29.99/8.47 YES 31.21/9.03 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 31.21/9.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.21/9.03 31.21/9.03 31.21/9.03 Termination w.r.t. Q of the given QTRS could be proven: 31.21/9.03 31.21/9.03 (0) QTRS 31.21/9.03 (1) QTRSRRRProof [EQUIVALENT, 390 ms] 31.21/9.03 (2) QTRS 31.21/9.03 (3) DependencyPairsProof [EQUIVALENT, 85 ms] 31.21/9.03 (4) QDP 31.21/9.03 (5) DependencyGraphProof [EQUIVALENT, 4 ms] 31.21/9.03 (6) QDP 31.21/9.03 (7) UsableRulesProof [EQUIVALENT, 0 ms] 31.21/9.03 (8) QDP 31.21/9.03 (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] 31.21/9.03 (10) YES 31.21/9.03 31.21/9.03 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (0) 31.21/9.03 Obligation: 31.21/9.03 Q restricted rewrite system: 31.21/9.03 The TRS R consists of the following rules: 31.21/9.03 31.21/9.03 0(0(2(0(1(1(1(1(3(3(2(3(x1)))))))))))) -> 3(2(4(0(0(5(4(4(0(4(4(4(1(3(1(4(5(x1))))))))))))))))) 31.21/9.03 0(0(2(2(1(1(2(3(1(5(1(2(x1)))))))))))) -> 0(5(4(5(4(4(5(2(0(0(5(5(4(0(2(4(5(1(x1)))))))))))))))))) 31.21/9.03 0(1(0(1(3(5(0(2(0(5(0(4(x1)))))))))))) -> 0(1(4(4(5(4(1(4(3(0(0(1(5(2(5(4(4(4(x1)))))))))))))))))) 31.21/9.03 0(1(2(3(2(3(5(1(3(3(5(3(x1)))))))))))) -> 0(4(5(0(4(2(4(1(4(4(4(5(5(1(5(x1))))))))))))))) 31.21/9.03 0(1(3(1(3(3(1(1(0(5(1(0(x1)))))))))))) -> 4(4(3(5(2(1(5(2(5(4(3(4(1(3(5(4(x1)))))))))))))))) 31.21/9.03 0(1(4(0(3(2(2(2(4(2(2(3(x1)))))))))))) -> 4(4(4(4(4(1(3(1(5(5(4(4(1(3(4(4(x1)))))))))))))))) 31.21/9.03 0(1(5(1(5(1(2(4(5(2(0(0(x1)))))))))))) -> 3(4(4(5(5(5(4(1(0(3(4(0(4(5(4(5(3(x1))))))))))))))))) 31.21/9.03 0(2(0(1(1(1(1(2(5(1(2(2(x1)))))))))))) -> 5(3(3(0(3(2(4(4(2(3(4(1(5(4(4(4(0(4(x1)))))))))))))))))) 31.21/9.03 0(2(2(0(1(1(0(1(3(0(3(5(x1)))))))))))) -> 4(2(1(3(3(4(5(2(5(4(5(5(4(4(2(3(4(1(x1)))))))))))))))))) 31.21/9.03 0(2(2(2(2(0(4(0(2(3(5(1(x1)))))))))))) -> 3(2(1(4(5(2(5(5(4(4(5(5(0(0(4(1(x1)))))))))))))))) 31.21/9.03 0(2(3(3(1(0(5(2(2(0(0(0(x1)))))))))))) -> 1(1(4(5(3(5(2(2(3(1(4(5(4(4(3(x1))))))))))))))) 31.21/9.03 0(2(5(1(5(0(2(0(2(3(2(0(x1)))))))))))) -> 5(2(3(4(4(1(4(5(4(5(0(0(1(4(5(5(1(1(x1)))))))))))))))))) 31.21/9.03 0(2(5(5(0(3(0(3(2(2(0(1(x1)))))))))))) -> 0(4(5(2(4(2(5(4(1(2(2(2(0(5(4(1(x1)))))))))))))))) 31.21/9.03 0(3(3(1(3(0(4(2(2(3(1(0(x1)))))))))))) -> 5(5(4(5(3(3(4(5(4(5(0(1(0(3(0(1(x1)))))))))))))))) 31.21/9.03 0(3(5(1(0(3(1(1(1(0(2(2(x1)))))))))))) -> 4(3(4(4(0(3(2(1(2(4(2(5(5(5(4(5(4(4(x1)))))))))))))))))) 31.21/9.03 0(3(5(2(1(3(0(3(2(3(1(0(x1)))))))))))) -> 5(2(5(3(1(3(4(0(4(0(0(4(4(3(2(x1))))))))))))))) 31.21/9.03 0(4(3(3(2(2(3(4(5(3(2(1(x1)))))))))))) -> 0(5(4(1(4(4(4(3(5(4(5(2(4(4(2(2(1(x1))))))))))))))))) 31.21/9.03 0(5(3(1(3(2(5(2(0(0(2(1(x1)))))))))))) -> 0(4(4(5(4(3(5(2(5(5(2(5(4(5(5(4(5(x1))))))))))))))))) 31.21/9.03 1(0(0(1(3(3(3(2(0(3(0(4(x1)))))))))))) -> 4(4(3(0(4(5(0(5(4(4(0(4(0(0(x1)))))))))))))) 31.21/9.03 1(0(0(2(4(2(2(2(2(4(2(0(x1)))))))))))) -> 5(1(5(3(5(4(5(0(3(3(4(1(4(4(x1)))))))))))))) 31.21/9.03 1(0(2(0(3(3(3(3(3(4(3(3(x1)))))))))))) -> 5(1(5(3(1(4(4(5(3(1(5(4(5(4(4(1(2(x1))))))))))))))))) 31.21/9.03 1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 3(5(3(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))))) 31.21/9.03 1(0(3(2(0(2(2(2(1(2(3(2(x1)))))))))))) -> 3(3(2(4(4(0(3(4(0(1(4(5(2(2(4(x1))))))))))))))) 31.21/9.03 1(0(3(3(2(2(1(1(0(2(3(1(x1)))))))))))) -> 2(4(3(4(4(1(4(5(1(5(1(0(5(4(3(x1))))))))))))))) 31.21/9.03 1(1(0(0(5(2(3(2(1(1(0(5(x1)))))))))))) -> 5(4(5(4(0(1(2(1(2(3(3(0(4(1(x1)))))))))))))) 31.21/9.03 1(1(0(2(3(2(2(2(0(5(1(4(x1)))))))))))) -> 4(4(4(1(4(4(4(4(5(5(2(1(4(3(0(5(4(2(x1)))))))))))))))))) 31.21/9.03 1(1(1(3(1(2(2(4(3(0(0(2(x1)))))))))))) -> 5(2(4(3(4(4(1(1(3(1(4(5(2(4(0(2(x1)))))))))))))))) 31.21/9.03 1(2(1(1(3(0(2(2(4(1(1(3(x1)))))))))))) -> 1(4(5(4(1(1(5(1(1(2(5(4(1(1(3(4(x1)))))))))))))))) 31.21/9.03 1(2(2(2(3(2(0(2(5(3(5(3(x1)))))))))))) -> 1(4(0(5(3(3(5(3(3(4(3(4(2(1(x1)))))))))))))) 