11.70/3.77 YES 12.88/4.02 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 12.88/4.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.88/4.02 12.88/4.02 12.88/4.02 Termination w.r.t. Q of the given QTRS could be proven: 12.88/4.02 12.88/4.02 (0) QTRS 12.88/4.02 (1) QTRSRRRProof [EQUIVALENT, 523 ms] 12.88/4.02 (2) QTRS 12.88/4.02 (3) Overlay + Local Confluence [EQUIVALENT, 8 ms] 12.88/4.02 (4) QTRS 12.88/4.02 (5) DependencyPairsProof [EQUIVALENT, 14 ms] 12.88/4.02 (6) QDP 12.88/4.02 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 12.88/4.02 (8) TRUE 12.88/4.02 12.88/4.02 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (0) 12.88/4.02 Obligation: 12.88/4.02 Q restricted rewrite system: 12.88/4.02 The TRS R consists of the following rules: 12.88/4.02 12.88/4.02 0(0(2(5(3(2(2(5(3(5(3(2(x1)))))))))))) -> 2(0(0(0(3(0(4(0(0(3(0(2(5(0(5(2(0(2(x1)))))))))))))))))) 12.88/4.02 0(1(5(5(4(4(2(5(4(2(5(1(x1)))))))))))) -> 0(0(0(5(0(5(3(4(1(0(4(2(2(4(x1)))))))))))))) 12.88/4.02 0(2(2(4(5(0(1(3(3(2(5(5(x1)))))))))))) -> 1(0(4(0(0(4(3(4(2(1(1(4(4(0(2(3(x1)))))))))))))))) 12.88/4.02 0(2(5(3(5(1(5(1(5(5(5(5(x1)))))))))))) -> 2(0(4(0(4(1(5(1(0(4(5(1(1(1(1(0(3(2(x1)))))))))))))))))) 12.88/4.02 0(3(0(2(5(2(5(3(3(3(5(4(x1)))))))))))) -> 2(4(4(2(0(4(4(2(4(4(2(3(1(2(1(1(1(5(x1)))))))))))))))))) 12.88/4.02 0(3(1(2(1(2(3(1(5(3(3(5(x1)))))))))))) -> 0(1(4(4(2(2(0(0(5(4(2(3(1(0(2(1(0(2(x1)))))))))))))))))) 12.88/4.02 0(5(3(2(2(1(2(3(3(2(5(0(x1)))))))))))) -> 3(0(5(5(4(3(1(1(5(4(0(1(4(0(x1)))))))))))))) 12.88/4.02 0(5(5(3(2(4(0(5(4(4(0(4(x1)))))))))))) -> 2(1(0(4(4(3(0(1(0(4(0(2(2(4(4(4(x1)))))))))))))))) 12.88/4.02 1(0(3(3(5(5(0(5(4(5(1(0(x1)))))))))))) -> 2(3(4(0(3(0(1(4(0(3(4(1(2(4(2(x1))))))))))))))) 12.88/4.02 1(1(2(5(0(1(2(3(5(5(3(4(x1)))))))))))) -> 2(4(2(4(4(3(3(2(2(3(2(1(4(0(x1)))))))))))))) 12.88/4.02 1(2(2(5(3(1(4(5(1(3(4(1(x1)))))))))))) -> 2(3(4(0(4(0(4(5(1(2(0(0(4(5(0(5(x1)))))))))))))))) 12.88/4.02 1(2(4(1(5(3(1(1(0(5(4(2(x1)))))))))))) -> 2(0(1(2(0(4(2(2(1(1(4(4(1(0(0(4(4(0(x1)))))))))))))))))) 12.88/4.02 1(3(0(5(5(0(1(2(5(1(5(4(x1)))))))))))) -> 4(0(4(3(0(3(0(4(0(1(0(4(5(4(x1)))))))))))))) 12.88/4.02 1(3(3(1(5(2(3(3(5(5(5(5(x1)))))))))))) -> 0(2(4(0(1(4(0(4(4(4(5(2(4(3(1(5(2(3(x1)))))))))))))))))) 12.88/4.02 1(3(5(5(1(3(2(4(2(3(2(5(x1)))))))))))) -> 1(2(0(3(0(4(4(1(4(0(1(5(1(1(x1)))))))))))))) 12.88/4.02 1(5(0(5(1(4(5(4(3(5(0(2(x1)))))))))))) -> 0(1(5(4(0(1(5(0(4(4(4(4(2(0(0(2(x1)))))))))))))))) 12.88/4.02 1(5(0(5(5(1(5(5(3(5(3(0(x1)))))))))))) -> 1(0(5(5(2(0(4(0(5(4(1(1(0(4(0(5(0(4(x1)))))))))))))))))) 12.88/4.02 1(5(1(3(3(2(2(1(5(1(5(5(x1)))))))))))) -> 0(2(1(1(1(4(1(2(4(5(2(2(0(1(2(4(x1)))))))))))))))) 12.88/4.02 1(5(2(0(3(3(5(3(1(5(2(3(x1)))))))))))) -> 5(2(4(0(5(4(5(0(5(3(4(2(0(3(x1)))))))))))))) 12.88/4.02 1(5(3(1(1(2(3(3(2(5(1(1(x1)))))))))))) -> 3(1(1(3(1(2(4(0(0(2(5(1(2(0(0(4(x1)))))))))))))))) 12.88/4.02 1(5(3(5(3(3(3(2(2(0(1(1(x1)))))))))))) -> 