))))))))))))) -> 2(1(1(2(2(1(2(2(2(1(0(0(2(2(0(1(0(1(2(0(0(2(1(1(x1)))))))))))))))))))))))) 68.76/18.52 1(0(0(1(2(1(2(0(0(0(2(1(0(2(0(2(0(0(0(0(0(1(1(2(2(x1))))))))))))))))))))))))) -> 1(1(1(1(2(0(1(2(2(2(1(2(1(0(1(2(2(0(2(2(2(0(0(1(0(2(x1)))))))))))))))))))))))))) 68.76/18.52 2(1(2(2(1(2(2(2(0(0(2(1(1(1(0(1(1(2(0(1(1(2(0(2(2(x1))))))))))))))))))))))))) -> 2(2(2(2(0(0(1(2(1(2(0(0(2(1(2(0(2(2(1(2(0(0(2(2(0(1(x1)))))))))))))))))))))))))) 68.76/18.52 1(0(0(2(1(1(1(1(1(2(2(1(1(1(0(2(1(0(1(2(1(2(0(0(1(2(x1)))))))))))))))))))))))))) -> 2(1(2(2(1(2(1(0(2(2(2(1(0(2(2(1(0(1(0(2(2(2(2(1(2(1(2(1(1(0(2(x1))))))))))))))))))))))))))))))) 68.76/18.52 0(1(2(1(2(2(0(0(0(1(2(1(0(2(0(0(0(1(2(2(2(0(0(0(1(2(1(x1))))))))))))))))))))))))))) -> 2(2(1(2(2(2(1(2(2(2(2(1(2(2(0(2(1(1(1(0(1(0(2(2(1(1(0(1(x1)))))))))))))))))))))))))))) 68.76/18.52 1(2(2(0(2(0(1(2(1(2(2(0(2(1(1(1(1(2(0(1(0(0(1(2(0(1(2(x1))))))))))))))))))))))))))) -> 1(2(0(0(2(2(0(2(2(0(0(2(0(0(1(2(0(0(2(2(2(0(1(2(1(0(1(2(x1)))))))))))))))))))))))))))) 68.76/18.52 0(2(0(2(0(1(0(0(1(0(2(0(0(0(0(1(0(0(2(2(2(1(1(2(0(2(1(2(2(2(x1)))))))))))))))))))))))))))))) -> 2(2(1(2(0(1(1(1(2(2(1(2(2(2(0(1(2(2(2(1(2(1(1(1(0(0(1(2(2(0(0(x1))))))))))))))))))))))))))))))) 68.76/18.52 1(0(2(0(2(0(2(0(0(1(1(1(2(0(1(0(0(0(1(2(0(1(1(2(0(0(2(1(0(0(x1)))))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(1(2(0(1(1(0(0(2(2(2(2(1(2(0(1(1(1(1(1(2(2(2(2(1(1(x1)))))))))))))))))))))))))))))))) 68.76/18.52 1(0(2(2(0(2(1(1(0(2(0(1(2(0(2(1(0(1(0(2(1(0(0(1(0(0(2(0(2(2(x1)))))))))))))))))))))))))))))) -> 1(1(0(1(2(2(1(1(1(2(1(2(2(0(0(2(2(1(1(2(0(1(2(1(2(0(2(0(2(0(0(2(x1)))))))))))))))))))))))))))))))) 68.76/18.52 1(2(0(2(0(0(1(2(2(1(1(0(1(2(0(1(0(1(0(0(2(0(1(0(1(0(1(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(2(0(0(2(1(2(2(2(0(1(2(2(2(1(1(0(1(1(0(1(1(0(2(x1)))))))))))))))))))))))))))))))) 68.76/18.52 2(2(2(1(2(0(0(1(1(1(2(0(0(2(0(1(1(0(2(1(0(2(0(2(1(1(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 2(2(2(1(2(1(2(2(2(1(0(0(2(2(1(0(2(2(0(0(2(0(0(0(2(1(1(2(1(1(1(2(2(2(x1)))))))))))))))))))))))))))))))))) 68.76/18.52 0(1(1(0(0(2(2(1(0(1(1(1(2(2(1(2(0(0(1(1(0(0(2(0(2(2(0(1(1(1(1(x1))))))))))))))))))))))))))))))) -> 0(2(2(0(1(0(1(1(2(1(2(0(0(0(0(0(1(0(1(0(1(2(2(2(2(0(0(0(1(2(1(2(x1)))))))))))))))))))))))))))))))) 68.76/18.52 0(1(1(1(2(1(1(0(1(2(2(2(0(1(2(1(0(0(1(2(2(1(1(2(0(1(1(1(2(1(1(x1))))))))))))))))))))))))))))))) -> 2(2(1(1(2(1(2(1(2(2(1(0(0(2(1(2(2(2(0(0(0(2(2(0(2(1(1(1(0(2(2(2(x1)))))))))))))))))))))))))))))))) 68.76/18.52 1(2(1(1(1(1(2(1(0(1(0(2(2(0(0(1(0(1(0(1(2(1(1(1(1(0(2(2(2(2(1(x1))))))))))))))))))))))))))))))) -> 2(0(1(2(2(2(1(2(0(0(2(2(1(1(2(2(2(0(1(2(1(2(1(2(2(1(2(1(1(2(0(1(0(x1))))))))))))))))))))))))))))))))) 68.76/18.52 2(0(1(0(1(2(1(2(2(2(0(1(0(0(0(1(2(0(1(1(1(1(2(2(0(0(0(1(0(0(0(x1))))))))))))))))))))))))))))))) -> 2(2(0(2(2(0(2(1(1(2(1(2(2(1(0(0(1(0(2(0(2(2(2(1(0(2(2(0(1(0(2(2(1(2(x1)))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 2(2(0(1(0(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))) 68.76/18.52 1(0(0(2(2(1(0(2(1(2(0(2(0(2(0(2(0(1(1(2(2(1(0(0(0(1(0(1(2(1(2(0(x1)))))))))))))))))))))))))))))))) -> 2(2(0(1(0(1(1(1(2(2(1(2(1(0(2(2(2(2(1(2(1(1(2(0(2(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))))))))))) 68.76/18.52 1(2(1(1(1(0(1(2(1(0(1(2(1(1(2(2(0(2(2(1(1(1(1(0(1(2(0(1(1(1(1(1(x1)))))))))))))))))))))))))))))))) -> 2(0(1(2(0(2(0(2(1(0(0(0(0(2(2(2(2(2(1(1(0(2(2(2(0(2(2(2(0(1(0(2(2(1(1(x1))))))))))))))))))))))))))))))))))) 68.76/18.52 0(1(0(0(1(2(1(2(0(1(1(1(0(1(0(0(2(1(2(0(2(1(1(0(1(0(0(1(1(0(1(0(1(x1))))))))))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(2(2(2(0(1(0(2(0(2(2(2(1(0(1(0(0(2(2(2(0(1(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(0(0(2(1(1(0(0(0(2(2(1(0(2(1(0(1(0(0(1(1(2(0(1(1(2(2(0(1(1(1(0(x1))))))))))))))))))))))))))))))))) -> 0(1(2(1(2(2(1(0(2(1(1(2(2(1(2(1(1(0(2(1(0(0(0(2(2(1(2(2(2(2(1(0(0(2(x1)))))))))))))))))))))))))))))))))) 68.76/18.52 1(2(2(2(0(1(0(0(1(2(1(0(1(1(0(1(1(1(2(1(1(1(2(1(0(0(0(1(0(0(0(1(2(x1))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(1(0(1(0(2(2(0(0(2(2(2(0(0(0(2(0(0(1(1(2(2(1(2(2(2(1(0(1(0(1(0(2(0(x1)))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(0(2(0(2(0(0(0(1(1(0(1(0(1(0(1(1(2(1(0(2(0(0(2(2(1(0(0(2(0(2(0(2(x1)))))))))))))))))))))))))))))))))) -> 