31.21/9.03 1(2(5(0(2(3(0(0(2(0(5(2(x1)))))))))))) -> 5(2(2(1(4(0(4(5(4(1(0(1(5(4(1(3(5(4(x1)))))))))))))))))) 31.21/9.03 1(3(0(0(2(3(0(4(2(0(2(5(x1)))))))))))) -> 0(2(1(4(2(1(4(5(0(5(5(4(5(5(4(1(4(5(x1)))))))))))))))))) 31.21/9.03 1(3(1(1(3(0(3(3(3(5(1(5(x1)))))))))))) -> 5(3(3(3(4(4(2(5(0(0(4(4(4(1(1(x1))))))))))))))) 31.21/9.03 1(3(1(2(0(2(0(3(3(1(1(1(x1)))))))))))) -> 1(5(4(4(5(4(4(4(3(0(1(5(4(1(x1)))))))))))))) 31.21/9.03 1(3(3(1(0(0(0(2(5(1(1(1(x1)))))))))))) -> 2(1(2(4(4(4(4(1(2(1(3(5(4(5(0(5(2(x1))))))))))))))))) 31.21/9.03 1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 1(3(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))))))))) 31.21/9.03 1(5(2(2(1(1(5(0(3(3(0(4(x1)))))))))))) -> 4(2(4(5(4(5(4(3(5(5(4(4(4(1(1(2(x1)))))))))))))))) 31.21/9.03 1(5(3(3(4(0(3(1(1(2(1(0(x1)))))))))))) -> 4(4(4(2(4(2(2(4(4(5(4(5(4(0(0(5(2(x1))))))))))))))))) 31.21/9.03 2(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 0(0(0(5(4(1(5(4(1(4(3(4(5(3(4(5(2(x1))))))))))))))))) 31.21/9.03 2(0(3(2(2(0(2(2(3(0(0(1(x1)))))))))))) -> 5(4(3(4(4(1(5(4(2(4(1(5(4(5(3(0(0(x1))))))))))))))))) 31.21/9.03 2(0(3(3(2(2(3(1(2(3(0(3(x1)))))))))))) -> 5(4(5(5(1(5(4(4(4(5(4(0(2(1(2(0(2(x1))))))))))))))))) 31.21/9.03 2(1(0(0(0(3(3(3(3(0(1(1(x1)))))))))))) -> 5(3(2(2(4(2(2(4(0(4(5(3(4(2(5(x1))))))))))))))) 31.21/9.03 2(1(0(2(1(3(1(2(5(1(3(5(x1)))))))))))) -> 2(5(1(3(5(1(4(4(3(1(0(1(4(5(x1)))))))))))))) 31.21/9.03 2(1(0(2(2(1(1(3(1(1(1(3(x1)))))))))))) -> 5(5(4(5(5(2(2(0(1(0(4(4(2(5(2(0(x1)))))))))))))))) 31.21/9.03 2(1(1(0(0(5(5(0(0(2(5(5(x1)))))))))))) -> 2(2(5(2(3(2(5(4(1(1(4(4(5(5(x1)))))))))))))) 31.21/9.03 2(1(3(0(0(1(0(3(3(1(0(4(x1)))))))))))) -> 4(4(5(3(3(4(2(3(5(4(2(4(4(5(3(3(x1)))))))))))))))) 31.21/9.03 2(1(5(1(1(5(0(2(5(1(3(0(x1)))))))))))) -> 3(5(4(2(3(4(4(3(3(4(0(5(2(0(5(4(x1)))))))))))))))) 31.21/9.03 2(2(0(3(2(0(1(0(2(3(3(2(x1)))))))))))) -> 5(5(5(0(2(2(4(1(4(4(3(3(0(0(2(x1))))))))))))))) 31.21/9.03 2(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 4(4(3(5(4(5(4(0(2(2(0(1(3(4(4(3(5(x1))))))))))))))))) 31.21/9.03 2(2(1(1(0(2(0(0(2(3(0(1(x1)))))))))))) -> 5(4(1(1(4(3(5(5(0(1(4(3(5(4(1(1(4(x1))))))))))))))))) 31.21/9.03 2(2(2(0(3(1(0(2(5(0(0(1(x1)))))))))))) -> 5(3(0(5(1(4(4(5(2(4(4(2(4(4(0(5(x1)))))))))))))))) 31.21/9.03 2(2(2(0(4(2(0(1(3(1(2(2(x1)))))))))))) -> 4(4(5(4(0(4(2(5(4(3(0(4(4(4(4(5(3(2(x1)))))))))))))))))) 31.21/9.03 2(2(2(4(1(1(0(1(1(1(4(0(x1)))))))))))) -> 3(3(5(4(1(4(4(3(5(4(4(4(1(4(4(1(4(4(x1)))))))))))))))))) 31.21/9.03 2(2(3(0(4(2(3(1(1(0(4(5(x1)))))))))))) -> 4(1(3(2(5(5(5(3(3(5(2(4(1(5(x1)))))))))))))) 31.21/9.03 2(2(3(4(3(3(5(1(2(4(2(2(x1)))))))))))) -> 3(4(3(5(3(4(1(4(0(4(5(5(0(2(x1)))))))))))))) 31.21/9.03 2(2(3(5(0(2(2(2(3(3(2(2(x1)))))))))))) -> 3(4(0(5(3(2(0(4(5(4(0(1(5(4(1(2(4(x1))))))))))))))))) 31.21/9.03 2(3(0(2(0(3(0(0(3(2(2(3(x1)))))))))))) -> 4(5(4(0(2(3(4(5(5(4(1(3(3(1(5(1(1(x1))))))))))))))))) 31.21/9.03 2(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 2(0(1(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))))) 31.21/9.03 2(3(1(2(1(1(2(0(4(5(1(3(x1)))))))))))) -> 4(0(4(1(4(1(4(5(3(3(3(4(1(5(0(4(1(x1))))))))))))))))) 31.21/9.03 2(3(1(3(5(1(4(5(1(1(5(1(x1)))))))))))) -> 5(0(4(0(4(1(0(4(1(5(5(3(4(4(3(x1))))))))))))))) 31.21/9.03 2(3(2(1(2(3(1(5(5(2(3(0(x1)))))))))))) -> 2(4(5(2(4(1(4(0(1(4(3(2(3(4(1(x1))))))))))))))) 31.21/9.03 2(3(2(2(3(2(0(3(4(5(2(1(x1)))))))))))) -> 3(4(1(5(0(0(2(5(2(0(5(3(4(2(x1)))))))))))))) 31.21/9.03 2(3(3(1(1(0(0(2(2(1(2(5(x1)))))))))))) -> 5(3(4(4(1(5(2(1(1(5(0(4(5(3(x1)))))))))))))) 31.21/9.03 2(3(3(2(4(3(0(2(3(3(5(1(x1)))))))))))) -> 0(0(4(3(4(4(3(0(4(1(0(1(4(4(x1)))))))))))))) 31.21/9.03 2(4(0(0(0(3(1(1(2(3(2(3(x1)))))))))))) -> 0(0(3(5(4(2(5(4(3(3(4(4(1(0(3(x1))))))))))))))) 31.21/9.03 2(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 0(4(1(5(4(0(5(4(0(2(4(0(1(2(x1)))))))))))))) 31.21/9.03 2(5(1(5(1(4(3(3(0(4(1(1(x1)))))))))))) -> 