2(4(0(2(2(0(0(4(1(1(5(3(5(1(3(4(1(x1))))))))))))))))) 12.88/4.02 1(5(5(0(5(1(5(3(5(0(3(4(x1)))))))))))) -> 4(1(2(0(0(1(3(1(1(0(5(4(2(3(2(x1))))))))))))))) 12.88/4.02 2(0(0(1(5(1(2(5(3(2(1(4(x1)))))))))))) -> 2(5(4(0(0(2(2(1(4(1(0(4(4(1(3(0(x1)))))))))))))))) 12.88/4.02 2(0(5(4(2(2(3(3(2(5(2(5(x1)))))))))))) -> 4(5(3(2(0(4(4(0(1(2(2(1(0(2(0(0(4(x1))))))))))))))))) 12.88/4.02 2(1(1(1(3(1(1(3(2(0(3(2(x1)))))))))))) -> 2(2(1(0(0(0(2(1(2(2(2(1(4(4(x1)))))))))))))) 12.88/4.02 2(2(0(1(2(5(0(3(2(5(1(2(x1)))))))))))) -> 3(2(1(4(4(4(2(1(0(1(2(0(0(0(4(0(4(5(x1)))))))))))))))))) 12.88/4.02 2(2(0(1(2(5(5(2(1(1(1(3(x1)))))))))))) -> 2(4(4(0(4(1(3(0(0(5(2(0(4(0(4(4(4(0(x1)))))))))))))))))) 12.88/4.02 2(2(0(3(2(1(0(3(5(5(5(5(x1)))))))))))) -> 4(1(2(2(3(4(0(2(4(1(0(4(2(4(0(0(4(3(x1)))))))))))))))))) 12.88/4.02 2(2(1(5(5(3(4(3(2(5(3(2(x1)))))))))))) -> 2(2(2(1(3(3(4(0(0(4(3(3(1(3(x1)))))))))))))) 12.88/4.02 2(2(4(1(5(5(3(3(5(2(5(5(x1)))))))))))) -> 5(0(5(0(4(4(1(2(1(3(3(4(2(4(4(x1))))))))))))))) 12.88/4.02 2(3(3(0(2(5(5(2(2(4(5(4(x1)))))))))))) -> 4(0(0(0(1(0(0(5(4(1(4(1(4(2(1(x1))))))))))))))) 12.88/4.02 2(3(4(3(2(5(3(5(1(0(1(4(x1)))))))))))) -> 2(0(0(4(4(5(0(2(3(5(1(2(2(2(4(x1))))))))))))))) 12.88/4.02 2(4(3(5(2(1(5(5(2(1(5(2(x1)))))))))))) -> 4(2(1(4(1(0(4(5(0(4(2(1(2(3(5(x1))))))))))))))) 12.88/4.02 2(5(0(5(5(2(4(3(2(5(1(5(x1)))))))))))) -> 3(4(1(4(0(1(1(0(4(1(1(0(0(2(4(4(5(2(x1)))))))))))))))))) 12.88/4.02 2(5(1(5(5(1(1(0(5(5(5(5(x1)))))))))))) -> 3(3(2(4(4(4(0(2(5(1(0(2(5(1(3(x1))))))))))))))) 12.88/4.02 2(5(1(5(5(5(5(3(4(0(2(4(x1)))))))))))) -> 4(2(4(4(2(2(4(5(0(4(2(2(1(0(x1)))))))))))))) 12.88/4.02 2(5(2(0(5(3(4(1(5(2(5(5(x1)))))))))))) -> 1(2(2(0(1(4(1(2(1(2(5(1(3(0(0(4(4(1(x1)))))))))))))))))) 12.88/4.02 2(5(3(3(3(3(5(2(1(4(2(0(x1)))))))))))) -> 0(1(3(4(0(5(5(3(0(2(2(4(3(2(3(x1))))))))))))))) 12.88/4.02 2(5(4(5(1(5(3(1(5(2(4(1(x1)))))))))))) -> 2(4(1(0(4(1(5(2(1(1(1(4(0(5(2(3(4(0(x1)))))))))))))))))) 12.88/4.02 3(0(5(5(5(2(0(3(1(2(5(0(x1)))))))))))) -> 0(4(0(4(2(2(2(0(1(3(4(4(1(0(5(x1))))))))))))))) 12.88/4.02 3(1(1(5(0(3(2(3(3(3(3(4(x1)))))))))))) -> 2(0(2(4(4(5(0(5(4(3(1(0(0(3(x1)))))))))))))) 12.88/4.02 3(1(3(5(3(5(5(2(5(3(0(1(x1)))))))))))) -> 2(3(1(2(0(3(2(3(5(4(0(0(0(5(0(0(x1)))))))))))))))) 12.88/4.02 3(2(1(1(5(4(1(5(0(2(3(5(x1)))))))))))) -> 2(5(4(2(3(0(0(4(5(4(4(2(4(0(0(0(2(x1))))))))))))))))) 12.88/4.02 3(2(3(1(5(2(0(3(3(4(0(5(x1)))))))))))) -> 3(0(0(0(4(0(3(0(2(3(3(2(1(4(1(x1))))))))))))))) 12.88/4.02 3(2(5(3(2(5(4(0(3(1(2(2(x1)))))))))))) -> 0(2(3(0(4(5(0(5(4(4(4(4(1(4(2(3(0(1(x1)))))))))))))))))) 12.88/4.02 3(2(5(4(3(5(2(5(1(5(2(2(x1)))))))))))) -> 4(2(3(3(0(5(3(5(1(0(0(2(1(5(0(4(x1)))))))))))))))) 12.88/4.02 3(2(5(5(5(4(4(3(2(3(1(0(x1)))))))))))) -> 0(0(2(2(4(5(4(0(4(5(5(4(0(5(x1)))))))))))))) 12.88/4.02 3(3(1(1(4(5(3(4(3(5(1(5(x1)))))))))))) -> 2(4(1(2(5(0(1(3(0(5(0(4(2(0(x1)))))))))))))) 12.88/4.02 3(3(3(1(0(2(4(3(3(4(4(5(x1)))))))))))) -> 