15.57/4.84 YES 16.27/5.00 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 16.27/5.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.27/5.00 16.27/5.00 16.27/5.00 Termination w.r.t. Q of the given QTRS could be proven: 16.27/5.00 16.27/5.00 (0) QTRS 16.27/5.00 (1) QTRS Reverse [EQUIVALENT, 0 ms] 16.27/5.00 (2) QTRS 16.27/5.00 (3) QTRSRRRProof [EQUIVALENT, 380 ms] 16.27/5.00 (4) QTRS 16.27/5.00 (5) DependencyPairsProof [EQUIVALENT, 20 ms] 16.27/5.00 (6) QDP 16.27/5.00 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 16.27/5.00 (8) QDP 16.27/5.00 (9) UsableRulesProof [EQUIVALENT, 0 ms] 16.27/5.00 (10) QDP 16.27/5.00 (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] 16.27/5.00 (12) YES 16.27/5.00 16.27/5.00 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (0) 16.27/5.00 Obligation: 16.27/5.00 Q restricted rewrite system: 16.27/5.00 The TRS R consists of the following rules: 16.27/5.00 16.27/5.00 0(0(0(3(0(4(3(1(4(5(2(0(x1)))))))))))) -> 1(0(2(3(5(5(1(0(3(2(2(3(3(4(2(4(x1)))))))))))))))) 16.27/5.00 0(0(0(3(1(5(0(5(1(0(3(1(x1)))))))))))) -> 3(3(1(2(5(5(1(2(4(4(4(1(2(3(3(x1))))))))))))))) 16.27/5.00 0(0(1(1(4(3(4(0(5(1(4(3(x1)))))))))))) -> 3(4(1(1(2(5(5(2(2(2(2(3(5(0(4(2(x1)))))))))))))))) 16.27/5.00 0(0(1(3(4(3(4(4(4(0(3(0(x1)))))))))))) -> 2(5(5(0(2(5(2(5(4(4(2(1(1(2(4(3(5(1(x1)))))))))))))))))) 16.27/5.00 0(0(2(1(0(3(0(0(1(0(1(0(x1)))))))))))) -> 2(1(2(4(3(4(2(5(5(3(5(1(0(0(3(x1))))))))))))))) 16.27/5.00 0(0(4(3(0(0(1(4(0(1(3(5(x1)))))))))))) -> 5(1(5(1(0(2(2(2(3(3(4(5(3(4(2(2(2(0(x1)))))))))))))))))) 16.27/5.00 0(0(5(4(0(0(3(1(3(0(1(5(x1)))))))))))) -> 3(1(0(5(5(5(5(4(1(1(2(2(2(4(5(2(1(2(x1)))))))))))))))))) 16.27/5.00 0(0(5(4(5(0(5(0(0(3(0(3(x1)))))))))))) -> 2(5(5(3(3(0(4(1(4(2(1(1(2(4(4(1(0(x1))))))))))))))))) 16.27/5.00 0(1(0(0(1(3(1(0(3(2(5(0(x1)))))))))))) -> 5(1(1(4(0(3(2(2(4(2(2(1(2(5(1(x1))))))))))))))) 16.27/5.00 0(1(0(0(1(4(4(4(4(2(1(0(x1)))))))))))) -> 5(5(2(4(1(5(3(1(2(2(2(4(2(3(2(1(3(4(x1)))))))))))))))))) 16.27/5.00 0(1(1(3(4(4(0(2(0(1(1(1(x1)))))))))))) -> 0(5(3(2(2(2(5(1(4(1(3(2(4(2(2(1(2(1(x1)))))))))))))))))) 16.27/5.00 0(1(4(5(0(0(5(1(3(0(4(5(x1)))))))))))) -> 2(3(3(1(2(5(4(1(2(5(3(4(1(2(5(5(3(5(x1)))))))))))))))))) 16.27/5.00 0(2(0(4(4(1(2(1(0(4(3(3(x1)))))))))))) -> 2(1(2(4(3(5(2(5(2(5(3(4(4(1(x1)))))))))))))) 16.27/5.00 0(2(4(3(4(1(2(0(1(4(4(5(x1)))))))))))) -> 4(2(5(1(2(1(2(3(0(2(2(2(2(2(3(3(x1)))))))))))))))) 16.27/5.00 0(3(0(4(4(0(0(4(4(0(1(3(x1)))))))))))) -> 5(2(1(2(4(2(2(4(0(4(3(1(0(2(3(2(5(3(x1)))))))))))))))))) 16.27/5.00 0(3(4(1(3(4(1(0(1(4(3(1(x1)))))))))))) -> 2(2(2(3(2(0(2(5(2(2(2(1(5(2(4(1(x1)))))))))))))))) 16.27/5.00 0(3(4(3(5(0(0(4(4(3(1(1(x1)))))))))))) -> 4(2(1(1(2(2(5(1(2(0(4(5(4(2(1(2(5(x1))))))))))))))))) 16.27/5.00 0(3(5(4(0(1(1(4(0(5(5(0(x1)))))))))))) -> 3(2(4(1(0(5(1(1(2(3(5(3(2(1(2(2(x1)))))))))))))))) 16.27/5.00 0(4(0(3(1(4(0(4(1(4(5(5(x1)))))))))))) -> 2(5(1(2(2(4(2(5(2(5(4(1(0(4(x1)))))))))))))) 16.27/5.00 0(4(3(1(3(0(4(5(1(5(0(0(x1)))))))))))) -> 3(5(1(2(1(3(2(2(2(2(0(3(2(2(2(2(4(5(x1)))))))))))))))))) 16.27/5.00 0(4(3(5(3(1(4(4(0(0(0(4(x1)))))))))))) -> 5(2(3(3(2(4(3(5(2(3(4(2(2(3(3(2(0(x1))))))))))))))))) 16.27/5.00 0(4(5(0(0(2(0(3(3(5(5(5(x1)))))))))))) -> 2(4(2(2(2(5(1(0(2(4(4(2(1(2(2(x1))))))))))))))) 16.27/5.00 0(5(0(4(1(0(1(0(5(4(0(5(x1)))))))))))) -> 5(3(1(5(3(2(5(3(1(0(2(3(5(2(0(4(x1)))))))))))))))) 16.27/5.00 0(5(1(5(0(0(5(4(5(0(4(1(x1)))))))))))) -> 5(5(2(4(2(5(5(0(4(0(1(1(2(5(5(5(5(x1))))))))))))))))) 16.27/5.00 0(5(3(1(1(1(4(4(3(0(1(4(x1)))))))))))) -> 2(0(2(4(5(5(2(2(3(3(5(0(5(2(3(2(x1)))))))))))))))) 16.27/5.00 0(5(3(1(2(5(1(3(4(3(5(0(x1)))))))))))) -> 5(2(2(5(2(0(5(5(2(5(5(5(3(5(4(2(x1)))))))))))))))) 16.27/5.00 0(5(4(2(1(0(4(3(0(2(3(3(x1)))))))))))) -> 3(3(3(2(3(2(0(5(4(2(3(4(1(2(3(x1))))))))))))))) 16.27/5.00 0(5(4(5(0(3(3(0(4(0(5(4(x1)))))))))))) -> 5(4(2(5(4(1(2(1(3(3(4(2(2(2(1(2(5(0(x1)))))))))))))))))) 16.27/5.00 1(0(0(0(1(0(5(0(1(1(3(0(x1)))))))))))) -> 3(5(5(2(1(2(5(5(5(0(2(3(3(1(0(2(x1)))))))))))))))) 16.27/5.00 1(0(1(3(2(5(2(2(3(4(1(2(x1)))))))))))) -> 3(2(1(2(0(2(3(5(4(1(2(2(2(2(x1)))))))))))))) 16.27/5.00 1(0(4(3(0(0(5(4(4(1(0(5(x1)))))))))))) -> 1(3(2(2(3(0(0(2(4(2(1(2(5(3(x1)))))))))))))) 16.27/5.00 1(1(4(5(0(5(4(4(0(5(0(0(x1)))))))))))) -> 5(4(4(1(1(4(1(2(2(5(0(2(1(2(0(5(x1)))))))))))))))) 16.27/5.00 1(2(5(4(4(0(0(4(3(1(1(2(x1)))))))))))) -> 5(2(2(2(3(0(4(1(5(4(2(3(2(2(x1)))))))))))))) 16.27/5.00 1(3(1(3(3(4(4(4(3(0(4(4(x1)))))))))))) -> 2(5(5(5(3(3(2(3(0(5(0(4(2(1(x1)))))))))))))) 16.27/5.00 1(3(3(5(4(0(4(4(5(2(0(0(x1)))))))))))) -> 4(2(2(1(2(5(3(3(3(5(4(5(1(5(5(x1))))))))))))))) 16.27/5.00 1(4(1(0(4(3(1(0(0(5(4(0(x1)))))))))))) -> 