4(3(5(5(5(3(1(3(4(0(3(5(4(2(x1)))))))))))))) 31.21/9.03 3(0(0(0(2(2(4(1(2(1(1(1(x1)))))))))))) -> 4(0(5(2(5(4(3(2(5(4(3(5(4(2(5(4(3(x1))))))))))))))))) 31.21/9.03 3(0(0(3(1(1(3(3(1(2(0(3(x1)))))))))))) -> 5(0(1(4(5(3(0(5(0(0(4(4(2(4(4(2(5(3(x1)))))))))))))))))) 31.21/9.03 3(0(1(4(2(0(3(0(5(1(4(2(x1)))))))))))) -> 0(5(4(5(2(1(5(5(4(3(5(4(5(5(4(3(2(x1))))))))))))))))) 31.21/9.03 3(0(2(3(3(0(5(3(4(5(0(0(x1)))))))))))) -> 5(4(4(0(4(5(3(3(5(3(5(0(4(4(4(x1))))))))))))))) 31.21/9.03 3(0(3(0(0(3(0(3(5(1(3(2(x1)))))))))))) -> 3(4(0(5(4(4(4(5(4(1(0(2(1(4(1(5(3(4(x1)))))))))))))))))) 31.21/9.03 3(0(3(3(4(0(5(1(3(2(3(1(x1)))))))))))) -> 3(4(5(2(1(1(3(4(4(4(3(5(5(0(4(4(5(x1))))))))))))))))) 31.21/9.03 3(1(0(0(5(4(3(2(2(3(3(2(x1)))))))))))) -> 5(2(1(4(1(5(3(3(4(4(0(5(2(5(1(x1))))))))))))))) 31.21/9.03 3(1(0(5(1(1(3(0(5(1(2(1(x1)))))))))))) -> 4(0(4(4(5(4(4(3(4(5(4(4(2(1(0(1(x1)))))))))))))))) 31.21/9.03 3(1(1(1(2(0(1(0(0(5(0(4(x1)))))))))))) -> 5(0(1(5(5(5(0(1(5(4(4(3(2(0(4(x1))))))))))))))) 31.21/9.03 3(1(1(1(3(0(3(1(0(3(4(0(x1)))))))))))) -> 0(5(3(1(4(4(1(5(5(5(5(4(1(5(x1)))))))))))))) 31.21/9.03 3(1(1(2(0(2(5(5(3(3(1(3(x1)))))))))))) -> 4(2(1(5(1(5(4(0(3(3(0(4(2(4(x1)))))))))))))) 31.21/9.03 3(1(5(0(0(1(0(4(2(1(5(3(x1)))))))))))) -> 1(5(0(0(4(1(4(5(4(5(4(1(4(4(0(4(x1)))))))))))))))) 31.21/9.03 3(2(0(0(3(0(2(3(1(3(3(2(x1)))))))))))) -> 1(4(5(4(4(0(3(1(5(4(3(3(0(4(4(5(4(x1))))))))))))))))) 31.21/9.03 3(2(2(5(1(5(0(3(4(2(4(3(x1)))))))))))) -> 1(5(4(5(2(4(1(5(4(4(4(2(4(4(5(4(0(4(x1)))))))))))))))))) 31.21/9.03 3(3(0(2(4(3(0(1(5(5(3(0(x1)))))))))))) -> 5(1(4(3(4(5(3(4(4(0(1(3(1(4(0(x1))))))))))))))) 31.21/9.03 3(3(1(1(2(3(5(5(2(4(0(0(x1)))))))))))) -> 0(1(5(5(4(5(5(2(4(4(4(1(2(5(4(5(4(x1))))))))))))))))) 31.21/9.03 3(3(1(2(2(1(3(3(0(2(0(4(x1)))))))))))) -> 2(5(4(3(1(4(4(4(0(4(2(3(0(2(x1)))))))))))))) 31.21/9.03 3(3(1(2(3(0(2(0(3(0(1(0(x1)))))))))))) -> 3(0(1(3(0(4(5(5(1(0(5(2(4(1(2(4(x1)))))))))))))))) 31.21/9.03 3(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 3(4(4(5(4(1(3(1(4(4(0(5(4(3(2(0(2(x1))))))))))))))))) 31.21/9.03 3(3(2(3(0(1(3(3(5(1(1(2(x1)))))))))))) -> 2(5(5(5(4(4(2(5(4(1(5(5(4(1(4(5(2(x1))))))))))))))))) 31.21/9.03 3(5(1(2(1(0(3(2(2(2(0(1(x1)))))))))))) -> 1(5(5(4(1(2(5(5(4(4(4(4(2(1(2(5(4(5(x1)))))))))))))))))) 31.21/9.03 3(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 0(0(4(5(4(5(2(1(3(0(5(4(4(2(x1)))))))))))))) 31.21/9.03 4(0(0(0(2(5(0(2(0(5(5(0(x1)))))))))))) -> 4(5(3(4(3(4(2(4(4(3(0(4(1(2(5(x1))))))))))))))) 31.21/9.03 4(0(0(3(1(3(5(0(3(3(2(4(x1)))))))))))) -> 4(0(2(4(0(1(2(4(4(0(4(1(4(2(4(4(x1)))))))))))))))) 31.21/9.03 4(0(1(3(1(2(3(3(1(1(2(2(x1)))))))))))) -> 1(4(5(3(0(1(4(3(2(4(1(5(3(4(0(x1))))))))))))))) 31.21/9.03 4(1(3(1(1(1(1(2(1(0(4(3(x1)))))))))))) -> 0(5(4(2(4(4(5(4(2(4(0(0(4(4(4(4(5(x1))))))))))))))))) 31.21/9.03 4(1(3(3(0(0(3(3(3(3(3(0(x1)))))))))))) -> 4(0(2(1(4(0(5(1(0(4(2(4(5(2(x1)))))))))))))) 31.21/9.03 4(1(5(0(2(2(1(3(0(0(3(1(x1)))))))))))) -> 4(5(4(1(4(1(4(4(5(5(4(4(3(4(4(3(2(4(x1)))))))))))))))))) 31.21/9.03 4(3(3(2(0(1(1(2(0(1(5(5(x1)))))))))))) -> 3(0(2(4(1(4(4(4(5(4(4(4(5(0(4(x1))))))))))))))) 31.21/9.03 4(4(3(0(0(2(2(5(5(3(1(1(x1)))))))))))) -> 5(5(4(4(0(4(2(5(4(2(4(1(4(1(1(x1))))))))))))))) 31.21/9.03 31.21/9.03 Q is empty. 31.21/9.03 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (1) QTRSRRRProof (EQUIVALENT) 31.21/9.03 Used ordering: 31.21/9.03 Polynomial interpretation [POLO]: 31.21/9.03 31.21/9.03 POL(0(x_1)) = 1 + x_1 31.21/9.03 POL(1(x_1)) = 1 + x_1 31.21/9.03 POL(2(x_1)) = 1 + x_1 31.21/9.03 POL(3(x_1)) = 1 + x_1 31.21/9.03 POL(4(x_1)) = x_1 31.21/9.03 POL(5(x_1)) = x_1 31.21/9.03 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 31.21/9.03 31.21/9.03 0(0(2(0(1(1(1(1(3(3(2(3(x1)))))))))))) -> 3(2(4(0(0(5(4(4(0(4(4(4(1(3(1(4(5(x1))))))))))))))))) 31.21/9.03 0(0(2(2(1(1(2(3(1(5(1(2(x1)))))))))))) -> 0(5(4(5(4(4(5(2(0(0(5(5(4(0(2(4(5(1(x1)))))))))))))))))) 31.21/9.03 