0(2(0(4(4(4(0(5(5(0(1(3(3(5(x1)))))))))))))) 12.88/4.02 3(4(0(5(3(4(0(0(4(5(2(4(x1)))))))))))) -> 0(0(0(5(4(5(4(4(0(4(2(4(4(0(0(x1))))))))))))))) 12.88/4.02 3(4(1(5(3(1(2(3(1(0(1(3(x1)))))))))))) -> 1(3(4(3(3(5(4(0(4(0(4(4(5(0(1(x1))))))))))))))) 12.88/4.02 3(4(3(3(4(5(2(5(4(2(4(5(x1)))))))))))) -> 4(0(0(3(5(1(0(0(4(2(4(4(3(5(0(2(2(x1))))))))))))))))) 12.88/4.02 3(4(5(3(5(3(1(5(3(1(1(1(x1)))))))))))) -> 1(2(3(0(4(4(4(4(4(1(4(4(4(0(5(x1))))))))))))))) 12.88/4.02 3(5(1(5(0(1(4(4(3(5(5(1(x1)))))))))))) -> 4(4(2(5(0(4(0(2(2(4(0(0(4(2(0(1(2(4(x1)))))))))))))))))) 12.88/4.02 3(5(1(5(3(3(1(3(3(2(4(5(x1)))))))))))) -> 2(3(4(5(1(0(0(2(4(2(3(1(3(1(4(4(x1)))))))))))))))) 12.88/4.02 3(5(3(2(1(3(2(1(5(5(3(5(x1)))))))))))) -> 3(3(2(1(4(2(1(2(1(5(0(1(0(4(x1)))))))))))))) 12.88/4.02 3(5(3(2(3(3(5(3(2(5(3(4(x1)))))))))))) -> 4(1(1(3(0(4(2(1(2(1(0(4(4(1(1(1(2(x1))))))))))))))))) 12.88/4.02 4(1(1(5(5(5(3(5(5(2(3(5(x1)))))))))))) -> 4(0(1(5(1(0(2(4(1(2(0(4(2(2(3(4(0(0(x1)))))))))))))))))) 12.88/4.02 4(1(2(4(5(4(1(5(5(5(2(1(x1)))))))))))) -> 4(4(3(0(4(1(1(2(1(1(0(4(1(3(0(4(0(0(x1)))))))))))))))))) 12.88/4.02 4(2(5(3(3(3(3(2(1(5(4(5(x1)))))))))))) -> 3(0(3(4(3(0(1(1(4(3(4(2(0(4(1(3(1(2(x1)))))))))))))))))) 12.88/4.02 4(2(5(5(3(4(5(4(2(5(2(0(x1)))))))))))) -> 0(2(2(2(5(1(4(0(4(0(2(1(5(0(x1)))))))))))))) 12.88/4.02 4(3(0(0(1(5(5(3(0(3(3(2(x1)))))))))))) -> 3(1(3(5(0(0(0(3(1(4(5(0(4(0(x1)))))))))))))) 12.88/4.02 4(3(5(2(5(3(5(1(3(0(5(2(x1)))))))))))) -> 2(5(0(4(4(1(4(4(0(4(0(0(4(2(4(1(3(x1))))))))))))))))) 12.88/4.02 4(5(0(5(0(1(1(2(1(2(4(0(x1)))))))))))) -> 4(2(0(0(0(5(4(2(3(0(4(4(0(1(x1)))))))))))))) 12.88/4.02 4(5(5(2(3(2(5(0(2(0(3(1(x1)))))))))))) -> 1(0(0(3(4(1(5(1(0(4(4(0(3(4(0(0(x1)))))))))))))))) 12.88/4.02 4(5(5(3(2(1(0(1(1(0(5(5(x1)))))))))))) -> 0(5(0(4(0(3(0(1(2(2(3(2(3(4(x1)))))))))))))) 12.88/4.02 5(0(5(5(3(1(5(5(3(3(5(0(x1)))))))))))) -> 0(4(4(5(4(0(3(5(3(4(3(5(0(4(1(3(1(2(x1)))))))))))))))))) 12.88/4.02 5(1(0(3(1(5(5(3(0(3(5(1(x1)))))))))))) -> 5(4(1(1(0(4(0(3(3(1(3(0(4(0(1(4(4(4(x1)))))))))))))))))) 12.88/4.02 5(1(1(0(3(1(5(3(1(1(0(5(x1)))))))))))) -> 4(1(0(5(4(0(4(5(2(1(5(1(4(0(3(x1))))))))))))))) 12.88/4.02 5(1(1(4(3(1(2(5(5(4(2(2(x1)))))))))))) -> 0(1(0(0(2(4(0(2(5(0(0(5(0(0(x1)))))))))))))) 12.88/4.02 5(1(2(2(5(2(4(1(3(2(3(1(x1)))))))))))) -> 2(1(4(4(2(4(4(0(0(4(4(4(3(1(4(0(3(1(x1)))))))))))))))))) 12.88/4.02 5(1(2(3(3(1(1(2(3(1(5(1(x1)))))))))))) -> 5(2(0(3(3(5(2(4(4(1(4(4(3(4(1(x1))))))))))))))) 12.88/4.02 5(1(5(1(3(2(4(5(3(5(4(0(x1)))))))))))) -> 0(1(4(0(0(4(0(5(2(1(4(4(4(3(3(3(x1)))))))))))))))) 12.88/4.02 5(2(1(4(3(5(3(1(5(3(5(1(x1)))))))))))) -> 0(1(1(1(1(2(0(5(0(0(0(2(3(0(0(1(x1)))))))))))))))) 12.88/4.02 5(2(1(5(5(0(3(5(5(5(3(0(x1)))))))))))) -> 2(3(4(1(1(0(2(3(0(4(1(0(2(0(0(0(3(3(x1)))))))))))))))))) 12.88/4.02 5(2(3(5(3(0(3(3(1(4(0(2(x1)))))))))))) -> 4(5(4(0(0(2(1(1(0(3(4(4(4(3(x1)))))))))))))) 12.88/4.02 5(2(4(3(0(2(5(2(1(1(5(0(x1)))))))))))) -> 