0(2(1(0(0(0(2(2(2(1(2(2(2(2(2(1(0(0(2(2(2(0(0(0(0(1(1(0(1(1(2(1(2(2(2(x1))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(2(1(0(2(0(0(0(2(0(0(2(0(1(0(0(0(0(2(1(0(0(0(0(1(2(2(0(1(1(2(0(1(x1)))))))))))))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(0(2(1(2(2(2(1(1(2(2(1(2(0(1(0(1(1(2(2(1(1(1(0(2(1(2(2(0(0(2(x1)))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(0(1(1(1(1(1(2(2(1(0(2(0(0(1(0(0(0(0(2(1(1(1(1(0(0(0(0(2(1(0(1(1(2(1(x1))))))))))))))))))))))))))))))))))) -> 0(2(0(1(1(2(1(1(1(2(2(0(2(0(2(2(1(2(1(1(2(0(1(2(1(1(2(1(2(1(1(0(1(0(2(1(x1)))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(2(0(0(0(1(1(0(1(0(2(2(1(2(1(0(2(2(2(0(2(1(1(2(0(0(0(2(0(1(2(0(0(1(x1))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(2(0(0(2(0(1(1(2(2(1(1(2(0(1(2(1(0(2(1(2(0(2(2(1(0(0(2(0(0(0(x1)))))))))))))))))))))))))))))))))))) 68.76/18.52 0(0(0(0(0(0(2(1(0(1(0(1(0(1(0(1(2(0(0(1(1(0(2(1(0(2(0(0(0(0(2(2(1(2(2(0(x1)))))))))))))))))))))))))))))))))))) -> 1(2(0(0(0(0(1(1(1(2(0(1(2(1(2(2(2(2(1(2(0(1(1(2(1(1(0(1(2(0(1(0(0(0(2(0(0(1(x1)))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(0(1(2(2(1(1(2(0(0(1(0(2(2(0(0(2(0(1(0(1(0(1(2(2(1(0(2(1(1(0(1(0(0(0(1(x1)))))))))))))))))))))))))))))))))))) -> 1(1(2(2(1(2(0(2(2(2(1(2(1(2(0(0(1(2(2(0(0(1(0(1(2(0(0(1(0(1(1(0(1(1(1(1(1(0(x1)))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(1(1(0(2(0(0(2(1(1(2(0(2(0(1(0(2(0(2(2(2(1(0(0(0(1(1(0(0(2(2(0(0(0(0(2(x1)))))))))))))))))))))))))))))))))))) -> 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2(2(1(0(1(2(0(1(2(1(2(2(2(2(2(1(0(2(1(2(0(2(1(1(2(1(1(1(0(0(0(2(0(2(0(2(2(1(x1)))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(0(2(0(2(1(1(1(2(2(2(1(1(2(1(0(2(0(2(0(2(1(2(1(1(1(2(0(2(1(1(2(2(0(1(0(x1))))))))))))))))))))))))))))))))))))) -> 1(2(2(2(1(2(2(0(1(2(2(1(1(2(1(0(0(2(2(0(2(0(1(2(1(2(2(0(1(2(2(2(1(1(0(0(2(0(x1)))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(1(0(1(0(0(1(0(0(0(1(1(2(2(1(0(0(1(1(1(0(1(0(1(2(1(2(1(0(1(2(1(0(2(0(0(1(x1))))))))))))))))))))))))))))))))))))) -> 1(1(2(2(0(0(2(0(2(1(2(0(2(0(1(2(2(2(1(1(1(0(0(1(0(0(1(1(1(1(1(1(2(1(0(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(1(0(0(1(1(1(1(0(1(1(0(1(2(0(0(2(2(0(2(1(2(1(2(2(2(0(0(1(0(2(1(2(1(0(2(1(2(x1)))))))))))))))))))))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(1(2(1(2(1(0(2(0(2(2(2(2(2(2(1(0(0(0(2(2(2(0(2(0(0(2(2(1(0(1(1(0(x1))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(0(0(0(2(1(2(1(1(0(0(1(1(1(2(2(0(0(0(1(0(1(0(1(0(2(1(0(0(1(0(1(1(1(2(2(1(0(x1))))))))))))))))))))))))))))))))))))))) -> 2(0(0(0(2(2(1(1(2(1(1(2(2(1(2(1(0(1(1(0(0(1(2(0(0(0(0(0(0(0(0(1(0(1(0(1(1(2(2(1(2(x1))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(0(2(0(2(1(2(1(1(0(1(1(2(1(2(2(0(1(0(0(2(2(0(1(1(0(1(1(1(2(2(0(1(0(0(1(2(0(2(x1))))))))))))))))))))))))))))))))))))))) -> 2(0(1(0(0(2(2(0(0(2(2(2(2(0(2(0(0(2(1(1(1(0(1(2(0(2(2(1(2(0(0(2(1(1(1(2(0(1(2(1(2(2(x1)))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(1(1(0(2(1(0(2(1(2(0(0(1(0(2(0(0(2(0(2(1(0(1(0(1(2(2(0(1(0(0(1(2(2(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))) -> 0(2(2(2(2(2(2(1(1(2(2(1(1(2(0(1(1(2(1(2(2(1(2(0(1(1(2(0(1(1(2(1(1(0(1(2(0(1(1(2(2(x1))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(1(0(1(0(0(2(0(2(0(1(0(2(1(0(1(0(1(2(0(0(0(1(0(2(2(0(2(0(0(0(1(1(1(1(1(0(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))) -> 1(1(0(0(1(2(2(0(0(2(1(1(2(2(0(0(1(1(1(0(2(2(2(0(1(0(2(2(0(2(0(2(1(2(1(1(2(1(0(1(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(0(2(0(1(2(0(0(1(1(0(0(2(1(0(1(0(1(2(1(2(2(0(1(1(2(0(1(2(1(0(1(1(0(1(0(1(0(1(2(x1))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(0(2(1(0(2(0(0(0(0(0(1(0(2(2(0(0(2(2(2(2(2(0(2(0(0(0(1(0(0(1(0(1(0(2(2(2(2(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(0(2(2(1(0(2(2(2(1(0(0(0(2(0(0(2(2(0(1(2(1(2(2(1(1(0(0(1(2(0(0(2(2(2(0(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))) -> 