0(1(0(1(3(5(0(2(0(5(0(4(x1)))))))))))) -> 0(1(4(4(5(4(1(4(3(0(0(1(5(2(5(4(4(4(x1)))))))))))))))))) 31.21/9.03 0(1(2(3(2(3(5(1(3(3(5(3(x1)))))))))))) -> 0(4(5(0(4(2(4(1(4(4(4(5(5(1(5(x1))))))))))))))) 31.21/9.03 0(1(3(1(3(3(1(1(0(5(1(0(x1)))))))))))) -> 4(4(3(5(2(1(5(2(5(4(3(4(1(3(5(4(x1)))))))))))))))) 31.21/9.03 0(1(4(0(3(2(2(2(4(2(2(3(x1)))))))))))) -> 4(4(4(4(4(1(3(1(5(5(4(4(1(3(4(4(x1)))))))))))))))) 31.21/9.03 0(1(5(1(5(1(2(4(5(2(0(0(x1)))))))))))) -> 3(4(4(5(5(5(4(1(0(3(4(0(4(5(4(5(3(x1))))))))))))))))) 31.21/9.03 0(2(0(1(1(1(1(2(5(1(2(2(x1)))))))))))) -> 5(3(3(0(3(2(4(4(2(3(4(1(5(4(4(4(0(4(x1)))))))))))))))))) 31.21/9.03 0(2(2(0(1(1(0(1(3(0(3(5(x1)))))))))))) -> 4(2(1(3(3(4(5(2(5(4(5(5(4(4(2(3(4(1(x1)))))))))))))))))) 31.21/9.03 0(2(2(2(2(0(4(0(2(3(5(1(x1)))))))))))) -> 3(2(1(4(5(2(5(5(4(4(5(5(0(0(4(1(x1)))))))))))))))) 31.21/9.03 0(2(3(3(1(0(5(2(2(0(0(0(x1)))))))))))) -> 1(1(4(5(3(5(2(2(3(1(4(5(4(4(3(x1))))))))))))))) 31.21/9.03 0(2(5(1(5(0(2(0(2(3(2(0(x1)))))))))))) -> 5(2(3(4(4(1(4(5(4(5(0(0(1(4(5(5(1(1(x1)))))))))))))))))) 31.21/9.03 0(2(5(5(0(3(0(3(2(2(0(1(x1)))))))))))) -> 0(4(5(2(4(2(5(4(1(2(2(2(0(5(4(1(x1)))))))))))))))) 31.21/9.03 0(3(3(1(3(0(4(2(2(3(1(0(x1)))))))))))) -> 5(5(4(5(3(3(4(5(4(5(0(1(0(3(0(1(x1)))))))))))))))) 31.21/9.03 0(3(5(1(0(3(1(1(1(0(2(2(x1)))))))))))) -> 4(3(4(4(0(3(2(1(2(4(2(5(5(5(4(5(4(4(x1)))))))))))))))))) 31.21/9.03 0(3(5(2(1(3(0(3(2(3(1(0(x1)))))))))))) -> 5(2(5(3(1(3(4(0(4(0(0(4(4(3(2(x1))))))))))))))) 31.21/9.03 0(4(3(3(2(2(3(4(5(3(2(1(x1)))))))))))) -> 0(5(4(1(4(4(4(3(5(4(5(2(4(4(2(2(1(x1))))))))))))))))) 31.21/9.03 0(5(3(1(3(2(5(2(0(0(2(1(x1)))))))))))) -> 0(4(4(5(4(3(5(2(5(5(2(5(4(5(5(4(5(x1))))))))))))))))) 31.21/9.03 1(0(0(1(3(3(3(2(0(3(0(4(x1)))))))))))) -> 4(4(3(0(4(5(0(5(4(4(0(4(0(0(x1)))))))))))))) 31.21/9.03 1(0(0(2(4(2(2(2(2(4(2(0(x1)))))))))))) -> 5(1(5(3(5(4(5(0(3(3(4(1(4(4(x1)))))))))))))) 31.21/9.03 1(0(2(0(3(3(3(3(3(4(3(3(x1)))))))))))) -> 5(1(5(3(1(4(4(5(3(1(5(4(5(4(4(1(2(x1))))))))))))))))) 31.21/9.03 1(0(3(2(0(2(2(2(1(2(3(2(x1)))))))))))) -> 3(3(2(4(4(0(3(4(0(1(4(5(2(2(4(x1))))))))))))))) 31.21/9.03 1(0(3(3(2(2(1(1(0(2(3(1(x1)))))))))))) -> 2(4(3(4(4(1(4(5(1(5(1(0(5(4(3(x1))))))))))))))) 31.21/9.03 1(1(0(0(5(2(3(2(1(1(0(5(x1)))))))))))) -> 5(4(5(4(0(1(2(1(2(3(3(0(4(1(x1)))))))))))))) 31.21/9.03 1(1(0(2(3(2(2(2(0(5(1(4(x1)))))))))))) -> 4(4(4(1(4(4(4(4(5(5(2(1(4(3(0(5(4(2(x1)))))))))))))))))) 31.21/9.03 1(1(1(3(1(2(2(4(3(0(0(2(x1)))))))))))) -> 5(2(4(3(4(4(1(1(3(1(4(5(2(4(0(2(x1)))))))))))))))) 31.21/9.03 1(2(1(1(3(0(2(2(4(1(1(3(x1)))))))))))) -> 1(4(5(4(1(1(5(1(1(2(5(4(1(1(3(4(x1)))))))))))))))) 31.21/9.03 1(2(2(2(3(2(0(2(5(3(5(3(x1)))))))))))) -> 1(4(0(5(3(3(5(3(3(4(3(4(2(1(x1)))))))))))))) 31.21/9.03 1(2(5(0(2(3(0(0(2(0(5(2(x1)))))))))))) -> 5(2(2(1(4(0(4(5(4(1(0(1(5(4(1(3(5(4(x1)))))))))))))))))) 31.21/9.03 1(3(0(0(2(3(0(4(2(0(2(5(x1)))))))))))) -> 0(2(1(4(2(1(4(5(0(5(5(4(5(5(4(1(4(5(x1)))))))))))))))))) 31.21/9.03 1(3(1(1(3(0(3(3(3(5(1(5(x1)))))))))))) -> 5(3(3(3(4(4(2(5(0(0(4(4(4(1(1(x1))))))))))))))) 31.21/9.03 1(3(1(2(0(2(0(3(3(1(1(1(x1)))))))))))) -> 1(5(4(4(5(4(4(4(3(0(1(5(4(1(x1)))))))))))))) 31.21/9.03 1(3(3(1(0(0(0(2(5(1(1(1(x1)))))))))))) -> 2(1(2(4(4(4(4(1(2(1(3(5(4(5(0(5(2(x1))))))))))))))))) 31.21/9.03 1(5(2(2(1(1(5(0(3(3(0(4(x1)))))))))))) -> 4(2(4(5(4(5(4(3(5(5(4(4(4(1(1(2(x1)))))))))))))))) 31.21/9.03 1(5(3(3(4(0(3(1(1(2(1(0(x1)))))))))))) -> 4(4(4(2(4(2(2(4(4(5(4(5(4(0(0(5(2(x1))))))))))))))))) 31.21/9.03 2(0(3(2(2(0(2(2(3(0(0(1(x1)))))))))))) -> 5(4(3(4(4(1(5(4(2(4(1(5(4(5(3(0(0(x1))))))))))))))))) 31.21/9.03 2(0(3(3(2(2(3(1(2(3(0(3(x1)))))))))))) -> 5(4(5(5(1(5(4(4(4(5(4(0(2(1(2(0(2(x1))))))))))))))))) 31.21/9.03 2(1(0(0(0(3(3(3(3(0(1(1(x1)))))))))))) -> 5(3(2(2(4(2(2(4(0(4(5(3(4(2(5(x1))))))))))))))) 31.21/9.03 2(1(0(2(1(3(1(2(5(1(3(5(x1)))))))))))) -> 2(5(1(3(5(1(4(4(3(1(0(1(4(5(x1)))))))))))))) 31.21/9.03 2(1(0(2(2(1(1(3(1(1(1(3(x1)))))))))))) -> 