2(5(1(5(1(3(3(1(4(1(0(2(0(0(2(x1))))))))))))))) 16.27/5.00 1(4(3(5(3(3(0(4(0(0(4(0(x1)))))))))))) -> 1(5(3(2(2(2(2(1(5(2(5(1(0(1(5(0(x1)))))))))))))))) 16.27/5.00 2(0(0(3(1(2(4(3(0(1(4(3(x1)))))))))))) -> 1(1(2(2(5(0(2(1(1(5(0(5(5(2(2(3(x1)))))))))))))))) 16.27/5.00 2(0(3(1(4(5(2(0(2(5(1(4(x1)))))))))))) -> 1(2(5(3(2(0(1(2(4(1(3(2(5(3(5(x1))))))))))))))) 16.27/5.00 2(1(0(1(5(3(1(3(1(0(3(5(x1)))))))))))) -> 5(3(5(2(4(4(0(3(5(2(2(1(2(2(1(3(x1)))))))))))))))) 16.27/5.00 2(2(4(0(4(0(0(5(5(4(3(5(x1)))))))))))) -> 2(2(5(4(2(3(0(1(2(2(1(2(2(3(5(3(x1)))))))))))))))) 16.27/5.00 2(4(0(4(4(4(0(4(1(3(2(0(x1)))))))))))) -> 3(0(5(5(2(2(0(2(2(5(2(2(5(3(x1)))))))))))))) 16.27/5.00 2(4(0(4(5(4(0(3(4(4(1(5(x1)))))))))))) -> 2(4(1(1(5(2(3(2(1(4(0(2(2(5(5(2(3(3(x1)))))))))))))))))) 16.27/5.00 2(5(1(4(0(0(5(4(0(0(4(1(x1)))))))))))) -> 5(5(4(1(3(3(1(1(2(2(3(3(2(2(2(3(5(5(x1)))))))))))))))))) 16.27/5.00 3(1(0(3(4(4(4(3(1(3(4(1(x1)))))))))))) -> 1(2(2(4(4(1(2(0(5(2(4(1(5(4(x1)))))))))))))) 16.27/5.00 3(3(4(0(4(2(2(3(4(3(0(0(x1)))))))))))) -> 1(2(3(0(4(1(5(3(0(2(2(5(2(4(1(x1))))))))))))))) 16.27/5.00 3(4(0(4(4(4(3(0(3(4(4(2(x1)))))))))))) -> 1(2(4(5(3(2(2(2(1(2(4(0(5(3(2(0(0(1(x1)))))))))))))))))) 16.27/5.00 3(4(4(4(0(4(0(0(2(3(1(4(x1)))))))))))) -> 2(5(2(2(2(2(3(5(2(1(3(2(1(3(4(5(5(2(x1)))))))))))))))))) 16.27/5.00 4(0(0(3(2(2(4(5(0(4(3(3(x1)))))))))))) -> 5(2(2(5(2(1(3(2(2(3(3(5(5(2(2(2(4(3(x1)))))))))))))))))) 16.27/5.00 4(0(1(0(1(0(0(3(3(4(0(4(x1)))))))))))) -> 4(4(5(2(1(3(2(5(1(2(0(2(5(1(3(2(2(x1))))))))))))))))) 16.27/5.00 4(0(1(1(4(1(3(4(5(4(3(5(x1)))))))))))) -> 5(2(5(2(3(2(4(1(3(2(2(0(5(1(4(x1))))))))))))))) 16.27/5.00 4(0(1(4(3(0(5(4(5(1(0(4(x1)))))))))))) -> 2(1(1(5(2(1(5(5(0(3(2(4(3(2(5(x1))))))))))))))) 16.27/5.00 4(0(3(1(5(1(3(1(4(0(1(2(x1)))))))))))) -> 2(2(5(2(3(2(3(5(5(3(4(4(1(5(3(5(2(2(x1)))))))))))))))))) 16.27/5.00 4(0(3(4(4(3(0(2(5(4(1(1(x1)))))))))))) -> 0(5(3(5(5(2(2(1(2(2(3(2(5(5(4(3(x1)))))))))))))))) 16.27/5.00 4(0(4(3(1(3(3(4(3(4(0(0(x1)))))))))))) -> 5(3(2(2(2(5(2(2(1(0(4(2(2(4(3(2(3(x1))))))))))))))))) 16.27/5.00 4(1(0(0(0(3(5(4(3(3(0(2(x1)))))))))))) -> 2(2(5(3(3(5(2(3(3(1(2(2(0(2(5(3(3(x1))))))))))))))))) 16.27/5.00 4(1(0(4(3(0(5(0(3(2(3(0(x1)))))))))))) -> 2(3(3(2(1(4(4(5(2(0(1(5(2(5(1(1(x1)))))))))))))))) 16.27/5.00 4(1(1(3(1(3(2(4(3(1(4(4(x1)))))))))))) -> 4(0(1(2(3(2(2(2(3(2(3(1(4(1(2(5(3(2(x1)))))))))))))))))) 16.27/5.00 4(1(1(3(2(3(1(5(0(4(0(0(x1)))))))))))) -> 5(0(5(5(3(4(2(2(3(2(2(2(5(1(0(5(x1)))))))))))))))) 16.27/5.00 4(1(5(2(3(0(1(5(4(3(3(0(x1)))))))))))) -> 5(5(4(2(2(0(5(3(2(3(2(1(3(2(1(3(5(1(x1)))))))))))))))))) 16.27/5.00 4(2(0(0(4(3(0(3(0(4(4(5(x1)))))))))))) -> 2(0(5(3(2(2(3(3(5(3(5(0(1(1(2(3(0(2(x1)))))))))))))))))) 16.27/5.00 4(2(2(0(4(1(4(4(0(0(3(4(x1)))))))))))) -> 3(5(1(2(3(4(1(2(5(2(0(5(3(3(2(x1))))))))))))))) 16.27/5.00 4(3(2(0(0(5(4(4(5(4(4(0(x1)))))))))))) -> 4(1(2(3(1(2(2(0(3(5(2(0(5(2(5(1(5(0(x1)))))))))))))))))) 16.27/5.00 4(3(2(1(4(4(5(0(3(0(0(4(x1)))))))))))) -> 2(1(2(5(3(3(5(2(0(5(3(4(2(5(2(3(5(3(x1)))))))))))))))))) 16.27/5.00 4(3(2(5(4(4(4(1(4(5(1(0(x1)))))))))))) -> 2(1(5(5(2(3(3(1(2(3(2(2(3(0(1(5(x1)))))))))))))))) 16.27/5.00 4(3(5(4(5(0(5(4(3(4(3(5(x1)))))))))))) -> 5(3(4(2(2(0(2(2(5(5(4(3(4(0(1(5(5(x1))))))))))))))))) 16.27/5.00 4(4(0(4(3(1(0(5(4(4(0(0(x1)))))))))))) -> 0(4(5(5(4(3(4(5(5(3(5(1(1(3(2(5(x1)))))))))))))))) 16.27/5.00 4(4(3(1(2(1(4(3(0(4(5(4(x1)))))))))))) -> 3(3(5(4(4(1(2(3(0(0(1(1(2(1(2(x1))))))))))))))) 16.27/5.00 4(4(3(4(3(1(4(3(4(5(0(4(x1)))))))))))) -> 0(2(4(2(5(1(3(2(0(2(0(0(1(2(x1)))))))))))))) 16.27/5.00 4(4(4(0(3(5(5(0(5(2(3(1(x1)))))))))))) -> 5(2(2(2(2(0(2(4(1(3(0(0(1(5(3(x1))))))))))))))) 16.27/5.00 4(4(4(4(4(0(3(5(1(0(2(0(x1)))))))))))) -> 1(2(5(5(3(3(3(1(2(3(0(2(5(3(3(3(0(2(x1)))))))))))))))))) 16.27/5.00 4(4(5(0(3(5(4(1(1(5(1(0(x1)))))))))))) -> 2(2(5(5(2(3(2(2(5(3(1(2(0(2(x1)))))))))))))) 16.27/5.00 4(5(0(0(1(0(2(5(4(4(0(4(x1)))))))))))) -> 3(5(5(0(2(4(2(2(4(0(1(1(2(2(1(x1))))))))))))))) 16.27/5.00 4(5(2(0(5(3(1(2(4(0(2(1(x1)))))))))))) -> 4(2(5(3(5(5(3(5(2(2(4(3(3(2(4(x1))))))))))))))) 16.27/5.00 4(5(2(1(4(2(0(3(0(0(4(0(x1)))))))))))) -> 3(4(5(3(5(2(5(2(1(4(0(2(2(2(0(x1))))))))))))))) 16.27/5.00 4(5(3(0(0(5(0(4(5(2(4(0(x1)))))))))))) -> 5(2(2(4(3(2(2(3(3(2(3(4(1(1(2(2(0(x1))))))))))))))))) 16.27/5.00 4(5(4(5(4(4(5(2(1(0(0(5(x1)))))))))))) -> 5(3(5(5(5(3(3(1(2(3(4(5(2(2(3(3(5(x1))))))))))))))))) 16.27/5.00 5(0(0(4(4(5(0(3(3(4(3(1(x1)))))))))))) -> 5(1(1(0(4(0(2(2(0(2(5(2(2(5(5(1(1(2(x1)))))))))))))))))) 16.27/5.00 5(0(1(4(0(5(2(0(0(0(0(0(x1)))))))))))) -> 1(0(1(1(1(2(3(3(2(2(5(5(3(0(4(5(x1)))))))))))))))) 16.27/5.00 5(0(3(5(3(4(2(1(0(3(0(4(x1)))))))))))) -> 