0(1(1(0(0(0(0(0(4(0(0(5(4(5(x1)))))))))))))) 12.88/4.02 5(2(5(4(4(2(3(5(0(5(2(5(x1)))))))))))) -> 4(1(4(2(3(4(3(4(4(4(2(1(4(0(0(0(1(x1))))))))))))))))) 12.88/4.02 5(3(2(0(2(0(4(2(5(1(5(2(x1)))))))))))) -> 4(3(0(4(5(0(3(4(0(3(5(1(1(1(4(x1))))))))))))))) 12.88/4.02 5(3(3(2(1(1(3(3(2(5(5(1(x1)))))))))))) -> 3(1(4(0(1(4(2(0(3(0(0(3(1(2(4(x1))))))))))))))) 12.88/4.02 5(3(3(3(1(5(2(0(1(5(4(0(x1)))))))))))) -> 3(5(0(3(5(0(0(4(2(3(4(0(1(2(2(3(0(0(x1)))))))))))))))))) 12.88/4.02 5(3(5(2(5(5(2(4(2(1(2(2(x1)))))))))))) -> 0(1(3(4(4(4(0(1(5(0(1(1(2(1(x1)))))))))))))) 12.88/4.02 5(3(5(4(4(5(1(3(4(5(5(5(x1)))))))))))) -> 5(3(4(4(0(4(4(0(1(5(0(5(2(2(3(4(0(4(x1)))))))))))))))))) 12.88/4.02 5(4(3(3(0(3(2(5(4(0(5(5(x1)))))))))))) -> 1(1(4(1(3(2(2(0(1(2(2(0(0(1(1(4(3(x1))))))))))))))))) 12.88/4.02 5(4(3(3(3(2(5(2(4(1(4(2(x1)))))))))))) -> 3(0(4(4(4(0(4(4(1(4(4(1(1(2(2(4(5(4(x1)))))))))))))))))) 12.88/4.02 5(5(0(0(3(4(3(2(3(4(5(5(x1)))))))))))) -> 0(2(1(0(1(2(4(0(0(5(3(2(2(2(0(x1))))))))))))))) 12.88/4.02 5(5(1(2(5(2(5(3(3(3(4(5(x1)))))))))))) -> 3(5(1(3(1(5(2(4(0(2(3(3(4(4(2(x1))))))))))))))) 12.88/4.02 5(5(1(3(3(2(0(5(5(1(0(0(x1)))))))))))) -> 5(0(4(0(3(4(5(1(2(4(4(4(3(0(0(0(1(x1))))))))))))))))) 12.88/4.02 5(5(1(5(1(5(3(4(2(5(4(5(x1)))))))))))) -> 0(5(4(0(4(0(4(1(2(2(1(1(3(4(4(0(3(3(x1)))))))))))))))))) 12.88/4.02 5(5(1(5(2(5(1(5(1(1(1(4(x1)))))))))))) -> 1(4(1(3(4(4(5(4(0(5(4(5(0(4(3(5(2(x1))))))))))))))))) 12.88/4.02 5(5(2(5(3(3(1(0(1(4(5(5(x1)))))))))))) -> 2(4(3(0(5(2(3(0(5(4(4(0(3(2(3(2(5(x1))))))))))))))))) 12.88/4.02 5(5(3(1(0(3(3(0(2(3(5(3(x1)))))))))))) -> 2(4(5(2(2(2(0(0(4(4(3(0(4(0(0(2(4(4(x1)))))))))))))))))) 12.88/4.02 5(5(3(3(5(3(3(0(4(5(3(0(x1)))))))))))) -> 4(4(0(2(4(0(3(4(1(4(1(3(3(4(4(4(4(3(x1)))))))))))))))))) 12.88/4.02 5(5(3(4(0(2(5(5(3(2(4(1(x1)))))))))))) -> 2(4(3(0(4(0(1(3(2(4(1(1(0(1(1(1(0(1(x1)))))))))))))))))) 12.88/4.02 5(5(4(5(5(2(5(3(1(2(1(1(x1)))))))))))) -> 0(3(0(2(2(4(4(3(1(4(4(2(5(0(0(0(x1)))))))))))))))) 12.88/4.02 5(5(5(5(5(3(2(5(2(0(5(5(x1)))))))))))) -> 5(3(5(3(3(1(5(5(4(1(3(4(0(1(x1)))))))))))))) 12.88/4.02 12.88/4.02 Q is empty. 12.88/4.02 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (1) QTRSRRRProof (EQUIVALENT) 12.88/4.02 Used ordering: 12.88/4.02 Polynomial interpretation [POLO]: 12.88/4.02 12.88/4.02 POL(0(x_1)) = x_1 12.88/4.02 POL(1(x_1)) = 11 + x_1 12.88/4.02 POL(2(x_1)) = 8 + x_1 12.88/4.02 POL(3(x_1)) = 15 + x_1 12.88/4.02 POL(4(x_1)) = x_1 12.88/4.02 POL(5(x_1)) = 21 + x_1 12.88/4.02 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 12.88/4.02 12.88/4.02 0(0(2(5(3(2(2(5(3(5(3(2(x1)))))))))))) -> 2(0(0(0(3(0(4(0(0(3(0(2(5(0(5(2(0(2(x1)))))))))))))))))) 12.88/4.02 0(1(5(5(4(4(2(5(4(2(5(1(x1)))))))))))) -> 0(0(0(5(0(5(3(4(1(0(4(2(2(4(x1)))))))))))))) 12.88/4.02 0(2(2(4(5(0(1(3(3(2(5(5(x1)))))))))))) -> 1(0(4(0(0(4(3(4(2(1(1(4(4(0(2(3(x1)))))))))))))))) 12.88/4.02 0(2(5(3(5(1(5(1(5(5(5(5(x1)))))))))))) -> 