1(1(1(2(2(2(2(2(2(1(1(2(0(2(0(1(0(2(1(0(0(0(1(2(2(2(1(2(2(2(0(2(2(0(1(1(2(2(2(2(2(1(2(2(x1)))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(2(1(2(0(0(0(0(0(1(2(2(0(1(0(0(2(1(1(0(1(2(1(0(0(1(0(1(0(2(0(0(1(0(2(2(2(1(1(0(2(x1))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(1(1(2(1(1(0(2(0(0(0(1(2(2(2(0(2(0(0(2(0(1(0(0(2(1(1(1(1(2(2(2(0(0(2(0(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(0(1(2(1(1(1(2(1(2(1(2(0(0(0(0(1(2(2(1(1(1(0(2(1(1(0(0(0(0(1(0(0(0(1(1(0(2(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(1(2(1(1(2(2(1(0(1(2(0(2(1(0(0(2(1(0(2(2(2(2(1(0(2(2(0(1(2(1(0(2(2(2(1(1(0(2(2(1(0(x1)))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(1(2(1(1(0(0(0(0(1(0(1(2(2(0(1(0(2(1(1(2(1(1(2(2(1(0(1(1(1(1(1(1(0(2(2(2(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(1(2(2(2(2(2(0(0(1(0(0(1(1(2(1(2(2(0(0(2(0(1(1(2(2(1(0(0(1(1(2(2(1(0(2(2(2(1(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(1(2(1(0(0(2(0(0(2(1(1(1(2(2(1(0(2(0(2(1(2(2(0(2(0(1(0(1(2(1(1(0(0(0(1(0(0(1(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(1(2(0(2(1(0(2(2(1(2(1(1(0(1(1(0(1(2(2(2(0(1(0(1(2(2(2(2(0(1(1(2(2(0(1(1(2(1(2(0(2(1(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(2(0(0(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(0(2(1(0(0(2(1(2(2(0(1(2(0(0(0(2(0(0(0(0(0(0(0(1(0(0(2(0(2(0(0(2(2(0(2(1(1(1(1(2(1(0(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(2(1(1(2(0(2(2(2(1(1(2(2(0(1(2(0(0(0(0(0(1(0(1(1(0(2(0(0(0(0(2(2(1(2(2(2(0(2(0(2(0(1(2(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(1(2(2(1(1(1(1(0(1(1(0(2(0(1(0(2(2(0(2(0(0(1(1(2(0(0(0(0(2(1(2(2(1(1(2(2(0(1(1(2(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(2(2(1(1(0(2(2(0(0(2(1(0(0(1(1(0(0(2(1(2(1(1(1(2(1(0(1(2(2(2(2(2(1(1(1(2(2(0(2(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(0(1(2(1(1(0(2(2(0(1(2(2(0(0(2(1(0(1(0(0(1(2(1(0(2(1(1(0(0(0(1(0(0(0(2(1(1(0(1(2(2(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(2(1(0(0(0(2(2(0(1(1(0(1(2(2(1(0(2(1(2(2(2(1(1(1(1(2(2(2(1(1(1(1(1(0(0(0(0(0(1(0(2(2(0(0(0(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(0(2(0(0(1(0(1(1(1(1(1(2(1(0(1(0(0(1(2(0(2(0(0(0(1(0(0(2(1(2(0(1(1(0(0(0(1(0(2(1(2(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(0(1(0(1(0(1(1(2(0(2(2(2(0(2(0(2(0(1(1(2(0(1(1(2(2(0(1(1(0(1(0(0(2(2(2(1(0(2(0(1(0(0(2(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(1(0(0(2(1(0(2(2(0(2(0(0(1(1(0(1(2(2(1(0(1(1(2(0(0(2(2(1(1(2(0(0(0(1(1(0(0(0(0(0(1(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(2(1(0(2(0(1(1(1(1(2(0(1(2(0(2(0(0(2(2(2(1(2(1(2(2(1(2(0(0(2(0(1(1(1(2(0(1(1(1(1(0(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(0(2(0(2(0(2(0(2(0(2(0(0(2(2(2(1(1(1(0(0(1(1(1(1(1(1(2(1(2(1(2(0(1(0(1(1(1(1(2(0(1(2(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(2(0(2(0(2(1(2(2(1(2(0(2(1(2(1(1(2(2(2(2(1(0(1(1(1(0(1(0(0(1(0(2(0(2(1(2(2(0(2(1(2(1(2(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(0(2(2(0(2(0(1(2(1(2(0(0(0(1(0(1(1(2(1(1(2(0(0(0(0(1(1(1(1(2(1(0(2(0(1(1(0(1(0(1(0(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(0(1(2(0(2(0(1(2(0(1(2(2(2(2(1(1(1(2(2(2(0(2(1(2(2(0(0(1(0(0(0(0(2(0(1(2(1(1(2(1(2(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(0(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(0(2(2(2(1(1(0(1(0(0(0(2(1(1(1(1(1(1(0(2(0(0(0(0(2(2(0(1(1(0(1(1(1(0(1(2(1(1(0(0(1(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(2(2(2(2(1(0(2(0(0(0(1(1(2(2(2(1(2(1(0(0(0(0(0(2(2(0(0(0(0(0(0(1(2(2(2(0(2(1(0(1(1(0(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(0(2(2(2(1(2(2(2(2(2(2(2(0(0(1(0(0(2(2(2(1(1(0(0(2(2(0(0(1(0(2(2(0(2(1(2(2(0(1(0(1(2(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(0(0(1(2(2(2(1(2(0(1(2(2(1(1(2(0(0(1(0(2(2(1(1(2(0(1(0(1(0(2(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(1(0(2(0(0(0(2(0(2(2(1(1(2(2(1(1(2(1(0(1(1(0(0(2(0(0(1(0(2(1(1(0(0(2(2(1(1(1(1(0(2(2(0(1(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(2(0(1(0(1(0(0(0(0(0(1(2(1(1(1(2(1(2(0(2(1(0(1(0(2(1(1(2(0(1(1(0(1(0(2(1(2(0(0(2(2(2(2(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 68.76/18.52 Q is empty. 68.76/18.52 68.76/18.52 ---------------------------------------- 68.76/18.52 68.76/18.52 (1) QTRSRRRProof (EQUIVALENT) 68.76/18.52 Used ordering: 68.76/18.52 Polynomial interpretation [POLO]: 68.76/18.52 68.76/18.52 POL(0(x_1)) = 6 + x_1 68.76/18.52 POL(1(x_1)) = 5 + x_1 68.76/18.52 POL(2(x_1)) = x_1 68.76/18.52 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 68.76/18.52 68.76/18.52 0(1(2(1(x1)))) -> 0(2(2(2(1(x1))))) 68.76/18.52 0(2(1(1(2(0(2(x1))))))) -> 2(2(2(0(2(1(2(2(x1)))))))) 68.76/18.52 2(0(0(0(0(1(0(x1))))))) -> 1(2(2(2(1(2(1(0(1(x1))))))))) 68.76/18.52 0(0(0(1(1(0(0(1(0(1(1(0(0(x1))))))))))))) -> 2(2(1(2(0(2(2(1(1(1(2(2(1(0(x1)))))))))))))) 68.76/18.52 0(1(1(0(0(1(1(2(1(2(0(0(2(x1))))))))))))) -> 