2(1(2(5(3(2(0(2(1(2(5(4(3(5(2(1(x1)))))))))))))))) 16.27/5.00 5(0(5(0(4(0(0(5(2(0(0(0(x1)))))))))))) -> 0(3(2(2(3(5(4(2(0(2(5(2(2(1(3(4(x1)))))))))))))))) 16.27/5.00 5(1(0(0(4(2(1(1(2(1(4(2(x1)))))))))))) -> 2(2(2(2(3(3(2(3(3(2(5(5(2(2(1(0(2(x1))))))))))))))))) 16.27/5.00 5(1(1(1(4(4(0(3(1(4(5(0(x1)))))))))))) -> 4(1(2(3(1(5(3(5(2(0(4(2(2(4(2(2(x1)))))))))))))))) 16.27/5.00 5(1(3(0(3(0(3(4(1(0(5(5(x1)))))))))))) -> 4(3(2(5(5(2(5(5(4(1(1(5(5(2(x1)))))))))))))) 16.27/5.00 5(1(5(0(0(3(5(2(1(4(4(5(x1)))))))))))) -> 3(4(2(3(2(5(2(2(3(2(2(2(1(2(3(2(5(3(x1)))))))))))))))))) 16.27/5.00 5(1(5(1(1(4(5(2(4(2(1(4(x1)))))))))))) -> 5(1(2(2(1(2(3(1(1(4(1(4(2(2(2(2(2(5(x1)))))))))))))))))) 16.27/5.00 5(3(0(3(5(1(0(0(0(0(5(4(x1)))))))))))) -> 2(3(3(1(2(2(3(2(1(5(4(1(5(1(2(1(2(x1))))))))))))))))) 16.27/5.00 5(4(0(3(4(0(0(2(3(0(0(2(x1)))))))))))) -> 2(1(3(5(1(1(1(2(5(4(3(3(2(1(3(x1))))))))))))))) 16.27/5.00 5(4(0(4(0(4(5(3(5(4(4(4(x1)))))))))))) -> 2(4(1(5(5(2(0(2(0(3(5(4(2(3(1(x1))))))))))))))) 16.27/5.00 5(4(3(4(4(3(4(2(4(3(2(0(x1)))))))))))) -> 2(1(2(3(0(4(2(4(2(5(3(4(1(5(x1)))))))))))))) 16.27/5.00 5(4(4(0(5(2(0(3(0(0(4(2(x1)))))))))))) -> 3(1(2(4(0(1(5(1(4(4(1(2(5(4(x1)))))))))))))) 16.27/5.00 5(4(4(4(0(2(0(4(5(4(3(4(x1)))))))))))) -> 5(2(0(2(1(1(1(1(1(0(4(2(1(1(4(x1))))))))))))))) 16.27/5.00 5(4(5(1(4(3(1(3(0(0(1(0(x1)))))))))))) -> 5(5(3(0(1(3(5(2(0(2(1(1(1(2(3(4(x1)))))))))))))))) 16.27/5.00 5(4(5(5(5(0(3(4(3(4(4(1(x1)))))))))))) -> 1(0(5(5(1(2(2(1(3(5(2(0(5(3(5(4(1(x1))))))))))))))))) 16.27/5.00 5(5(0(5(0(5(0(0(3(0(3(4(x1)))))))))))) -> 3(4(2(2(1(4(0(1(5(1(2(1(2(5(4(5(3(1(x1)))))))))))))))))) 16.27/5.00 5(5(2(2(1(0(4(0(0(5(5(0(x1)))))))))))) -> 5(3(2(1(3(1(1(2(2(2(0(5(3(3(2(5(5(x1))))))))))))))))) 16.27/5.00 16.27/5.00 Q is empty. 16.27/5.00 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (1) QTRS Reverse (EQUIVALENT) 16.27/5.00 We applied the QTRS Reverse Processor [REVERSE]. 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (2) 16.27/5.00 Obligation: 16.27/5.00 Q restricted rewrite system: 16.27/5.00 The TRS R consists of the following rules: 16.27/5.00 16.27/5.00 0(2(5(4(1(3(4(0(3(0(0(0(x1)))))))))))) -> 4(2(4(3(3(2(2(3(0(1(5(5(3(2(0(1(x1)))))))))))))))) 16.27/5.00 1(3(0(1(5(0(5(1(3(0(0(0(x1)))))))))))) -> 3(3(2(1(4(4(4(2(1(5(5(2(1(3(3(x1))))))))))))))) 16.27/5.00 3(4(1(5(0(4(3(4(1(1(0(0(x1)))))))))))) -> 2(4(0(5(3(2(2(2(2(5(5(2(1(1(4(3(x1)))))))))))))))) 16.27/5.00 0(3(0(4(4(4(3(4(3(1(0(0(x1)))))))))))) -> 1(5(3(4(2(1(1(2(4(4(5(2(5(2(0(5(5(2(x1)))))))))))))))))) 16.27/5.00 0(1(0(1(0(0(3(0(1(2(0(0(x1)))))))))))) -> 3(0(0(1(5(3(5(5(2(4(3(4(2(1(2(x1))))))))))))))) 16.27/5.00 5(3(1(0(4(1(0(0(3(4(0(0(x1)))))))))))) -> 0(2(2(2(4(3(5(4(3(3(2(2(2(0(1(5(1(5(x1)))))))))))))))))) 16.27/5.00 5(1(0(3(1(3(0(0(4(5(0(0(x1)))))))))))) -> 2(1(2(5(4(2(2(2(1(1(4(5(5(5(5(0(1(3(x1)))))))))))))))))) 16.27/5.00 3(0(3(0(0(5(0(5(4(5(0(0(x1)))))))))))) -> 0(1(4(4(2(1(1(2(4(1(4(0(3(3(5(5(2(x1))))))))))))))))) 16.27/5.00 0(5(2(3(0(1(3(1(0(0(1(0(x1)))))))))))) -> 1(5(2(1(2(2(4(2(2(3(0(4(1(1(5(x1))))))))))))))) 16.27/5.00 0(1(2(4(4(4(4(1(0(0(1(0(x1)))))))))))) -> 4(3(1(2(3(2(4(2(2(2(1(3(5(1(4(2(5(5(x1)))))))))))))))))) 16.27/5.00 1(1(1(0(2(0(4(4(3(1(1(0(x1)))))))))))) -> 1(2(1(2(2(4(2(3(1(4(1(5(2(2(2(3(5(0(x1)))))))))))))))))) 16.27/5.00 5(4(0(3(1(5(0(0(5(4(1(0(x1)))))))))))) -> 5(3(5(5(2(1(4(3(5(2(1(4(5(2(1(3(3(2(x1)))))))))))))))))) 16.27/5.00 3(3(4(0(1(2(1(4(4(0(2(0(x1)))))))))))) -> 1(4(4(3(5(2(5(2(5(3(4(2(1(2(x1)))))))))))))) 16.27/5.00 5(4(4(1(0(2(1(4(3(4(2(0(x1)))))))))))) -> 3(3(2(2(2(2(2(0(3(2(1(2(1(5(2(4(x1)))))))))))))))) 16.27/5.00 3(1(0(4(4(0(0(4(4(0(3(0(x1)))))))))))) -> 3(5(2(3(2(0(1(3(4(0(4(2(2(4(2(1(2(5(x1)))))))))))))))))) 16.27/5.00 1(3(4(1(0(1(4(3(1(4(3(0(x1)))))))))))) -> 1(4(2(5(1(2(2(2(5(2(0(2(3(2(2(2(x1)))))))))))))))) 16.27/5.00 1(1(3(4(4(0(0(5(3(4(3(0(x1)))))))))))) -> 5(2(1(2(4(5(4(0(2(1(5(2(2(1(1(2(4(x1))))))))))))))))) 16.27/5.00 0(5(5(0(4(1(1(0(4(5(3(0(x1)))))))))))) -> 2(2(1(2(3(5(3(2(1(1(5(0(1(4(2(3(x1)))))))))))))))) 16.27/5.00 5(5(4(1(4(0(4(1(3(0(4(0(x1)))))))))))) -> 4(0(1(4(5(2(5(2(4(2(2(1(5(2(x1)))))))))))))) 16.27/5.00 0(0(5(1(5(4(0(3(1(3(4(0(x1)))))))))))) -> 5(4(2(2(2(2(3(0(2(2(2(2(3(1(2(1(5(3(x1)))))))))))))))))) 16.27/5.00 4(0(0(0(4(4(1(3(5(3(4(0(x1)))))))))))) -> 0(2(3(3(2(2(4(3(2(5(3(4(2(3(3(2(5(x1))))))))))))))))) 16.27/5.00 5(5(5(3(3(0(2(0(0(5(4(0(x1)))))))))))) -> 2(2(1(2(4(4(2(0(1(5(2(2(2(4(2(x1))))))))))))))) 16.27/5.00 5(0(4(5(0(1(0(1(4(0(5(0(x1)))))))))))) -> 4(0(2(5(3(2(0(1(3(5(2(3(5(1(3(5(x1)))))))))))))))) 16.27/5.00 1(4(0(5(4(5(0(0(5(1(5(0(x1)))))))))))) -> 5(5(5(5(2(1(1(0(4(0(5(5(2(4(2(5(5(x1))))))))))))))))) 16.27/5.00 