5(5(4(5(5(2(2(0(1(0(4(4(2(5(2(0(x1)))))))))))))))) 31.21/9.03 2(1(1(0(0(5(5(0(0(2(5(5(x1)))))))))))) -> 2(2(5(2(3(2(5(4(1(1(4(4(5(5(x1)))))))))))))) 31.21/9.03 2(1(3(0(0(1(0(3(3(1(0(4(x1)))))))))))) -> 4(4(5(3(3(4(2(3(5(4(2(4(4(5(3(3(x1)))))))))))))))) 31.21/9.03 2(1(5(1(1(5(0(2(5(1(3(0(x1)))))))))))) -> 3(5(4(2(3(4(4(3(3(4(0(5(2(0(5(4(x1)))))))))))))))) 31.21/9.03 2(2(0(3(2(0(1(0(2(3(3(2(x1)))))))))))) -> 5(5(5(0(2(2(4(1(4(4(3(3(0(0(2(x1))))))))))))))) 31.21/9.03 2(2(1(1(0(2(0(0(2(3(0(1(x1)))))))))))) -> 5(4(1(1(4(3(5(5(0(1(4(3(5(4(1(1(4(x1))))))))))))))))) 31.21/9.03 2(2(2(0(3(1(0(2(5(0(0(1(x1)))))))))))) -> 5(3(0(5(1(4(4(5(2(4(4(2(4(4(0(5(x1)))))))))))))))) 31.21/9.03 2(2(2(0(4(2(0(1(3(1(2(2(x1)))))))))))) -> 4(4(5(4(0(4(2(5(4(3(0(4(4(4(4(5(3(2(x1)))))))))))))))))) 31.21/9.03 2(2(2(4(1(1(0(1(1(1(4(0(x1)))))))))))) -> 3(3(5(4(1(4(4(3(5(4(4(4(1(4(4(1(4(4(x1)))))))))))))))))) 31.21/9.03 2(2(3(0(4(2(3(1(1(0(4(5(x1)))))))))))) -> 4(1(3(2(5(5(5(3(3(5(2(4(1(5(x1)))))))))))))) 31.21/9.03 2(2(3(4(3(3(5(1(2(4(2(2(x1)))))))))))) -> 3(4(3(5(3(4(1(4(0(4(5(5(0(2(x1)))))))))))))) 31.21/9.03 2(2(3(5(0(2(2(2(3(3(2(2(x1)))))))))))) -> 3(4(0(5(3(2(0(4(5(4(0(1(5(4(1(2(4(x1))))))))))))))))) 31.21/9.03 2(3(0(2(0(3(0(0(3(2(2(3(x1)))))))))))) -> 4(5(4(0(2(3(4(5(5(4(1(3(3(1(5(1(1(x1))))))))))))))))) 31.21/9.03 2(3(1(2(1(1(2(0(4(5(1(3(x1)))))))))))) -> 4(0(4(1(4(1(4(5(3(3(3(4(1(5(0(4(1(x1))))))))))))))))) 31.21/9.03 2(3(1(3(5(1(4(5(1(1(5(1(x1)))))))))))) -> 5(0(4(0(4(1(0(4(1(5(5(3(4(4(3(x1))))))))))))))) 31.21/9.03 2(3(2(1(2(3(1(5(5(2(3(0(x1)))))))))))) -> 2(4(5(2(4(1(4(0(1(4(3(2(3(4(1(x1))))))))))))))) 31.21/9.03 2(3(2(2(3(2(0(3(4(5(2(1(x1)))))))))))) -> 3(4(1(5(0(0(2(5(2(0(5(3(4(2(x1)))))))))))))) 31.21/9.03 2(3(3(1(1(0(0(2(2(1(2(5(x1)))))))))))) -> 5(3(4(4(1(5(2(1(1(5(0(4(5(3(x1)))))))))))))) 31.21/9.03 2(3(3(2(4(3(0(2(3(3(5(1(x1)))))))))))) -> 0(0(4(3(4(4(3(0(4(1(0(1(4(4(x1)))))))))))))) 31.21/9.03 2(4(0(0(0(3(1(1(2(3(2(3(x1)))))))))))) -> 0(0(3(5(4(2(5(4(3(3(4(4(1(0(3(x1))))))))))))))) 31.21/9.03 2(5(1(5(1(4(3(3(0(4(1(1(x1)))))))))))) -> 4(3(5(5(5(3(1(3(4(0(3(5(4(2(x1)))))))))))))) 31.21/9.03 3(0(0(0(2(2(4(1(2(1(1(1(x1)))))))))))) -> 4(0(5(2(5(4(3(2(5(4(3(5(4(2(5(4(3(x1))))))))))))))))) 31.21/9.03 3(0(0(3(1(1(3(3(1(2(0(3(x1)))))))))))) -> 5(0(1(4(5(3(0(5(0(0(4(4(2(4(4(2(5(3(x1)))))))))))))))))) 31.21/9.03 3(0(1(4(2(0(3(0(5(1(4(2(x1)))))))))))) -> 0(5(4(5(2(1(5(5(4(3(5(4(5(5(4(3(2(x1))))))))))))))))) 31.21/9.03 3(0(2(3(3(0(5(3(4(5(0(0(x1)))))))))))) -> 5(4(4(0(4(5(3(3(5(3(5(0(4(4(4(x1))))))))))))))) 31.21/9.03 3(0(3(0(0(3(0(3(5(1(3(2(x1)))))))))))) -> 3(4(0(5(4(4(4(5(4(1(0(2(1(4(1(5(3(4(x1)))))))))))))))))) 31.21/9.03 3(0(3(3(4(0(5(1(3(2(3(1(x1)))))))))))) -> 3(4(5(2(1(1(3(4(4(4(3(5(5(0(4(4(5(x1))))))))))))))))) 31.21/9.03 3(1(0(0(5(4(3(2(2(3(3(2(x1)))))))))))) -> 5(2(1(4(1(5(3(3(4(4(0(5(2(5(1(x1))))))))))))))) 31.21/9.03 3(1(0(5(1(1(3(0(5(1(2(1(x1)))))))))))) -> 4(0(4(4(5(4(4(3(4(5(4(4(2(1(0(1(x1)))))))))))))))) 31.21/9.03 3(1(1(1(2(0(1(0(0(5(0(4(x1)))))))))))) -> 5(0(1(5(5(5(0(1(5(4(4(3(2(0(4(x1))))))))))))))) 31.21/9.03 3(1(1(1(3(0(3(1(0(3(4(0(x1)))))))))))) -> 0(5(3(1(4(4(1(5(5(5(5(4(1(5(x1)))))))))))))) 31.21/9.03 3(1(1(2(0(2(5(5(3(3(1(3(x1)))))))))))) -> 4(2(1(5(1(5(4(0(3(3(0(4(2(4(x1)))))))))))))) 31.21/9.03 3(1(5(0(0(1(0(4(2(1(5(3(x1)))))))))))) -> 1(5(0(0(4(1(4(5(4(5(4(1(4(4(0(4(x1)))))))))))))))) 31.21/9.03 3(2(0(0(3(0(2(3(1(3(3(2(x1)))))))))))) -> 1(4(5(4(4(0(3(1(5(4(3(3(0(4(4(5(4(x1))))))))))))))))) 31.21/9.03 3(2(2(5(1(5(0(3(4(2(4(3(x1)))))))))))) -> 1(5(4(5(2(4(1(5(4(4(4(2(4(4(5(4(0(4(x1)))))))))))))))))) 31.21/9.03 3(3(0(2(4(3(0(1(5(5(3(0(x1)))))))))))) -> 5(1(4(3(4(5(3(4(4(0(1(3(1(4(0(x1))))))))))))))) 31.21/9.03 3(3(1(1(2(3(5(5(2(4(0(0(x1)))))))))))) -> 0(1(5(5(4(5(5(2(4(4(4(1(2(5(4(5(4(x1))))))))))))))))) 31.21/9.03 3(3(1(2(2(1(3(3(0(2(0(4(x1)))))))))))) -> 2(5(4(3(1(4(4(4(0(4(2(3(0(2(x1)))))))))))))) 31.21/9.03 