1(2(2(2(1(2(1(0(2(2(0(0(1(2(2(2(2(x1))))))))))))))))) 68.76/18.52 1(0(0(0(1(0(1(1(0(1(1(0(1(2(0(1(x1)))))))))))))))) -> 2(2(1(1(2(1(2(0(0(1(2(0(0(1(1(0(0(0(x1)))))))))))))))))) 68.76/18.52 1(1(0(1(1(2(0(0(0(0(0(0(1(2(0(0(x1)))))))))))))))) -> 2(0(1(1(0(0(2(0(0(2(2(2(0(2(1(2(2(x1))))))))))))))))) 68.76/18.52 2(0(0(2(2(2(0(1(2(1(2(0(1(1(0(0(x1)))))))))))))))) -> 2(2(2(2(2(2(2(1(2(0(0(2(1(0(1(0(1(2(1(2(x1)))))))))))))))))))) 68.76/18.52 1(1(1(1(1(1(2(1(0(1(2(1(0(2(2(0(1(x1))))))))))))))))) -> 1(1(2(2(0(2(2(2(2(1(0(1(2(0(2(1(0(0(0(x1))))))))))))))))))) 68.76/18.52 0(2(0(0(2(1(0(0(0(0(1(0(2(1(1(1(0(1(x1)))))))))))))))))) -> 0(1(2(2(1(0(0(2(2(1(1(1(1(2(1(1(2(1(0(x1))))))))))))))))))) 68.76/18.52 1(1(2(1(2(1(1(1(1(1(1(2(2(1(0(1(2(1(x1)))))))))))))))))) -> 2(0(2(2(2(2(2(1(1(1(2(0(1(0(2(1(2(2(1(2(2(2(1(2(2(2(x1)))))))))))))))))))))))))) 68.76/18.52 0(0(1(0(2(0(1(0(1(1(2(0(0(1(0(0(0(1(1(x1))))))))))))))))))) -> 0(2(2(2(0(2(0(1(2(1(1(0(1(2(2(0(1(0(0(2(2(2(2(x1))))))))))))))))))))))) 68.76/18.52 0(2(0(2(1(0(2(2(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) -> 2(2(0(0(1(2(1(2(1(2(2(2(2(1(0(2(1(1(2(0(x1)))))))))))))))))))) 68.76/18.52 1(0(0(2(2(0(2(0(2(0(0(2(1(1(0(0(0(1(2(x1))))))))))))))))))) -> 2(2(1(0(2(1(0(2(1(2(1(2(1(0(2(2(2(1(2(2(1(2(x1)))))))))))))))))))))) 68.76/18.52 0(1(0(0(1(2(2(0(1(0(1(1(1(2(1(1(1(1(0(2(0(x1))))))))))))))))))))) -> 1(0(1(1(1(1(2(2(1(1(2(1(0(0(0(2(2(0(2(0(0(2(x1)))))))))))))))))))))) 68.76/18.52 1(1(0(1(0(1(1(2(1(0(0(0(1(0(2(0(1(0(0(1(0(1(x1)))))))))))))))))))))) -> 0(1(1(1(1(1(0(0(2(1(0(0(2(1(2(0(2(2(1(2(2(1(1(x1))))))))))))))))))))))) 68.76/18.52 0(2(0(2(2(1(0(1(2(1(0(0(1(0(2(0(0(0(0(0(2(2(0(x1))))))))))))))))))))))) -> 2(1(1(2(2(1(2(2(2(1(0(0(2(2(0(1(0(1(2(0(0(2(1(1(x1)))))))))))))))))))))))) 68.76/18.52 1(0(0(1(2(1(2(0(0(0(2(1(0(2(0(2(0(0(0(0(0(1(1(2(2(x1))))))))))))))))))))))))) -> 1(1(1(1(2(0(1(2(2(2(1(2(1(0(1(2(2(0(2(2(2(0(0(1(0(2(x1)))))))))))))))))))))))))) 68.76/18.52 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2(2(1(2(0(0(0(0(0(1(2(2(0(1(0(0(2(1(1(0(1(2(1(0(0(1(0(1(0(2(0(0(1(0(2(2(2(1(1(0(2(x1))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(1(1(2(1(1(0(2(0(0(0(1(2(2(2(0(2(0(0(2(0(1(0(0(2(1(1(1(1(2(2(2(0(0(2(0(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(0(1(2(1(1(1(2(1(2(1(2(0(0(0(0(1(2(2(1(1(1(0(2(1(1(0(0(0(0(1(0(0(0(1(1(0(2(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(1(2(1(1(2(2(1(0(1(2(0(2(1(0(0(2(1(0(2(2(2(2(1(0(2(2(0(1(2(1(0(2(2(2(1(1(0(2(2(1(0(x1)))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(1(2(1(1(0(0(0(0(1(0(1(2(2(0(1(0(2(1(1(2(1(1(2(2(1(0(1(1(1(1(1(1(0(2(2(2(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(1(2(2(2(2(2(0(0(1(0(0(1(1(2(1(2(2(0(0(2(0(1(1(2(2(1(0(0(1(1(2(2(1(0(2(2(2(1(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(1(2(1(0(0(2(0(0(2(1(1(1(2(2(1(0(2(0(2(1(2(2(0(2(0(1(0(1(2(1(1(0(0(0(1(0(0(1(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(1(2(0(2(1(0(2(2(1(2(1(1(0(1(1(0(1(2(2(2(0(1(0(1(2(2(2(2(0(1(1(2(2(0(1(1(2(1(2(0(2(1(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(0(2(1(0(0(2(1(2(2(0(1(2(0(0(0(2(0(0(0(0(0(0(0(1(0(0(2(0(2(0(0(2(2(0(2(1(1(1(1(2(1(0(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(2(1(1(2(0(2(2(2(1(1(2(2(0(1(2(0(0(0(0(0(1(0(1(1(0(2(0(0(0(0(2(2(1(2(2(2(0(2(0(2(0(1(2(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(1(2(2(1(1(1(1(0(1(1(0(2(0(1(0(2(2(0(2(0(0(1(1(2(0(0(0(0(2(1(2(2(1(1(2(2(0(1(1(2(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(2(2(1(1(0(2(2(0(0(2(1(0(0(1(1(0(0(2(1(2(1(1(1(2(1(0(1(2(2(2(2(2(1(1(1(2(2(0(2(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(0(1(2(1(1(0(2(2(0(1(2(2(0(0(2(1(0(1(0(0(1(2(1(0(2(1(1(0(0(0(1(0(0(0(2(1(1(0(1(2(2(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(2(1(0(0(0(2(2(0(1(1(0(1(2(2(1(0(2(1(2(2(2(1(1(1(1(2(2(2(1(1(1(1(1(0(0(0(0(0(1(0(2(2(0(0(0(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(0(2(0(0(1(0(1(1(1(1(1(2(1(0(1(0(0(1(2(0(2(0(0(0(1(0(0(2(1(2(0(1(1(0(0(0(1(0(2(1(2(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(0(1(0(1(0(1(1(2(0(2(2(2(0(2(0(2(0(1(1(2(0(1(1(2(2(0(1(1(0(1(0(0(2(2(2(1(0(2(0(1(0(0(2(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(1(0(0(2(1(0(2(2(0(2(0(0(1(1(0(1(2(2(1(0(1(1(2(0(0(2(2(1(1(2(0(0(0(1(1(0(0(0(0(0(1(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(2(1(0(2(0(1(1(1(1(2