2(0(4(0(4(1(5(1(0(4(5(1(1(1(1(0(3(2(x1)))))))))))))))))) 12.88/4.02 0(3(0(2(5(2(5(3(3(3(5(4(x1)))))))))))) -> 2(4(4(2(0(4(4(2(4(4(2(3(1(2(1(1(1(5(x1)))))))))))))))))) 12.88/4.02 0(3(1(2(1(2(3(1(5(3(3(5(x1)))))))))))) -> 0(1(4(4(2(2(0(0(5(4(2(3(1(0(2(1(0(2(x1)))))))))))))))))) 12.88/4.02 0(5(3(2(2(1(2(3(3(2(5(0(x1)))))))))))) -> 3(0(5(5(4(3(1(1(5(4(0(1(4(0(x1)))))))))))))) 12.88/4.02 0(5(5(3(2(4(0(5(4(4(0(4(x1)))))))))))) -> 2(1(0(4(4(3(0(1(0(4(0(2(2(4(4(4(x1)))))))))))))))) 12.88/4.02 1(0(3(3(5(5(0(5(4(5(1(0(x1)))))))))))) -> 2(3(4(0(3(0(1(4(0(3(4(1(2(4(2(x1))))))))))))))) 12.88/4.02 1(1(2(5(0(1(2(3(5(5(3(4(x1)))))))))))) -> 2(4(2(4(4(3(3(2(2(3(2(1(4(0(x1)))))))))))))) 12.88/4.02 1(2(2(5(3(1(4(5(1(3(4(1(x1)))))))))))) -> 2(3(4(0(4(0(4(5(1(2(0(0(4(5(0(5(x1)))))))))))))))) 12.88/4.02 1(2(4(1(5(3(1(1(0(5(4(2(x1)))))))))))) -> 2(0(1(2(0(4(2(2(1(1(4(4(1(0(0(4(4(0(x1)))))))))))))))))) 12.88/4.02 1(3(0(5(5(0(1(2(5(1(5(4(x1)))))))))))) -> 4(0(4(3(0(3(0(4(0(1(0(4(5(4(x1)))))))))))))) 12.88/4.02 1(3(3(1(5(2(3(3(5(5(5(5(x1)))))))))))) -> 0(2(4(0(1(4(0(4(4(4(5(2(4(3(1(5(2(3(x1)))))))))))))))))) 12.88/4.02 1(3(5(5(1(3(2(4(2(3(2(5(x1)))))))))))) -> 1(2(0(3(0(4(4(1(4(0(1(5(1(1(x1)))))))))))))) 12.88/4.02 1(5(0(5(1(4(5(4(3(5(0(2(x1)))))))))))) -> 0(1(5(4(0(1(5(0(4(4(4(4(2(0(0(2(x1)))))))))))))))) 12.88/4.02 1(5(0(5(5(1(5(5(3(5(3(0(x1)))))))))))) -> 1(0(5(5(2(0(4(0(5(4(1(1(0(4(0(5(0(4(x1)))))))))))))))))) 12.88/4.02 1(5(1(3(3(2(2(1(5(1(5(5(x1)))))))))))) -> 0(2(1(1(1(4(1(2(4(5(2(2(0(1(2(4(x1)))))))))))))))) 12.88/4.02 1(5(2(0(3(3(5(3(1(5(2(3(x1)))))))))))) -> 5(2(4(0(5(4(5(0(5(3(4(2(0(3(x1)))))))))))))) 12.88/4.02 1(5(3(1(1(2(3(3(2(5(1(1(x1)))))))))))) -> 3(1(1(3(1(2(4(0(0(2(5(1(2(0(0(4(x1)))))))))))))))) 12.88/4.02 1(5(3(5(3(3(3(2(2(0(1(1(x1)))))))))))) -> 2(4(0(2(2(0(0(4(1(1(5(3(5(1(3(4(1(x1))))))))))))))))) 12.88/4.02 1(5(5(0(5(1(5(3(5(0(3(4(x1)))))))))))) -> 4(1(2(0(0(1(3(1(1(0(5(4(2(3(2(x1))))))))))))))) 12.88/4.02 2(0(0(1(5(1(2(5(3(2(1(4(x1)))))))))))) -> 2(5(4(0(0(2(2(1(4(1(0(4(4(1(3(0(x1)))))))))))))))) 12.88/4.02 2(0(5(4(2(2(3(3(2(5(2(5(x1)))))))))))) -> 4(5(3(2(0(4(4(0(1(2(2(1(0(2(0(0(4(x1))))))))))))))))) 12.88/4.02 2(1(1(1(3(1(1(3(2(0(3(2(x1)))))))))))) -> 2(2(1(0(0(0(2(1(2(2(2(1(4(4(x1)))))))))))))) 12.88/4.02 2(2(0(1(2(5(0(3(2(5(1(2(x1)))))))))))) -> 3(2(1(4(4(4(2(1(0(1(2(0(0(0(4(0(4(5(x1)))))))))))))))))) 12.88/4.02 2(2(0(1(2(5(5(2(1(1(1(3(x1)))))))))))) -> 2(4(4(0(4(1(3(0(0(5(2(0(4(0(4(4(4(0(x1)))))))))))))))))) 12.88/4.02 2(2(0(3(2(1(0(3(5(5(5(5(x1)))))))))))) -> 4(1(2(2(3(4(0(2(4(1(0(4(2(4(0(0(4(3(x1)))))))))))))))))) 12.88/4.02 2(2(1(5(5(3(4(3(2(5(3(2(x1)))))))))))) -> 2(2(2(1(3(3(4(0(0(4(3(3(1(3(x1)))))))))))))) 12.88/4.02 2(2(4(1(5(5(3(3(5(2(5(5(x1)))))))))))) -> 5(0(5(0(4(4(1(2(1(3(3(4(2(4(4(x1))))))))))))))) 12.88/4.02 2(3(3(0(2(5(5(2(2(4(5(4(x1)))))))))))) -> 4(0(0(0(1(0(0(5(4(1(4(1(4(2(1(x1))))))))))))))) 12.88/4.02 