3(3(1(2(3(0(2(0(3(0(1(0(x1)))))))))))) -> 3(0(1(3(0(4(5(5(1(0(5(2(4(1(2(4(x1)))))))))))))))) 31.21/9.03 3(3(2(3(0(1(3(3(5(1(1(2(x1)))))))))))) -> 2(5(5(5(4(4(2(5(4(1(5(5(4(1(4(5(2(x1))))))))))))))))) 31.21/9.03 3(5(1(2(1(0(3(2(2(2(0(1(x1)))))))))))) -> 1(5(5(4(1(2(5(5(4(4(4(4(2(1(2(5(4(5(x1)))))))))))))))))) 31.21/9.03 4(0(0(0(2(5(0(2(0(5(5(0(x1)))))))))))) -> 4(5(3(4(3(4(2(4(4(3(0(4(1(2(5(x1))))))))))))))) 31.21/9.03 4(0(0(3(1(3(5(0(3(3(2(4(x1)))))))))))) -> 4(0(2(4(0(1(2(4(4(0(4(1(4(2(4(4(x1)))))))))))))))) 31.21/9.03 4(0(1(3(1(2(3(3(1(1(2(2(x1)))))))))))) -> 1(4(5(3(0(1(4(3(2(4(1(5(3(4(0(x1))))))))))))))) 31.21/9.03 4(1(3(1(1(1(1(2(1(0(4(3(x1)))))))))))) -> 0(5(4(2(4(4(5(4(2(4(0(0(4(4(4(4(5(x1))))))))))))))))) 31.21/9.03 4(1(3(3(0(0(3(3(3(3(3(0(x1)))))))))))) -> 4(0(2(1(4(0(5(1(0(4(2(4(5(2(x1)))))))))))))) 31.21/9.03 4(1(5(0(2(2(1(3(0(0(3(1(x1)))))))))))) -> 4(5(4(1(4(1(4(4(5(5(4(4(3(4(4(3(2(4(x1)))))))))))))))))) 31.21/9.03 4(3(3(2(0(1(1(2(0(1(5(5(x1)))))))))))) -> 3(0(2(4(1(4(4(4(5(4(4(4(5(0(4(x1))))))))))))))) 31.21/9.03 4(4(3(0(0(2(2(5(5(3(1(1(x1)))))))))))) -> 5(5(4(4(0(4(2(5(4(2(4(1(4(1(1(x1))))))))))))))) 31.21/9.03 31.21/9.03 31.21/9.03 31.21/9.03 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (2) 31.21/9.03 Obligation: 31.21/9.03 Q restricted rewrite system: 31.21/9.03 The TRS R consists of the following rules: 31.21/9.03 31.21/9.03 1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 3(5(3(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))))) 31.21/9.03 1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 1(3(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))))))))) 31.21/9.03 2(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 0(0(0(5(4(1(5(4(1(4(3(4(5(3(4(5(2(x1))))))))))))))))) 31.21/9.03 2(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 4(4(3(5(4(5(4(0(2(2(0(1(3(4(4(3(5(x1))))))))))))))))) 31.21/9.03 2(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 2(0(1(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))))) 31.21/9.03 2(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 0(4(1(5(4(0(5(4(0(2(4(0(1(2(x1)))))))))))))) 31.21/9.03 3(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 3(4(4(5(4(1(3(1(4(4(0(5(4(3(2(0(2(x1))))))))))))))))) 31.21/9.03 3(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 0(0(4(5(4(5(2(1(3(0(5(4(4(2(x1)))))))))))))) 31.21/9.03 31.21/9.03 Q is empty. 31.21/9.03 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (3) DependencyPairsProof (EQUIVALENT) 31.21/9.03 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (4) 31.21/9.03 Obligation: 31.21/9.03 Q DP problem: 31.21/9.03 The TRS P consists of the following rules: 31.21/9.03 31.21/9.03 1^1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 3^1(5(3(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))))) 31.21/9.03 1^1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 3^1(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))) 31.21/9.03 1^1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 2^1(3(0(2(4(0(2(3(4(x1))))))))) 31.21/9.03 1^1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 3^1(0(2(4(0(2(3(4(x1)))))))) 31.21/9.03 1^1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 2^1(4(0(2(3(4(x1)))))) 31.21/9.03 1^1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 2^1(3(4(x1))) 31.21/9.03 1^1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 3^1(4(x1)) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 1^1(3(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))))))))) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 3^1(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1))))))))))))))))) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 3^1(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 3^1(3(5(2(1(5(4(1(5(2(5(x1))))))))))) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 3^1(5(2(1(5(4(1(5(2(5(x1)))))))))) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 