(0(1(2(0(2(0(0(2(2(2(1(2(1(2(2(1(2(0(0(2(0(1(1(1(2(0(1(1(1(1(0(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(0(2(0(2(0(2(0(2(0(2(0(0(2(2(2(1(1(1(0(0(1(1(1(1(1(1(2(1(2(1(2(0(1(0(1(1(1(1(2(0(1(2(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(2(0(2(0(2(1(2(2(1(2(0(2(1(2(1(1(2(2(2(2(1(0(1(1(1(0(1(0(0(1(0(2(0(2(1(2(2(0(2(1(2(1(2(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(0(2(2(0(2(0(1(2(1(2(0(0(0(1(0(1(1(2(1(1(2(0(0(0(0(1(1(1(1(2(1(0(2(0(1(1(0(1(0(1(0(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(0(1(2(0(2(0(1(2(0(1(2(2(2(2(1(1(1(2(2(2(0(2(1(2(2(0(0(1(0(0(0(0(2(0(1(2(1(1(2(1(2(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 1(1(0(2(2(2(1(1(0(1(0(0(0(2(1(1(1(1(1(1(0(2(0(0(0(0(2(2(0(1(1(0(1(1(1(0(1(2(1(1(0(0(1(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(2(2(2(2(1(0(2(0(0(0(1(1(2(2(2(1(2(1(0(0(0(0(0(2(2(0(0(0(0(0(0(1(2(2(2(0(2(1(0(1(1(0(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(0(2(2(2(1(2(2(2(2(2(2(2(0(0(1(0(0(2(2(2(1(1(0(0(2(2(0(0(1(0(2(2(0(2(1(2(2(0(1(0(1(2(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(0(0(1(2(2(2(1(2(0(1(2(2(1(1(2(0(0(1(0(2(2(1(1(2(0(1(0(1(0(2(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 2(1(0(2(0(0(0(2(0(2(2(1(1(2(2(1(1(2(1(0(1(1(0(0(2(0(0(1(0(2(1(1(0(0(2(2(1(1(1(1(0(2(2(0(1(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(2(0(1(0(1(0(0(0(0(0(1(2(1(1(1(2(1(2(0(2(1(0(1(0(2(1(1(2(0(1(1(0(1(0(2(1(2(0(0(2(2(2(2(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 68.76/18.52 68.76/18.52 68.76/18.52 68.76/18.52 ---------------------------------------- 68.76/18.52 68.76/18.52 (2) 68.76/18.52 Obligation: 68.76/18.52 Q restricted rewrite system: 68.76/18.52 The TRS R consists of the following rules: 68.76/18.52 68.76/18.52 1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0(0(2(1(2(0(2(0(0(2(0(1(2(0(2(2(x1)))))))))))))))) 68.76/18.52 0(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 2(2(0(1(0(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))) 68.76/18.52 1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1(1(1(2(0(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(2(0(0(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(0(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 68.76/18.52 Q is empty. 68.76/18.52 68.76/18.52 ---------------------------------------- 68.76/18.52 68.76/18.52 (3) DependencyPairsProof (EQUIVALENT) 68.76/18.52 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 68.76/18.52 ---------------------------------------- 68.76/18.52 68.76/18.52 (4) 68.76/18.52 Obligation: 68.76/18.52 Q DP problem: 68.76/18.52 The TRS P consists of the following rules: 68.76/18.52 68.76/18.52 1^1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0^1(0(2(1(2(0(2(0(0(2(0(1(2(0(2(2(x1)))))))))))))))) 68.76/18.52 1^1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0^1(2(1(2(0(2(0(0(2(0(1(2(0(2(2(x1))))))))))))))) 68.76/18.52 1^1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 1^1(2(0(2(0(0(2(0(1(2(0(2(2(x1))))))))))))) 68.76/18.52 1^1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0^1(2(0(0(2(0(1(2(0(2(2(x1))))))))))) 68.76/18.52 1^1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0^1(0(2(0(1(2(0(2(2(x1))))))))) 68.76/18.52 1^1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0^1(2(0(1(2(0(2(2(x1)))))))) 68.76/18.52 1^1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0^1(1(2(0(2(2(x1)))))) 68.76/18.52 1^1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 1^1(2(0(2(2(x1))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(0(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(0(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(1(1(2(0(1(1(1(1(x1))))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(0(1(1(2(0(1(1(1(1(x1))))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(0(1(1(2(0(1(1(1(1(x1)))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(2(0(1(1(1(1(x1))))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(2(0(1(1(1(1(x1)))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(2(0(1(1(1(1(x1))))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(1(1(x1))))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(1(x1)))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(x1))) 68.76/18.52 