4(1(0(3(4(4(1(1(1(3(5(0(x1)))))))))))) -> 2(3(2(5(0(5(3(3(2(2(5(5(4(2(0(2(x1)))))))))))))))) 16.27/5.00 0(5(3(4(3(1(5(2(1(3(5(0(x1)))))))))))) -> 2(4(5(3(5(5(5(2(5(5(0(2(5(2(2(5(x1)))))))))))))))) 16.27/5.00 3(3(2(0(3(4(0(1(2(4(5(0(x1)))))))))))) -> 3(2(1(4(3(2(4(5(0(2(3(2(3(3(3(x1))))))))))))))) 16.27/5.00 4(5(0(4(0(3(3(0(5(4(5(0(x1)))))))))))) -> 0(5(2(1(2(2(2(4(3(3(1(2(1(4(5(2(4(5(x1)))))))))))))))))) 16.27/5.00 0(3(1(1(0(5(0(1(0(0(0(1(x1)))))))))))) -> 2(0(1(3(3(2(0(5(5(5(2(1(2(5(5(3(x1)))))))))))))))) 16.27/5.00 2(1(4(3(2(2(5(2(3(1(0(1(x1)))))))))))) -> 2(2(2(2(1(4(5(3(2(0(2(1(2(3(x1)))))))))))))) 16.27/5.00 5(0(1(4(4(5(0(0(3(4(0(1(x1)))))))))))) -> 3(5(2(1(2(4(2(0(0(3(2(2(3(1(x1)))))))))))))) 16.27/5.00 0(0(5(0(4(4(5(0(5(4(1(1(x1)))))))))))) -> 5(0(2(1(2(0(5(2(2(1(4(1(1(4(4(5(x1)))))))))))))))) 16.27/5.00 2(1(1(3(4(0(0(4(4(5(2(1(x1)))))))))))) -> 2(2(3(2(4(5(1(4(0(3(2(2(2(5(x1)))))))))))))) 16.27/5.00 4(4(0(3(4(4(4(3(3(1(3(1(x1)))))))))))) -> 1(2(4(0(5(0(3(2(3(3(5(5(5(2(x1)))))))))))))) 16.27/5.00 0(0(2(5(4(4(0(4(5(3(3(1(x1)))))))))))) -> 5(5(1(5(4(5(3(3(3(5(2(1(2(2(4(x1))))))))))))))) 16.27/5.00 0(4(5(0(0(1(3(4(0(1(4(1(x1)))))))))))) -> 2(0(0(2(0(1(4(1(3(3(1(5(1(5(2(x1))))))))))))))) 16.27/5.00 0(4(0(0(4(0(3(3(5(3(4(1(x1)))))))))))) -> 0(5(1(0(1(5(2(5(1(2(2(2(2(3(5(1(x1)))))))))))))))) 16.27/5.00 3(4(1(0(3(4(2(1(3(0(0(2(x1)))))))))))) -> 3(2(2(5(5(0(5(1(1(2(0(5(2(2(1(1(x1)))))))))))))))) 16.27/5.00 4(1(5(2(0(2(5(4(1(3(0(2(x1)))))))))))) -> 5(3(5(2(3(1(4(2(1(0(2(3(5(2(1(x1))))))))))))))) 16.27/5.00 5(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 3(1(2(2(1(2(2(5(3(0(4(4(2(5(3(5(x1)))))))))))))))) 16.27/5.00 5(3(4(5(5(0(0(4(0(4(2(2(x1)))))))))))) -> 3(5(3(2(2(1(2(2(1(0(3(2(4(5(2(2(x1)))))))))))))))) 16.27/5.00 0(2(3(1(4(0(4(4(4(0(4(2(x1)))))))))))) -> 3(5(2(2(5(2(2(0(2(2(5(5(0(3(x1)))))))))))))) 16.27/5.00 5(1(4(4(3(0(4(5(4(0(4(2(x1)))))))))))) -> 3(3(2(5(5(2(2(0(4(1(2(3(2(5(1(1(4(2(x1)))))))))))))))))) 16.27/5.00 1(4(0(0(4(5(0(0(4(1(5(2(x1)))))))))))) -> 5(5(3(2(2(2(3(3(2(2(1(1(3(3(1(4(5(5(x1)))))))))))))))))) 16.27/5.00 1(4(3(1(3(4(4(4(3(0(1(3(x1)))))))))))) -> 4(5(1(4(2(5(0(2(1(4(4(2(2(1(x1)))))))))))))) 16.27/5.00 0(0(3(4(3(2(2(4(0(4(3(3(x1)))))))))))) -> 1(4(2(5(2(2(0(3(5(1(4(0(3(2(1(x1))))))))))))))) 16.27/5.00 2(4(4(3(0(3(4(4(4(0(4(3(x1)))))))))))) -> 1(0(0(2(3(5(0(4(2(1(2(2(2(3(5(4(2(1(x1)))))))))))))))))) 16.27/5.00 4(1(3(2(0(0(4(0(4(4(4(3(x1)))))))))))) -> 2(5(5(4(3(1(2(3(1(2(5(3(2(2(2(2(5(2(x1)))))))))))))))))) 16.27/5.00 3(3(4(0(5(4(2(2(3(0(0(4(x1)))))))))))) -> 3(4(2(2(2(5(5(3(3(2(2(3(1(2(5(2(2(5(x1)))))))))))))))))) 16.27/5.00 4(0(4(3(3(0(0(1(0(1(0(4(x1)))))))))))) -> 2(2(3(1(5(2(0(2(1(5(2(3(1(2(5(4(4(x1))))))))))))))))) 16.27/5.00 5(3(4(5(4(3(1(4(1(1(0(4(x1)))))))))))) -> 4(1(5(0(2(2(3(1(4(2(3(2(5(2(5(x1))))))))))))))) 16.27/5.00 4(0(1(5(4(5(0(3(4(1(0(4(x1)))))))))))) -> 5(2(3(4(2(3(0(5(5(1(2(5(1(1(2(x1))))))))))))))) 16.27/5.00 2(1(0(4(1(3(1(5(1(3(0(4(x1)))))))))))) -> 2(2(5(3(5(1(4(4(3(5(5(3(2(3(2(5(2(2(x1)))))))))))))))))) 16.27/5.00 1(1(4(5(2(0(3(4(4(3(0(4(x1)))))))))))) -> 3(4(5(5(2(3(2(2(1(2(2(5(5(3(5(0(x1)))))))))))))))) 16.27/5.00 0(0(4(3(4(3(3(1(3(4(0(4(x1)))))))))))) -> 3(2(3(4(2(2(4(0(1(2(2(5(2(2(2(3(5(x1))))))))))))))))) 16.27/5.00 2(0(3(3(4(5(3(0(0(0(1(4(x1)))))))))))) -> 3(3(5(2(0(2(2(1(3(3(2(5(3(3(5(2(2(x1))))))))))))))))) 16.27/5.00 0(3(2(3(0(5(0(3(4(0(1(4(x1)))))))))))) -> 1(1(5(2(5(1(0(2(5(4(4(1(2(3(3(2(x1)))))))))))))))) 16.27/5.00 4(4(1(3(4(2(3(1(3(1(1(4(x1)))))))))))) -> 2(3(5(2(1(4(1(3(2(3(2(2(2(3(2(1(0(4(x1)))))))))))))))))) 16.27/5.00 0(0(4(0(5(1(3(2(3(1(1(4(x1)))))))))))) -> 5(0(1(5(2(2(2(3(2(2(4(3(5(5(0(5(x1)))))))))))))))) 16.27/5.00 0(3(3(4(5(1(0(3(2(5(1(4(x1)))))))))))) -> 1(5(3(1(2(3(1(2(3(2(3(5(0(2(2(4(5(5(x1)))))))))))))))))) 16.27/5.00 5(4(4(0(3(0(3(4(0(0(2(4(x1)))))))))))) -> 2(0(3(2(1(1(0(5(3(5(3(3(2(2(3(5(0(2(x1)))))))))))))))))) 16.27/5.00 4(3(0(0(4(4(1(4(0(2(2(4(x1)))))))))))) -> 2(3(3(5(0(2(5(2(1(4(3(2(1(5(3(x1))))))))))))))) 16.27/5.00 0(4(4(5(4(4(5(0(0(2(3(4(x1)))))))))))) -> 0(5(1(5(2(5(0(2(5(3(0(2(2(1(3(2(1(4(x1)))))))))))))))))) 16.27/5.00 4(0(0(3(0(5(4(4(1(2(3(4(x1)))))))))))) -> 3(5(3(2(5(2(4(3(5(0(2(5(3(3(5(2(1(2(x1)))))))))))))))))) 16.27/5.00 0(1(5(4(1(4(4(4(5(2(3(4(x1)))))))))))) -> 5(1(0(3(2(2(3(2(1(3(3(2(5(5(1(2(x1)))))))))))))))) 16.27/5.00 5(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5(5(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))))))) 16.27/5.00 0(0(4(4(5(0(1(3(4(0(4(4(x1)))))))))))) -> 5(2(3(1(1(5(3(5(5(4(3(4(5(5(4(0(x1)))))))))))))))) 16.27/5.00 4(5(4(0(3(4(1(2(1(3(4(4(x1)))))))))))) -> 2(1(2(1(1(0(0(3(2(1(4(4(5(3(3(x1))))))))))))))) 16.27/5.00 