2^1(1(5(4(1(5(2(5(x1)))))))) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 1^1(5(4(1(5(2(5(x1))))))) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 1^1(5(2(5(x1)))) 31.21/9.03 1^1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 2^1(5(x1)) 31.21/9.03 2^1(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 1^1(5(4(1(4(3(4(5(3(4(5(2(x1)))))))))))) 31.21/9.03 2^1(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 1^1(4(3(4(5(3(4(5(2(x1))))))))) 31.21/9.03 2^1(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 3^1(4(5(3(4(5(2(x1))))))) 31.21/9.03 2^1(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 3^1(4(5(2(x1)))) 31.21/9.03 2^1(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 3^1(5(4(5(4(0(2(2(0(1(3(4(4(3(5(x1))))))))))))))) 31.21/9.03 2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 2^1(2(0(1(3(4(4(3(5(x1))))))))) 31.21/9.03 2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 2^1(0(1(3(4(4(3(5(x1)))))))) 31.21/9.03 2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 1^1(3(4(4(3(5(x1)))))) 31.21/9.03 2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 3^1(4(4(3(5(x1))))) 31.21/9.03 2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 3^1(5(x1)) 31.21/9.03 2^1(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 2^1(0(1(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))))) 31.21/9.03 2^1(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 1^1(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))) 31.21/9.03 2^1(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 2^1(4(3(4(1(4(4(3(4(1(4(4(0(3(x1)))))))))))))) 31.21/9.03 2^1(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 3^1(4(1(4(4(3(4(1(4(4(0(3(x1)))))))))))) 31.21/9.03 2^1(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 1^1(4(4(3(4(1(4(4(0(3(x1)))))))))) 31.21/9.03 2^1(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 3^1(4(1(4(4(0(3(x1))))))) 31.21/9.03 2^1(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 1^1(4(4(0(3(x1))))) 31.21/9.03 2^1(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 1^1(5(4(0(5(4(0(2(4(0(1(2(x1)))))))))))) 31.21/9.03 2^1(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 2^1(4(0(1(2(x1))))) 31.21/9.03 2^1(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 1^1(2(x1)) 31.21/9.03 2^1(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 2^1(x1) 31.21/9.03 3^1(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 3^1(4(4(5(4(1(3(1(4(4(0(5(4(3(2(0(2(x1))))))))))))))))) 31.21/9.03 3^1(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 1^1(3(1(4(4(0(5(4(3(2(0(2(x1)))))))))))) 31.21/9.03 3^1(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 3^1(1(4(4(0(5(4(3(2(0(2(x1))))))))))) 31.21/9.03 3^1(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 1^1(4(4(0(5(4(3(2(0(2(x1)))))))))) 31.21/9.03 3^1(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 3^1(2(0(2(x1)))) 31.21/9.03 3^1(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 2^1(0(2(x1))) 31.21/9.03 3^1(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 3^1(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 2^1(1(3(0(5(4(4(2(x1)))))))) 31.21/9.03 3^1(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 1^1(3(0(5(4(4(2(x1))))))) 31.21/9.03 3^1(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 3^1(0(5(4(4(2(x1)))))) 31.21/9.03 3^1(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 31.21/9.03 The TRS R consists of the following rules: 31.21/9.03 31.21/9.03 1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 3(5(3(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))))) 31.21/9.03 1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 1(3(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))))))))) 31.21/9.03 2(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 0(0(0(5(4(1(5(4(1(4(3(4(5(3(4(5(2(x1))))))))))))))))) 31.21/9.03 2(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 4(4(3(5(4(5(4(0(2(2(0(1(3(4(4(3(5(x1))))))))))))))))) 31.21/9.03 2(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 2(0(1(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))))) 31.21/9.03 2(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 0(4(1(5(4(0(5(4(0(2(4(0(1(2(x1)))))))))))))) 31.21/9.03 3(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 3(4(4(5(4(1(3(1(4(4(0(5(4(3(2(0(2(x1))))))))))))))))) 31.21/9.03 3(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 0(0(4(5(4(5(2(1(3(0(5(4(4(2(x1)))))))))))))) 31.21/9.03 31.21/9.03 Q is empty. 