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(x1)) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(1(2(0(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(2(0(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1))))))))))))))))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(2(0(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1))))))))))))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1))))))))))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1))))))))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1))))))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1))))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1))))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(1(2(1(1(1(1(2(0(2(1(0(2(x1))))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(1(1(2(0(2(1(0(2(x1)))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(1(2(0(2(1(0(2(x1))))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(2(0(2(1(0(2(x1)))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(2(0(2(1(0(2(x1))))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(2(1(0(2(x1))))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(0(2(x1))) 68.76/18.52 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(2(x1)) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(2(0(0(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(1(0(1(1(1(0(x1)))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(0(1(1(1(0(x1))))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(1(1(1(0(x1)))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(1(1(1(0(x1))))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(x1)))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(x1))))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(0(x1)))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(0(x1))) 68.76/18.52 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(x1)) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(2(0(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(0(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))) 68.76/18.52 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(0(0(2(0(0(2(0(0(x1))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(0(0(2(0(0(x1)))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(2(0(0(x1))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(0(0(x1))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(x1)))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(x1)) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(x1) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(0(0(x1)))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(0(0(x1))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(0(0(0(x1)))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(0(0(0(x1))))) 68.76/18.54 68.76/18.54 The TRS R consists of the following rules: 68.76/18.54 68.76/18.54 1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0(0(2(1(2(0(2(0(0(2(0(1(2(0(2(2(x1)))))))))))))))) 68.76/18.54 0(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 2(2(0(1(0(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))) 68.76/18.54 1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1(1(1(2(0(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))))))))))))) 68.76/18.54 0(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(2(0(0(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(0(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 68.76/18.54 Q is empty. 68.76/18.54 We have to consider all minimal (P,Q,R)-chains. 68.76/18.54 ---------------------------------------- 68.76/18.54 68.76/18.54 (5) DependencyGraphProof (EQUIVALENT) 68.76/18.54 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 79 less nodes. 68.76/18.54 ---------------------------------------- 68.76/18.54 68.76/18.54 (6) 68.76/18.54 Obligation: 68.76/18.54 Q DP problem: 68.76/18.54 The TRS P consists of the following rules: 68.76/18.54 