2(3(4(3(2(5(3(5(1(0(1(4(x1)))))))))))) -> 2(0(0(4(4(5(0(2(3(5(1(2(2(2(4(x1))))))))))))))) 12.88/4.02 2(4(3(5(2(1(5(5(2(1(5(2(x1)))))))))))) -> 4(2(1(4(1(0(4(5(0(4(2(1(2(3(5(x1))))))))))))))) 12.88/4.02 2(5(0(5(5(2(4(3(2(5(1(5(x1)))))))))))) -> 3(4(1(4(0(1(1(0(4(1(1(0(0(2(4(4(5(2(x1)))))))))))))))))) 12.88/4.02 2(5(1(5(5(1(1(0(5(5(5(5(x1)))))))))))) -> 3(3(2(4(4(4(0(2(5(1(0(2(5(1(3(x1))))))))))))))) 12.88/4.02 2(5(1(5(5(5(5(3(4(0(2(4(x1)))))))))))) -> 4(2(4(4(2(2(4(5(0(4(2(2(1(0(x1)))))))))))))) 12.88/4.02 2(5(2(0(5(3(4(1(5(2(5(5(x1)))))))))))) -> 1(2(2(0(1(4(1(2(1(2(5(1(3(0(0(4(4(1(x1)))))))))))))))))) 12.88/4.02 2(5(4(5(1(5(3(1(5(2(4(1(x1)))))))))))) -> 2(4(1(0(4(1(5(2(1(1(1(4(0(5(2(3(4(0(x1)))))))))))))))))) 12.88/4.02 3(0(5(5(5(2(0(3(1(2(5(0(x1)))))))))))) -> 0(4(0(4(2(2(2(0(1(3(4(4(1(0(5(x1))))))))))))))) 12.88/4.02 3(1(1(5(0(3(2(3(3(3(3(4(x1)))))))))))) -> 2(0(2(4(4(5(0(5(4(3(1(0(0(3(x1)))))))))))))) 12.88/4.02 3(1(3(5(3(5(5(2(5(3(0(1(x1)))))))))))) -> 2(3(1(2(0(3(2(3(5(4(0(0(0(5(0(0(x1)))))))))))))))) 12.88/4.02 3(2(1(1(5(4(1(5(0(2(3(5(x1)))))))))))) -> 2(5(4(2(3(0(0(4(5(4(4(2(4(0(0(0(2(x1))))))))))))))))) 12.88/4.02 3(2(3(1(5(2(0(3(3(4(0(5(x1)))))))))))) -> 3(0(0(0(4(0(3(0(2(3(3(2(1(4(1(x1))))))))))))))) 12.88/4.02 3(2(5(3(2(5(4(0(3(1(2(2(x1)))))))))))) -> 0(2(3(0(4(5(0(5(4(4(4(4(1(4(2(3(0(1(x1)))))))))))))))))) 12.88/4.02 3(2(5(4(3(5(2(5(1(5(2(2(x1)))))))))))) -> 4(2(3(3(0(5(3(5(1(0(0(2(1(5(0(4(x1)))))))))))))))) 12.88/4.02 3(2(5(5(5(4(4(3(2(3(1(0(x1)))))))))))) -> 0(0(2(2(4(5(4(0(4(5(5(4(0(5(x1)))))))))))))) 12.88/4.02 3(3(1(1(4(5(3(4(3(5(1(5(x1)))))))))))) -> 2(4(1(2(5(0(1(3(0(5(0(4(2(0(x1)))))))))))))) 12.88/4.02 3(3(3(1(0(2(4(3(3(4(4(5(x1)))))))))))) -> 0(2(0(4(4(4(0(5(5(0(1(3(3(5(x1)))))))))))))) 12.88/4.02 3(4(0(5(3(4(0(0(4(5(2(4(x1)))))))))))) -> 0(0(0(5(4(5(4(4(0(4(2(4(4(0(0(x1))))))))))))))) 12.88/4.02 3(4(1(5(3(1(2(3(1(0(1(3(x1)))))))))))) -> 1(3(4(3(3(5(4(0(4(0(4(4(5(0(1(x1))))))))))))))) 12.88/4.02 3(4(3(3(4(5(2(5(4(2(4(5(x1)))))))))))) -> 4(0(0(3(5(1(0(0(4(2(4(4(3(5(0(2(2(x1))))))))))))))))) 12.88/4.02 3(4(5(3(5(3(1(5(3(1(1(1(x1)))))))))))) -> 1(2(3(0(4(4(4(4(4(1(4(4(4(0(5(x1))))))))))))))) 12.88/4.02 3(5(1(5(0(1(4(4(3(5(5(1(x1)))))))))))) -> 4(4(2(5(0(4(0(2(2(4(0(0(4(2(0(1(2(4(x1)))))))))))))))))) 12.88/4.02 3(5(1(5(3(3(1(3(3(2(4(5(x1)))))))))))) -> 2(3(4(5(1(0(0(2(4(2(3(1(3(1(4(4(x1)))))))))))))))) 12.88/4.02 3(5(3(2(1(3(2(1(5(5(3(5(x1)))))))))))) -> 3(3(2(1(4(2(1(2(1(5(0(1(0(4(x1)))))))))))))) 12.88/4.02 3(5(3(2(3(3(5(3(2(5(3(4(x1)))))))))))) -> 4(1(1(3(0(4(2(1(2(1(0(4(4(1(1(1(2(x1))))))))))))))))) 12.88/4.02 4(1(1(5(5(5(3(5(5(2(3(5(x1)))))))))))) -> 4(0(1(5(1(0(2(4(1(2(0(4(2(2(3(4(0(0(x1)))))))))))))))))) 12.88/4.02 4(1(2(4(5(4(1(5(5(5(2(1(x1)))))))))))) -> 4(4(3(0(4(1(1(2(1(1(0(4(1(3(0(4(0(0(x1)))))))))))))))))) 12.88/4.02 4(2(5(3(3(3(3(2(1(5(4(5(x1)))))))))))) -> 3(0(3(4(3(0(1(1(4(3(4(2(0(4(1(3(1(2(x1)))))))))))))))))) 