4(0(5(4(3(4(1(3(4(3(4(4(x1)))))))))))) -> 2(1(0(0(2(0(2(3(1(5(2(4(2(0(x1)))))))))))))) 16.27/5.00 1(3(2(5(0(5(5(3(0(4(4(4(x1)))))))))))) -> 3(5(1(0(0(3(1(4(2(0(2(2(2(2(5(x1))))))))))))))) 16.27/5.00 0(2(0(1(5(3(0(4(4(4(4(4(x1)))))))))))) -> 2(0(3(3(3(5(2(0(3(2(1(3(3(3(5(5(2(1(x1)))))))))))))))))) 16.27/5.00 0(1(5(1(1(4(5(3(0(5(4(4(x1)))))))))))) -> 2(0(2(1(3(5(2(2(3(2(5(5(2(2(x1)))))))))))))) 16.27/5.00 4(0(4(4(5(2(0(1(0(0(5(4(x1)))))))))))) -> 1(2(2(1(1(0(4(2(2(4(2(0(5(5(3(x1))))))))))))))) 16.27/5.00 1(2(0(4(2(1(3(5(0(2(5(4(x1)))))))))))) -> 4(2(3(3(4(2(2(5(3(5(5(3(5(2(4(x1))))))))))))))) 16.27/5.00 0(4(0(0(3(0(2(4(1(2(5(4(x1)))))))))))) -> 0(2(2(2(0(4(1(2(5(2(5(3(5(4(3(x1))))))))))))))) 16.27/5.00 0(4(2(5(4(0(5(0(0(3(5(4(x1)))))))))))) -> 0(2(2(1(1(4(3(2(3(3(2(2(3(4(2(2(5(x1))))))))))))))))) 16.27/5.00 5(0(0(1(2(5(4(4(5(4(5(4(x1)))))))))))) -> 5(3(3(2(2(5(4(3(2(1(3(3(5(5(5(3(5(x1))))))))))))))))) 16.27/5.00 1(3(4(3(3(0(5(4(4(0(0(5(x1)))))))))))) -> 2(1(1(5(5(2(2(5(2(0(2(2(0(4(0(1(1(5(x1)))))))))))))))))) 16.27/5.00 0(0(0(0(0(2(5(0(4(1(0(5(x1)))))))))))) -> 5(4(0(3(5(5(2(2(3(3(2(1(1(1(0(1(x1)))))))))))))))) 16.27/5.00 4(0(3(0(1(2(4(3(5(3(0(5(x1)))))))))))) -> 1(2(5(3(4(5(2(1(2(0(2(3(5(2(1(2(x1)))))))))))))))) 16.27/5.00 0(0(0(2(5(0(0(4(0(5(0(5(x1)))))))))))) -> 4(3(1(2(2(5(2(0(2(4(5(3(2(2(3(0(x1)))))))))))))))) 16.27/5.00 2(4(1(2(1(1(2(4(0(0(1(5(x1)))))))))))) -> 2(0(1(2(2(5(5(2(3(3(2(3(3(2(2(2(2(x1))))))))))))))))) 16.27/5.00 0(5(4(1(3(0(4(4(1(1(1(5(x1)))))))))))) -> 2(2(4(2(2(4(0(2(5(3(5(1(3(2(1(4(x1)))))))))))))))) 16.27/5.00 5(5(0(1(4(3(0(3(0(3(1(5(x1)))))))))))) -> 2(5(5(1(1(4(5(5(2(5(5(2(3(4(x1)))))))))))))) 16.27/5.00 5(4(4(1(2(5(3(0(0(5(1(5(x1)))))))))))) -> 3(5(2(3(2(1(2(2(2(3(2(2(5(2(3(2(4(3(x1)))))))))))))))))) 16.27/5.00 4(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) -> 5(2(2(2(2(2(4(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))))))))) 16.27/5.00 4(5(0(0(0(0(1(5(3(0(3(5(x1)))))))))))) -> 2(1(2(1(5(1(4(5(1(2(3(2(2(1(3(3(2(x1))))))))))))))))) 16.27/5.00 2(0(0(3(2(0(0(4(3(0(4(5(x1)))))))))))) -> 3(1(2(3(3(4(5(2(1(1(1(5(3(1(2(x1))))))))))))))) 16.27/5.00 4(4(4(5(3(5(4(0(4(0(4(5(x1)))))))))))) -> 1(3(2(4(5(3(0(2(0(2(5(5(1(4(2(x1))))))))))))))) 16.27/5.00 0(2(3(4(2(4(3(4(4(3(4(5(x1)))))))))))) -> 5(1(4(3(5(2(4(2(4(0(3(2(1(2(x1)))))))))))))) 16.27/5.00 2(4(0(0(3(0(2(5(0(4(4(5(x1)))))))))))) -> 4(5(2(1(4(4(1(5(1(0(4(2(1(3(x1)))))))))))))) 16.27/5.00 4(3(4(5(4(0(2(0(4(4(4(5(x1)))))))))))) -> 4(1(1(2(4(0(1(1(1(1(1(2(0(2(5(x1))))))))))))))) 16.27/5.00 0(1(0(0(3(1(3(4(1(5(4(5(x1)))))))))))) -> 4(3(2(1(1(1(2(0(2(5(3(1(0(3(5(5(x1)))))))))))))))) 16.27/5.00 1(4(4(3(4(3(0(5(5(5(4(5(x1)))))))))))) -> 1(4(5(3(5(0(2(5(3(1(2(2(1(5(5(0(1(x1))))))))))))))))) 16.27/5.00 4(3(0(3(0(0(5(0(5(0(5(5(x1)))))))))))) -> 1(3(5(4(5(2(1(2(1(5(1(0(4(1(2(2(4(3(x1)))))))))))))))))) 16.27/5.00 0(5(5(0(0(4(0(1(2(2(5(5(x1)))))))))))) -> 5(5(2(3(3(5(0(2(2(2(1(1(3(1(2(3(5(x1))))))))))))))))) 16.27/5.00 16.27/5.00 Q is empty. 16.27/5.00 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (3) QTRSRRRProof (EQUIVALENT) 16.27/5.00 Used ordering: 16.27/5.00 Polynomial interpretation [POLO]: 16.27/5.00 16.27/5.00 POL(0(x_1)) = 4 + x_1 16.27/5.00 POL(1(x_1)) = 1 + x_1 16.27/5.00 POL(2(x_1)) = x_1 16.27/5.00 POL(3(x_1)) = 2 + x_1 16.27/5.00 POL(4(x_1)) = 3 + x_1 16.27/5.00 POL(5(x_1)) = x_1 16.27/5.00 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 16.27/5.00 16.27/5.00 0(2(5(4(1(3(4(0(3(0(0(0(x1)))))))))))) -> 4(2(4(3(3(2(2(3(0(1(5(5(3(2(0(1(x1)))))))))))))))) 16.27/5.00 1(3(0(1(5(0(5(1(3(0(0(0(x1)))))))))))) -> 3(3(2(1(4(4(4(2(1(5(5(2(1(3(3(x1))))))))))))))) 16.27/5.00 3(4(1(5(0(4(3(4(1(1(0(0(x1)))))))))))) -> 2(4(0(5(3(2(2(2(2(5(5(2(1(1(4(3(x1)))))))))))))))) 16.27/5.00 0(3(0(4(4(4(3(4(3(1(0(0(x1)))))))))))) -> 1(5(3(4(2(1(1(2(4(4(5(2(5(2(0(5(5(2(x1)))))))))))))))))) 16.27/5.00 0(1(0(1(0(0(3(0(1(2(0(0(x1)))))))))))) -> 3(0(0(1(5(3(5(5(2(4(3(4(2(1(2(x1))))))))))))))) 16.27/5.00 5(3(1(0(4(1(0(0(3(4(0(0(x1)))))))))))) -> 0(2(2(2(4(3(5(4(3(3(2(2(2(0(1(5(1(5(x1)))))))))))))))))) 16.27/5.00 5(1(0(3(1(3(0(0(4(5(0(0(x1)))))))))))) -> 2(1(2(5(4(2(2(2(1(1(4(5(5(5(5(0(1(3(x1)))))))))))))))))) 16.27/5.00 3(0(3(0(0(5(0(5(4(5(0(0(x1)))))))))))) -> 0(1(4(4(2(1(1(2(4(1(4(0(3(3(5(5(2(x1))))))))))))))))) 16.27/5.00 0(5(2(3(0(1(3(1(0(0(1(0(x1)))))))))))) -> 1(5(2(1(2(2(4(2(2(3(0(4(1(1(5(x1))))))))))))))) 16.27/5.00 0(1(2(4(4(4(4(1(0(0(1(0(x1)))))))))))) -> 4(3(1(2(3(2(4(2(2(2(1(3(5(1(4(2(5(5(x1)))))))))))))))))) 16.27/5.00 1(1(1(0(2(0(4(4(3(1(1(0(x1)))))))))))) -> 1(2(1(2(2(4(2(3(1(4(1(5(2(2(2(3(5(0(x1)))))))))))))))))) 16.27/5.00 5(4(0(3(1(5(0(0(5(4(1(0(x1)))))))))))) -> 