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(1(1(2(0(2(1(0(2(x1)))))))))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(1(2(0(2(1(0(2(x1))))))))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(2(0(2(1(0(2(x1)))))))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(2(1(0(2(x1))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(0(2(x1))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(2(x1)) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(1(1(2(0(1(1(1(1(x1))))))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(0(1(1(2(0(1(1(1(1(x1))))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(0(1(1(2(0(1(1(1(1(x1)))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(2(0(1(1(1(1(x1))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(2(0(1(1(1(1(x1)))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(1(1(x1))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(1(x1)))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(x1))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(x1)) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(1(0(1(1(1(0(x1)))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(0(1(1(1(0(x1))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(1(1(1(0(x1)))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(1(1(1(0(x1))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(x1)))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(x1))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(0(x1)))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(0(x1))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(x1)) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(0(0(2(0(0(2(0(0(x1))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(0(0(2(0(0(x1)))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(2(0(0(x1))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(0(0(x1))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(x1)))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(x1)) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(x1) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(0(0(x1)))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(0(0(x1))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(0(0(0(x1)))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(0(0(0(x1))))) 68.76/18.54 68.76/18.54 The TRS R consists of the following rules: 68.76/18.54 68.76/18.54 1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0(0(2(1(2(0(2(0(0(2(0(1(2(0(2(2(x1)))))))))))))))) 68.76/18.54 0(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 2(2(0(1(0(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))) 68.76/18.54 1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1(1(1(2(0(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))))))))))))) 68.76/18.54 0(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(2(0(0(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(0(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 68.76/18.54 Q is empty. 68.76/18.54 We have to consider all minimal (P,Q,R)-chains. 68.76/18.54 ---------------------------------------- 68.76/18.54 68.76/18.54 (7) QDPOrderProof (EQUIVALENT) 68.76/18.54 We use the reduction pair processor [LPAR04,JAR06]. 68.76/18.54 68.76/18.54 68.76/18.54 The following pairs can be oriented strictly and are deleted. 68.76/18.54 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(1(1(2(0(2(1(0(2(x1)))))))))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(1(2(0(2(1(0(2(x1))))))))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(1(2(0(2(1(0(2(x1)))))))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(2(1(0(2(x1))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1^1(0(2(x1))) 68.76/18.54 1^1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 0^1(2(x1)) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(1(1(2(0(1(1(1(1(x1))))))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(0(1(1(2(0(1(1(1(1(x1))))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(0(1(1(2(0(1(1(1(1(x1)))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(2(0(1(1(1(1(x1))))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(2(0(1(1(1(1(x1)))))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 0^1(1(1(1(1(x1))))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(1(x1)))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(1(x1))) 68.76/18.54 0^1(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 1^1(1(x1)) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(2(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(1(0(1(1(1(0(x1)))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(0(1(1(1(0(x1))))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(1(1(1(0(x1)))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(1(1(1(0(x1))))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(x1)))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(x1))))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(0(x1)))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(0(x1))) 