31.21/9.03 We have to consider all minimal (P,Q,R)-chains. 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (5) DependencyGraphProof (EQUIVALENT) 31.21/9.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 45 less nodes. 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (6) 31.21/9.03 Obligation: 31.21/9.03 Q DP problem: 31.21/9.03 The TRS P consists of the following rules: 31.21/9.03 31.21/9.03 2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 3^1(5(x1)) 31.21/9.03 3^1(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 2^1(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 2^1(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 2^1(x1) 31.21/9.03 31.21/9.03 The TRS R consists of the following rules: 31.21/9.03 31.21/9.03 1(0(2(2(5(1(3(1(3(3(2(5(x1)))))))))))) -> 3(5(3(5(0(5(2(3(0(2(4(0(2(3(4(x1))))))))))))))) 31.21/9.03 1(5(1(1(1(5(1(3(2(3(1(5(x1)))))))))))) -> 1(3(4(4(4(5(3(3(3(5(2(1(5(4(1(5(2(5(x1)))))))))))))))))) 31.21/9.03 2(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 0(0(0(5(4(1(5(4(1(4(3(4(5(3(4(5(2(x1))))))))))))))))) 31.21/9.03 2(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 4(4(3(5(4(5(4(0(2(2(0(1(3(4(4(3(5(x1))))))))))))))))) 31.21/9.03 2(3(1(1(3(0(3(0(4(0(5(3(x1)))))))))))) -> 2(0(1(2(4(3(4(1(4(4(3(4(1(4(4(0(3(x1))))))))))))))))) 31.21/9.03 2(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 0(4(1(5(4(0(5(4(0(2(4(0(1(2(x1)))))))))))))) 31.21/9.03 3(3(1(2(5(1(2(0(5(5(0(0(x1)))))))))))) -> 3(4(4(5(4(1(3(1(4(4(0(5(4(3(2(0(2(x1))))))))))))))))) 31.21/9.03 3(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 0(0(4(5(4(5(2(1(3(0(5(4(4(2(x1)))))))))))))) 31.21/9.03 31.21/9.03 Q is empty. 31.21/9.03 We have to consider all minimal (P,Q,R)-chains. 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (7) UsableRulesProof (EQUIVALENT) 31.21/9.03 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (8) 31.21/9.03 Obligation: 31.21/9.03 Q DP problem: 31.21/9.03 The TRS P consists of the following rules: 31.21/9.03 31.21/9.03 2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 3^1(5(x1)) 31.21/9.03 3^1(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 2^1(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 2^1(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 2^1(x1) 31.21/9.03 31.21/9.03 R is empty. 31.21/9.03 Q is empty. 31.21/9.03 We have to consider all minimal (P,Q,R)-chains. 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (9) QDPSizeChangeProof (EQUIVALENT) 31.21/9.03 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 31.21/9.03 31.21/9.03 From the DPs we obtained the following set of size-change graphs: 31.21/9.03 *3^1(5(5(0(2(3(5(0(5(0(4(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 The graph contains the following edges 1 > 1 31.21/9.03 31.21/9.03 31.21/9.03 *2^1(2(1(0(2(5(1(2(1(5(4(5(x1)))))))))))) -> 3^1(5(x1)) 31.21/9.03 The graph contains the following edges 1 > 1 31.21/9.03 31.21/9.03 31.21/9.03 *2^1(0(2(4(5(1(2(2(5(3(5(0(x1)))))))))))) -> 2^1(x1) 31.21/9.03 The graph contains the following edges 1 > 1 31.21/9.03 31.21/9.03 31.21/9.03 *2^1(5(1(3(0(0(4(5(3(1(3(4(x1)))))))))))) -> 2^1(x1) 31.21/9.03 The graph contains the following edges 1 > 1 31.21/9.03 31.21/9.03 31.21/9.03 ---------------------------------------- 31.21/9.03 31.21/9.03 (10) 31.21/9.03 YES 31.25/9.21 EOF