5(3(5(5(2(1(4(3(5(2(1(4(5(2(1(3(3(2(x1)))))))))))))))))) 16.27/5.00 3(3(4(0(1(2(1(4(4(0(2(0(x1)))))))))))) -> 1(4(4(3(5(2(5(2(5(3(4(2(1(2(x1)))))))))))))) 16.27/5.00 5(4(4(1(0(2(1(4(3(4(2(0(x1)))))))))))) -> 3(3(2(2(2(2(2(0(3(2(1(2(1(5(2(4(x1)))))))))))))))) 16.27/5.00 3(1(0(4(4(0(0(4(4(0(3(0(x1)))))))))))) -> 3(5(2(3(2(0(1(3(4(0(4(2(2(4(2(1(2(5(x1)))))))))))))))))) 16.27/5.00 1(3(4(1(0(1(4(3(1(4(3(0(x1)))))))))))) -> 1(4(2(5(1(2(2(2(5(2(0(2(3(2(2(2(x1)))))))))))))))) 16.27/5.00 1(1(3(4(4(0(0(5(3(4(3(0(x1)))))))))))) -> 5(2(1(2(4(5(4(0(2(1(5(2(2(1(1(2(4(x1))))))))))))))))) 16.27/5.00 0(5(5(0(4(1(1(0(4(5(3(0(x1)))))))))))) -> 2(2(1(2(3(5(3(2(1(1(5(0(1(4(2(3(x1)))))))))))))))) 16.27/5.00 5(5(4(1(4(0(4(1(3(0(4(0(x1)))))))))))) -> 4(0(1(4(5(2(5(2(4(2(2(1(5(2(x1)))))))))))))) 16.27/5.00 0(0(5(1(5(4(0(3(1(3(4(0(x1)))))))))))) -> 5(4(2(2(2(2(3(0(2(2(2(2(3(1(2(1(5(3(x1)))))))))))))))))) 16.27/5.00 4(0(0(0(4(4(1(3(5(3(4(0(x1)))))))))))) -> 0(2(3(3(2(2(4(3(2(5(3(4(2(3(3(2(5(x1))))))))))))))))) 16.27/5.00 5(5(5(3(3(0(2(0(0(5(4(0(x1)))))))))))) -> 2(2(1(2(4(4(2(0(1(5(2(2(2(4(2(x1))))))))))))))) 16.27/5.00 5(0(4(5(0(1(0(1(4(0(5(0(x1)))))))))))) -> 4(0(2(5(3(2(0(1(3(5(2(3(5(1(3(5(x1)))))))))))))))) 16.27/5.00 1(4(0(5(4(5(0(0(5(1(5(0(x1)))))))))))) -> 5(5(5(5(2(1(1(0(4(0(5(5(2(4(2(5(5(x1))))))))))))))))) 16.27/5.00 4(1(0(3(4(4(1(1(1(3(5(0(x1)))))))))))) -> 2(3(2(5(0(5(3(3(2(2(5(5(4(2(0(2(x1)))))))))))))))) 16.27/5.00 0(5(3(4(3(1(5(2(1(3(5(0(x1)))))))))))) -> 2(4(5(3(5(5(5(2(5(5(0(2(5(2(2(5(x1)))))))))))))))) 16.27/5.00 3(3(2(0(3(4(0(1(2(4(5(0(x1)))))))))))) -> 3(2(1(4(3(2(4(5(0(2(3(2(3(3(3(x1))))))))))))))) 16.27/5.00 4(5(0(4(0(3(3(0(5(4(5(0(x1)))))))))))) -> 0(5(2(1(2(2(2(4(3(3(1(2(1(4(5(2(4(5(x1)))))))))))))))))) 16.27/5.00 0(3(1(1(0(5(0(1(0(0(0(1(x1)))))))))))) -> 2(0(1(3(3(2(0(5(5(5(2(1(2(5(5(3(x1)))))))))))))))) 16.27/5.00 2(1(4(3(2(2(5(2(3(1(0(1(x1)))))))))))) -> 2(2(2(2(1(4(5(3(2(0(2(1(2(3(x1)))))))))))))) 16.27/5.00 5(0(1(4(4(5(0(0(3(4(0(1(x1)))))))))))) -> 3(5(2(1(2(4(2(0(0(3(2(2(3(1(x1)))))))))))))) 16.27/5.00 0(0(5(0(4(4(5(0(5(4(1(1(x1)))))))))))) -> 5(0(2(1(2(0(5(2(2(1(4(1(1(4(4(5(x1)))))))))))))))) 16.27/5.00 2(1(1(3(4(0(0(4(4(5(2(1(x1)))))))))))) -> 2(2(3(2(4(5(1(4(0(3(2(2(2(5(x1)))))))))))))) 16.27/5.00 4(4(0(3(4(4(4(3(3(1(3(1(x1)))))))))))) -> 1(2(4(0(5(0(3(2(3(3(5(5(5(2(x1)))))))))))))) 16.27/5.00 0(0(2(5(4(4(0(4(5(3(3(1(x1)))))))))))) -> 5(5(1(5(4(5(3(3(3(5(2(1(2(2(4(x1))))))))))))))) 16.27/5.00 0(4(5(0(0(1(3(4(0(1(4(1(x1)))))))))))) -> 2(0(0(2(0(1(4(1(3(3(1(5(1(5(2(x1))))))))))))))) 16.27/5.00 0(4(0(0(4(0(3(3(5(3(4(1(x1)))))))))))) -> 0(5(1(0(1(5(2(5(1(2(2(2(2(3(5(1(x1)))))))))))))))) 16.27/5.00 3(4(1(0(3(4(2(1(3(0(0(2(x1)))))))))))) -> 3(2(2(5(5(0(5(1(1(2(0(5(2(2(1(1(x1)))))))))))))))) 16.27/5.00 4(1(5(2(0(2(5(4(1(3(0(2(x1)))))))))))) -> 5(3(5(2(3(1(4(2(1(0(2(3(5(2(1(x1))))))))))))))) 16.27/5.00 5(3(4(5(5(0(0(4(0(4(2(2(x1)))))))))))) -> 3(5(3(2(2(1(2(2(1(0(3(2(4(5(2(2(x1)))))))))))))))) 16.27/5.00 0(2(3(1(4(0(4(4(4(0(4(2(x1)))))))))))) -> 3(5(2(2(5(2(2(0(2(2(5(5(0(3(x1)))))))))))))) 16.27/5.00 5(1(4(4(3(0(4(5(4(0(4(2(x1)))))))))))) -> 3(3(2(5(5(2(2(0(4(1(2(3(2(5(1(1(4(2(x1)))))))))))))))))) 16.27/5.00 1(4(0(0(4(5(0(0(4(1(5(2(x1)))))))))))) -> 5(5(3(2(2(2(3(3(2(2(1(1(3(3(1(4(5(5(x1)))))))))))))))))) 16.27/5.00 1(4(3(1(3(4(4(4(3(0(1(3(x1)))))))))))) -> 4(5(1(4(2(5(0(2(1(4(4(2(2(1(x1)))))))))))))) 16.27/5.00 0(0(3(4(3(2(2(4(0(4(3(3(x1)))))))))))) -> 1(4(2(5(2(2(0(3(5(1(4(0(3(2(1(x1))))))))))))))) 16.27/5.00 2(4(4(3(0(3(4(4(4(0(4(3(x1)))))))))))) -> 1(0(0(2(3(5(0(4(2(1(2(2(2(3(5(4(2(1(x1)))))))))))))))))) 16.27/5.00 4(1(3(2(0(0(4(0(4(4(4(3(x1)))))))))))) -> 2(5(5(4(3(1(2(3(1(2(5(3(2(2(2(2(5(2(x1)))))))))))))))))) 16.27/5.00 3(3(4(0(5(4(2(2(3(0(0(4(x1)))))))))))) -> 3(4(2(2(2(5(5(3(3(2(2(3(1(2(5(2(2(5(x1)))))))))))))))))) 16.27/5.00 4(0(4(3(3(0(0(1(0(1(0(4(x1)))))))))))) -> 2(2(3(1(5(2(0(2(1(5(2(3(1(2(5(4(4(x1))))))))))))))))) 16.27/5.00 5(3(4(5(4(3(1(4(1(1(0(4(x1)))))))))))) -> 4(1(5(0(2(2(3(1(4(2(3(2(5(2(5(x1))))))))))))))) 16.27/5.00 4(0(1(5(4(5(0(3(4(1(0(4(x1)))))))))))) -> 5(2(3(4(2(3(0(5(5(1(2(5(1(1(2(x1))))))))))))))) 16.27/5.00 2(1(0(4(1(3(1(5(1(3(0(4(x1)))))))))))) -> 2(2(5(3(5(1(4(4(3(5(5(3(2(3(2(5(2(2(x1)))))))))))))))))) 16.27/5.00 1(1(4(5(2(0(3(4(4(3(0(4(x1)))))))))))) -> 3(4(5(5(2(3(2(2(1(2(2(5(5(3(5(0(x1)))))))))))))))) 16.27/5.00 0(0(4(3(4(3(3(1(3(4(0(4(x1)))))))))))) -> 3(2(3(4(2(2(4(0(1(2(2(5(2(2(2(3(5(x1))))))))))))))))) 16.27/5.00 2(0(3(3(4(5(3(0(0(0(1(4(x1)))))))))))) -> 3(3(5(2(0(2(2(1(3(3(2(5(3(3(5(2(2(x1))))))))))))))))) 16.27/5.00 0(3(2(3(0(5(0(3(4(0(1(4(x1)))))))))))) -> 1(1(5(2(5(1(0(2(5(4(4(1(2(3(3(2(x1)))))))))))))))) 16.27/5.00 