12.88/4.02 4(2(5(5(3(4(5(4(2(5(2(0(x1)))))))))))) -> 0(2(2(2(5(1(4(0(4(0(2(1(5(0(x1)))))))))))))) 12.88/4.02 4(3(0(0(1(5(5(3(0(3(3(2(x1)))))))))))) -> 3(1(3(5(0(0(0(3(1(4(5(0(4(0(x1)))))))))))))) 12.88/4.02 4(3(5(2(5(3(5(1(3(0(5(2(x1)))))))))))) -> 2(5(0(4(4(1(4(4(0(4(0(0(4(2(4(1(3(x1))))))))))))))))) 12.88/4.02 4(5(0(5(0(1(1(2(1(2(4(0(x1)))))))))))) -> 4(2(0(0(0(5(4(2(3(0(4(4(0(1(x1)))))))))))))) 12.88/4.02 4(5(5(2(3(2(5(0(2(0(3(1(x1)))))))))))) -> 1(0(0(3(4(1(5(1(0(4(4(0(3(4(0(0(x1)))))))))))))))) 12.88/4.02 4(5(5(3(2(1(0(1(1(0(5(5(x1)))))))))))) -> 0(5(0(4(0(3(0(1(2(2(3(2(3(4(x1)))))))))))))) 12.88/4.02 5(0(5(5(3(1(5(5(3(3(5(0(x1)))))))))))) -> 0(4(4(5(4(0(3(5(3(4(3(5(0(4(1(3(1(2(x1)))))))))))))))))) 12.88/4.02 5(1(0(3(1(5(5(3(0(3(5(1(x1)))))))))))) -> 5(4(1(1(0(4(0(3(3(1(3(0(4(0(1(4(4(4(x1)))))))))))))))))) 12.88/4.02 5(1(1(0(3(1(5(3(1(1(0(5(x1)))))))))))) -> 4(1(0(5(4(0(4(5(2(1(5(1(4(0(3(x1))))))))))))))) 12.88/4.02 5(1(1(4(3(1(2(5(5(4(2(2(x1)))))))))))) -> 0(1(0(0(2(4(0(2(5(0(0(5(0(0(x1)))))))))))))) 12.88/4.02 5(1(2(2(5(2(4(1(3(2(3(1(x1)))))))))))) -> 2(1(4(4(2(4(4(0(0(4(4(4(3(1(4(0(3(1(x1)))))))))))))))))) 12.88/4.02 5(1(2(3(3(1(1(2(3(1(5(1(x1)))))))))))) -> 5(2(0(3(3(5(2(4(4(1(4(4(3(4(1(x1))))))))))))))) 12.88/4.02 5(1(5(1(3(2(4(5(3(5(4(0(x1)))))))))))) -> 0(1(4(0(0(4(0(5(2(1(4(4(4(3(3(3(x1)))))))))))))))) 12.88/4.02 5(2(1(4(3(5(3(1(5(3(5(1(x1)))))))))))) -> 0(1(1(1(1(2(0(5(0(0(0(2(3(0(0(1(x1)))))))))))))))) 12.88/4.02 5(2(1(5(5(0(3(5(5(5(3(0(x1)))))))))))) -> 2(3(4(1(1(0(2(3(0(4(1(0(2(0(0(0(3(3(x1)))))))))))))))))) 12.88/4.02 5(2(3(5(3(0(3(3(1(4(0(2(x1)))))))))))) -> 4(5(4(0(0(2(1(1(0(3(4(4(4(3(x1)))))))))))))) 12.88/4.02 5(2(4(3(0(2(5(2(1(1(5(0(x1)))))))))))) -> 0(1(1(0(0(0(0(0(4(0(0(5(4(5(x1)))))))))))))) 12.88/4.02 5(2(5(4(4(2(3(5(0(5(2(5(x1)))))))))))) -> 4(1(4(2(3(4(3(4(4(4(2(1(4(0(0(0(1(x1))))))))))))))))) 12.88/4.02 5(3(2(0(2(0(4(2(5(1(5(2(x1)))))))))))) -> 4(3(0(4(5(0(3(4(0(3(5(1(1(1(4(x1))))))))))))))) 12.88/4.02 5(3(3(2(1(1(3(3(2(5(5(1(x1)))))))))))) -> 3(1(4(0(1(4(2(0(3(0(0(3(1(2(4(x1))))))))))))))) 12.88/4.02 5(3(3(3(1(5(2(0(1(5(4(0(x1)))))))))))) -> 3(5(0(3(5(0(0(4(2(3(4(0(1(2(2(3(0(0(x1)))))))))))))))))) 12.88/4.02 5(3(5(2(5(5(2(4(2(1(2(2(x1)))))))))))) -> 0(1(3(4(4(4(0(1(5(0(1(1(2(1(x1)))))))))))))) 12.88/4.02 5(3(5(4(4(5(1(3(4(5(5(5(x1)))))))))))) -> 5(3(4(4(0(4(4(0(1(5(0(5(2(2(3(4(0(4(x1)))))))))))))))))) 12.88/4.02 5(4(3(3(0(3(2(5(4(0(5(5(x1)))))))))))) -> 1(1(4(1(3(2(2(0(1(2(2(0(0(1(1(4(3(x1))))))))))))))))) 12.88/4.02 5(4(3(3(3(2(5(2(4(1(4(2(x1)))))))))))) -> 3(0(4(4(4(0(4(4(1(4(4(1(1(2(2(4(5(4(x1)))))))))))))))))) 12.88/4.02 5(5(0(0(3(4(3(2(3(4(5(5(x1)))))))))))) -> 0(2(1(0(1(2(4(0(0(5(3(2(2(2(0(x1))))))))))))))) 12.88/4.02 5(5(1(2(5(2(5(3(3(3(4(5(x1)))))))))))) -> 3(5(1(3(1(5(2(4(0(2(3(3(4(4(2(x1))))))))))))))) 12.88/4.02 5(5(1(3(3(2(0(5(5(1(0(0(x1)))))))))))) -> 5(0(4(0(3(4(5(1(2(4(4(4(3(0(0(0(1(x1))))))))))))))))) 