68.76/18.54 0^1(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(x1)) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(2(2(0(0(2(0(0(2(0(0(x1))))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(0(0(2(0(0(2(0(0(x1))))))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(0(0(2(0(0(x1)))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(2(0(0(x1))))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(2(0(0(x1))))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(0(0(x1)))) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(x1)) 68.76/18.54 0^1(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(x1) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(0(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(2(2(2(1(0(1(1(1(0(0(0(x1)))))))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(0(1(1(1(0(0(0(x1)))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0^1(1(1(1(0(0(0(x1))))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(1(0(0(0(x1)))))) 68.76/18.54 0^1(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 1^1(1(0(0(0(x1))))) 68.76/18.54 The remaining pairs can at least be oriented weakly. 68.76/18.54 Used ordering: Polynomial interpretation [POLO]: 68.76/18.54 68.76/18.54 POL(0(x_1)) = 1 + x_1 68.76/18.54 POL(0^1(x_1)) = x_1 68.76/18.54 POL(1(x_1)) = x_1 68.76/18.54 POL(1^1(x_1)) = 1 + x_1 68.76/18.54 POL(2(x_1)) = x_1 68.76/18.54 68.76/18.54 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 68.76/18.54 68.76/18.54 0(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 2(2(0(1(0(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))) 68.76/18.54 0(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(2(0(0(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(0(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0(0(2(1(2(0(2(0(0(2(0(1(2(0(2(2(x1)))))))))))))))) 68.76/18.54 1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1(1(1(2(0(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))))))))))))) 68.76/18.54 0(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 68.76/18.54 68.76/18.54 ---------------------------------------- 68.76/18.54 68.76/18.54 (8) 68.76/18.54 Obligation: 68.76/18.54 Q DP problem: 68.76/18.54 P is empty. 68.76/18.54 The TRS R consists of the following rules: 68.76/18.54 68.76/18.54 1(0(0(2(0(2(1(0(0(2(0(2(2(0(2(2(x1)))))))))))))))) -> 0(0(2(1(2(0(2(0(0(2(0(1(2(0(2(2(x1)))))))))))))))) 68.76/18.54 0(2(2(2(0(1(2(1(0(2(0(1(2(2(0(1(2(1(1(1(1(1(2(0(1(1(2(2(0(1(0(1(x1)))))))))))))))))))))))))))))))) -> 2(2(0(1(0(1(2(0(0(2(0(2(2(2(1(2(2(2(1(0(1(1(1(0(1(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))) 68.76/18.54 1(1(2(2(0(1(2(1(2(1(2(2(0(2(0(0(2(2(1(1(0(1(0(0(0(2(1(1(1(1(2(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))) -> 1(1(1(2(0(0(2(1(2(0(1(2(2(2(2(0(2(2(2(1(0(1(0(0(1(2(1(1(1(1(2(0(2(1(0(2(x1)))))))))))))))))))))))))))))))))))) 68.76/18.54 0(2(2(2(1(2(2(0(2(0(2(0(0(0(2(0(0(1(1(2(1(1(1(0(1(2(2(2(1(0(1(2(2(0(0(0(2(1(1(1(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(2(0(0(2(1(2(0(2(1(0(1(2(0(2(1(1(2(0(1(2(1(1(2(2(2(1(0(0(2(2(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0(2(2(0(0(2(0(0(1(0(1(0(1(0(1(2(0(2(0(0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(0(2(0(0(0(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(0(0(1(0(1(0(2(1(0(2(0(1(0(0(1(2(0(2(0(0(1(0(0(0(0(1(0(0(0(0(2(2(0(0(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 0(0(0(2(1(1(2(0(1(1(0(2(0(1(1(2(2(1(2(2(1(2(2(1(0(1(0(0(2(1(1(1(0(1(1(0(2(2(2(1(0(1(2(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(1(1(1(0(2(2(2(1(2(1(0(2(2(1(2(2(1(2(0(1(2(0(0(0(1(1(2(1(0(0(1(0(2(2(2(1(0(1(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 68.76/18.54 68.76/18.54 Q is empty. 68.76/18.54 We have to consider all minimal (P,Q,R)-chains. 68.76/18.54 ---------------------------------------- 68.76/18.54 68.76/18.54 (9) PisEmptyProof (EQUIVALENT) 68.76/18.54 The TRS P is empty. Hence, there is no (P,Q,R) chain. 68.76/18.54 ---------------------------------------- 68.76/18.54 68.76/18.54 (10) 68.76/18.54 YES 69.23/18.64 EOF