4(4(1(3(4(2(3(1(3(1(1(4(x1)))))))))))) -> 2(3(5(2(1(4(1(3(2(3(2(2(2(3(2(1(0(4(x1)))))))))))))))))) 16.27/5.00 0(0(4(0(5(1(3(2(3(1(1(4(x1)))))))))))) -> 5(0(1(5(2(2(2(3(2(2(4(3(5(5(0(5(x1)))))))))))))))) 16.27/5.00 0(3(3(4(5(1(0(3(2(5(1(4(x1)))))))))))) -> 1(5(3(1(2(3(1(2(3(2(3(5(0(2(2(4(5(5(x1)))))))))))))))))) 16.27/5.00 5(4(4(0(3(0(3(4(0(0(2(4(x1)))))))))))) -> 2(0(3(2(1(1(0(5(3(5(3(3(2(2(3(5(0(2(x1)))))))))))))))))) 16.27/5.00 4(3(0(0(4(4(1(4(0(2(2(4(x1)))))))))))) -> 2(3(3(5(0(2(5(2(1(4(3(2(1(5(3(x1))))))))))))))) 16.27/5.00 0(4(4(5(4(4(5(0(0(2(3(4(x1)))))))))))) -> 0(5(1(5(2(5(0(2(5(3(0(2(2(1(3(2(1(4(x1)))))))))))))))))) 16.27/5.00 4(0(0(3(0(5(4(4(1(2(3(4(x1)))))))))))) -> 3(5(3(2(5(2(4(3(5(0(2(5(3(3(5(2(1(2(x1)))))))))))))))))) 16.27/5.00 0(1(5(4(1(4(4(4(5(2(3(4(x1)))))))))))) -> 5(1(0(3(2(2(3(2(1(3(3(2(5(5(1(2(x1)))))))))))))))) 16.27/5.00 0(0(4(4(5(0(1(3(4(0(4(4(x1)))))))))))) -> 5(2(3(1(1(5(3(5(5(4(3(4(5(5(4(0(x1)))))))))))))))) 16.27/5.00 4(5(4(0(3(4(1(2(1(3(4(4(x1)))))))))))) -> 2(1(2(1(1(0(0(3(2(1(4(4(5(3(3(x1))))))))))))))) 16.27/5.00 4(0(5(4(3(4(1(3(4(3(4(4(x1)))))))))))) -> 2(1(0(0(2(0(2(3(1(5(2(4(2(0(x1)))))))))))))) 16.27/5.00 1(3(2(5(0(5(5(3(0(4(4(4(x1)))))))))))) -> 3(5(1(0(0(3(1(4(2(0(2(2(2(2(5(x1))))))))))))))) 16.27/5.00 0(2(0(1(5(3(0(4(4(4(4(4(x1)))))))))))) -> 2(0(3(3(3(5(2(0(3(2(1(3(3(3(5(5(2(1(x1)))))))))))))))))) 16.27/5.00 0(1(5(1(1(4(5(3(0(5(4(4(x1)))))))))))) -> 2(0(2(1(3(5(2(2(3(2(5(5(2(2(x1)))))))))))))) 16.27/5.00 4(0(4(4(5(2(0(1(0(0(5(4(x1)))))))))))) -> 1(2(2(1(1(0(4(2(2(4(2(0(5(5(3(x1))))))))))))))) 16.27/5.00 1(2(0(4(2(1(3(5(0(2(5(4(x1)))))))))))) -> 4(2(3(3(4(2(2(5(3(5(5(3(5(2(4(x1))))))))))))))) 16.27/5.00 0(4(0(0(3(0(2(4(1(2(5(4(x1)))))))))))) -> 0(2(2(2(0(4(1(2(5(2(5(3(5(4(3(x1))))))))))))))) 16.27/5.00 0(4(2(5(4(0(5(0(0(3(5(4(x1)))))))))))) -> 0(2(2(1(1(4(3(2(3(3(2(2(3(4(2(2(5(x1))))))))))))))))) 16.27/5.00 5(0(0(1(2(5(4(4(5(4(5(4(x1)))))))))))) -> 5(3(3(2(2(5(4(3(2(1(3(3(5(5(5(3(5(x1))))))))))))))))) 16.27/5.00 1(3(4(3(3(0(5(4(4(0(0(5(x1)))))))))))) -> 2(1(1(5(5(2(2(5(2(0(2(2(0(4(0(1(1(5(x1)))))))))))))))))) 16.27/5.00 0(0(0(0(0(2(5(0(4(1(0(5(x1)))))))))))) -> 5(4(0(3(5(5(2(2(3(3(2(1(1(1(0(1(x1)))))))))))))))) 16.27/5.00 4(0(3(0(1(2(4(3(5(3(0(5(x1)))))))))))) -> 1(2(5(3(4(5(2(1(2(0(2(3(5(2(1(2(x1)))))))))))))))) 16.27/5.00 0(0(0(2(5(0(0(4(0(5(0(5(x1)))))))))))) -> 4(3(1(2(2(5(2(0(2(4(5(3(2(2(3(0(x1)))))))))))))))) 16.27/5.00 2(4(1(2(1(1(2(4(0(0(1(5(x1)))))))))))) -> 2(0(1(2(2(5(5(2(3(3(2(3(3(2(2(2(2(x1))))))))))))))))) 16.27/5.00 0(5(4(1(3(0(4(4(1(1(1(5(x1)))))))))))) -> 2(2(4(2(2(4(0(2(5(3(5(1(3(2(1(4(x1)))))))))))))))) 16.27/5.00 5(5(0(1(4(3(0(3(0(3(1(5(x1)))))))))))) -> 2(5(5(1(1(4(5(5(2(5(5(2(3(4(x1)))))))))))))) 16.27/5.00 5(4(4(1(2(5(3(0(0(5(1(5(x1)))))))))))) -> 3(5(2(3(2(1(2(2(2(3(2(2(5(2(3(2(4(3(x1)))))))))))))))))) 16.27/5.00 4(5(0(0(0(0(1(5(3(0(3(5(x1)))))))))))) -> 2(1(2(1(5(1(4(5(1(2(3(2(2(1(3(3(2(x1))))))))))))))))) 16.27/5.00 2(0(0(3(2(0(0(4(3(0(4(5(x1)))))))))))) -> 3(1(2(3(3(4(5(2(1(1(1(5(3(1(2(x1))))))))))))))) 16.27/5.00 4(4(4(5(3(5(4(0(4(0(4(5(x1)))))))))))) -> 1(3(2(4(5(3(0(2(0(2(5(5(1(4(2(x1))))))))))))))) 16.27/5.00 0(2(3(4(2(4(3(4(4(3(4(5(x1)))))))))))) -> 5(1(4(3(5(2(4(2(4(0(3(2(1(2(x1)))))))))))))) 16.27/5.00 2(4(0(0(3(0(2(5(0(4(4(5(x1)))))))))))) -> 4(5(2(1(4(4(1(5(1(0(4(2(1(3(x1)))))))))))))) 16.27/5.00 4(3(4(5(4(0(2(0(4(4(4(5(x1)))))))))))) -> 4(1(1(2(4(0(1(1(1(1(1(2(0(2(5(x1))))))))))))))) 16.27/5.00 0(1(0(0(3(1(3(4(1(5(4(5(x1)))))))))))) -> 4(3(2(1(1(1(2(0(2(5(3(1(0(3(5(5(x1)))))))))))))))) 16.27/5.00 1(4(4(3(4(3(0(5(5(5(4(5(x1)))))))))))) -> 1(4(5(3(5(0(2(5(3(1(2(2(1(5(5(0(1(x1))))))))))))))))) 16.27/5.00 4(3(0(3(0(0(5(0(5(0(5(5(x1)))))))))))) -> 1(3(5(4(5(2(1(2(1(5(1(0(4(1(2(2(4(3(x1)))))))))))))))))) 16.27/5.00 0(5(5(0(0(4(0(1(2(2(5(5(x1)))))))))))) -> 5(5(2(3(3(5(0(2(2(2(1(1(3(1(2(3(5(x1))))))))))))))))) 16.27/5.00 16.27/5.00 16.27/5.00 16.27/5.00 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (4) 16.27/5.00 Obligation: 16.27/5.00 Q restricted rewrite system: 16.27/5.00 The TRS R consists of the following rules: 16.27/5.00 16.27/5.00 5(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 3(1(2(2(1(2(2(5(3(0(4(4(2(5(3(5(x1)))))))))))))))) 16.27/5.00 5(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5(5(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))))))) 16.27/5.00 4(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) -> 5(2(2(2(2(2(4(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))))))))) 16.27/5.00 16.27/5.00 Q is empty. 