12.88/4.02 5(5(1(5(1(5(3(4(2(5(4(5(x1)))))))))))) -> 0(5(4(0(4(0(4(1(2(2(1(1(3(4(4(0(3(3(x1)))))))))))))))))) 12.88/4.02 5(5(1(5(2(5(1(5(1(1(1(4(x1)))))))))))) -> 1(4(1(3(4(4(5(4(0(5(4(5(0(4(3(5(2(x1))))))))))))))))) 12.88/4.02 5(5(2(5(3(3(1(0(1(4(5(5(x1)))))))))))) -> 2(4(3(0(5(2(3(0(5(4(4(0(3(2(3(2(5(x1))))))))))))))))) 12.88/4.02 5(5(3(1(0(3(3(0(2(3(5(3(x1)))))))))))) -> 2(4(5(2(2(2(0(0(4(4(3(0(4(0(0(2(4(4(x1)))))))))))))))))) 12.88/4.02 5(5(3(3(5(3(3(0(4(5(3(0(x1)))))))))))) -> 4(4(0(2(4(0(3(4(1(4(1(3(3(4(4(4(4(3(x1)))))))))))))))))) 12.88/4.02 5(5(3(4(0(2(5(5(3(2(4(1(x1)))))))))))) -> 2(4(3(0(4(0(1(3(2(4(1(1(0(1(1(1(0(1(x1)))))))))))))))))) 12.88/4.02 5(5(4(5(5(2(5(3(1(2(1(1(x1)))))))))))) -> 0(3(0(2(2(4(4(3(1(4(4(2(5(0(0(0(x1)))))))))))))))) 12.88/4.02 5(5(5(5(5(3(2(5(2(0(5(5(x1)))))))))))) -> 5(3(5(3(3(1(5(5(4(1(3(4(0(1(x1)))))))))))))) 12.88/4.02 12.88/4.02 12.88/4.02 12.88/4.02 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (2) 12.88/4.02 Obligation: 12.88/4.02 Q restricted rewrite system: 12.88/4.02 The TRS R consists of the following rules: 12.88/4.02 12.88/4.02 2(5(3(3(3(3(5(2(1(4(2(0(x1)))))))))))) -> 0(1(3(4(0(5(5(3(0(2(2(4(3(2(3(x1))))))))))))))) 12.88/4.02 12.88/4.02 Q is empty. 12.88/4.02 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (3) Overlay + Local Confluence (EQUIVALENT) 12.88/4.02 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (4) 12.88/4.02 Obligation: 12.88/4.02 Q restricted rewrite system: 12.88/4.02 The TRS R consists of the following rules: 12.88/4.02 12.88/4.02 2(5(3(3(3(3(5(2(1(4(2(0(x1)))))))))))) -> 0(1(3(4(0(5(5(3(0(2(2(4(3(2(3(x1))))))))))))))) 12.88/4.02 12.88/4.02 The set Q consists of the following terms: 12.88/4.02 12.88/4.02 2(5(3(3(3(3(5(2(1(4(2(0(x0)))))))))))) 12.88/4.02 12.88/4.02 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (5) DependencyPairsProof (EQUIVALENT) 12.88/4.02 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (6) 12.88/4.02 Obligation: 12.88/4.02 Q DP problem: 12.88/4.02 The TRS P consists of the following rules: 12.88/4.02 12.88/4.02 2^1(5(3(3(3(3(5(2(1(4(2(0(x1)))))))))))) -> 2^1(2(4(3(2(3(x1)))))) 12.88/4.02 2^1(5(3(3(3(3(5(2(1(4(2(0(x1)))))))))))) -> 2^1(4(3(2(3(x1))))) 12.88/4.02 2^1(5(3(3(3(3(5(2(1(4(2(0(x1)))))))))))) -> 2^1(3(x1)) 12.88/4.02 12.88/4.02 The TRS R consists of the following rules: 12.88/4.02 12.88/4.02 2(5(3(3(3(3(5(2(1(4(2(0(x1)))))))))))) -> 0(1(3(4(0(5(5(3(0(2(2(4(3(2(3(x1))))))))))))))) 12.88/4.02 12.88/4.02 The set Q consists of the following terms: 12.88/4.02 12.88/4.02 2(5(3(3(3(3(5(2(1(4(2(0(x0)))))))))))) 12.88/4.02 12.88/4.02 We have to consider all minimal (P,Q,R)-chains. 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (7) DependencyGraphProof (EQUIVALENT) 12.88/4.02 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes. 12.88/4.02 ---------------------------------------- 12.88/4.02 12.88/4.02 (8) 12.88/4.02 TRUE 12.88/4.09 EOF