16.27/5.00 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (5) DependencyPairsProof (EQUIVALENT) 16.27/5.00 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (6) 16.27/5.00 Obligation: 16.27/5.00 Q DP problem: 16.27/5.00 The TRS P consists of the following rules: 16.27/5.00 16.27/5.00 5^1(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 5^1(3(0(4(4(2(5(3(5(x1))))))))) 16.27/5.00 5^1(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 4^1(4(2(5(3(5(x1)))))) 16.27/5.00 5^1(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 4^1(2(5(3(5(x1))))) 16.27/5.00 5^1(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 5^1(3(5(x1))) 16.27/5.00 5^1(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 5^1(x1) 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5^1(5(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))))))) 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5^1(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1)))))))))))))))) 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 4^1(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))) 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 4^1(5(5(2(2(0(2(2(4(3(5(x1))))))))))) 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5^1(5(2(2(0(2(2(4(3(5(x1)))))))))) 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5^1(2(2(0(2(2(4(3(5(x1))))))))) 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 4^1(3(5(x1))) 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5^1(x1) 16.27/5.00 4^1(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) -> 5^1(2(2(2(2(2(4(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))))))))) 16.27/5.00 4^1(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) -> 4^1(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))) 16.27/5.00 4^1(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) -> 4^1(1(1(3(2(1(2(2(1(5(x1)))))))))) 16.27/5.00 16.27/5.00 The TRS R consists of the following rules: 16.27/5.00 16.27/5.00 5(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 3(1(2(2(1(2(2(5(3(0(4(4(2(5(3(5(x1)))))))))))))))) 16.27/5.00 5(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5(5(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))))))) 16.27/5.00 4(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) -> 5(2(2(2(2(2(4(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))))))))) 16.27/5.00 16.27/5.00 Q is empty. 16.27/5.00 We have to consider all minimal (P,Q,R)-chains. 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (7) DependencyGraphProof (EQUIVALENT) 16.27/5.00 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 14 less nodes. 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (8) 16.27/5.00 Obligation: 16.27/5.00 Q DP problem: 16.27/5.00 The TRS P consists of the following rules: 16.27/5.00 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5^1(x1) 16.27/5.00 5^1(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 5^1(x1) 16.27/5.00 16.27/5.00 The TRS R consists of the following rules: 16.27/5.00 16.27/5.00 5(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 3(1(2(2(1(2(2(5(3(0(4(4(2(5(3(5(x1)))))))))))))))) 16.27/5.00 5(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5(5(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))))))) 16.27/5.00 4(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) -> 5(2(2(2(2(2(4(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))))))))) 16.27/5.00 16.27/5.00 Q is empty. 16.27/5.00 We have to consider all minimal (P,Q,R)-chains. 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (9) UsableRulesProof (EQUIVALENT) 16.27/5.00 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. 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (10) 16.27/5.00 Obligation: 16.27/5.00 Q DP problem: 16.27/5.00 The TRS P consists of the following rules: 16.27/5.00 16.27/5.00 5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5^1(x1) 16.27/5.00 5^1(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 5^1(x1) 16.27/5.00 16.27/5.00 R is empty. 16.27/5.00 Q is empty. 16.27/5.00 We have to consider all minimal (P,Q,R)-chains. 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (11) QDPSizeChangeProof (EQUIVALENT) 16.27/5.00 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. 16.27/5.00 16.27/5.00 From the DPs we obtained the following set of size-change graphs: 16.27/5.00 *5^1(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) -> 5^1(x1) 16.27/5.00 The graph contains the following edges 1 > 1 16.27/5.00 16.27/5.00 16.27/5.00 *5^1(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) -> 5^1(x1) 16.27/5.00 The graph contains the following edges 1 > 1 16.27/5.00 16.27/5.00 16.27/5.00 ---------------------------------------- 16.27/5.00 16.27/5.00 (12) 16.27/5.00 YES 16.53/5.06 EOF