15.32/4.72 YES 15.32/4.79 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 15.32/4.79 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.32/4.79 15.32/4.79 15.32/4.79 Termination w.r.t. Q of the given QTRS could be proven: 15.32/4.79 15.32/4.79 (0) QTRS 15.32/4.79 (1) QTRS Reverse [EQUIVALENT, 0 ms] 15.32/4.79 (2) QTRS 15.32/4.79 (3) QTRSRRRProof [EQUIVALENT, 393 ms] 15.32/4.79 (4) QTRS 15.32/4.79 (5) DependencyPairsProof [EQUIVALENT, 57 ms] 15.32/4.79 (6) QDP 15.32/4.79 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 15.32/4.79 (8) TRUE 15.32/4.79 15.32/4.79 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (0) 15.32/4.79 Obligation: 15.32/4.79 Q restricted rewrite system: 15.32/4.79 The TRS R consists of the following rules: 15.32/4.79 15.32/4.79 0(0(1(1(1(2(0(1(1(3(2(1(x1)))))))))))) -> 3(5(5(4(3(3(0(5(0(4(1(5(4(0(3(1(x1)))))))))))))))) 15.32/4.79 0(0(4(1(1(3(1(4(1(1(3(1(x1)))))))))))) -> 3(5(5(5(2(4(5(0(5(2(5(2(0(5(1(0(4(x1))))))))))))))))) 15.32/4.79 0(1(0(4(2(2(0(3(4(1(1(5(x1)))))))))))) -> 4(0(1(5(4(3(1(2(3(5(3(5(0(1(x1)))))))))))))) 15.32/4.79 0(1(2(2(2(2(2(4(3(0(4(0(x1)))))))))))) -> 5(5(5(2(2(4(5(3(5(3(3(3(5(0(5(5(0(2(x1)))))))))))))))))) 15.32/4.79 0(1(2(4(1(5(3(4(2(1(2(1(x1)))))))))))) -> 0(5(2(3(5(5(2(1(0(4(5(3(1(1(5(x1))))))))))))))) 15.32/4.79 0(1(3(1(1(2(2(4(2(5(0(2(x1)))))))))))) -> 2(5(4(5(3(5(1(3(4(3(3(5(5(5(2(5(4(x1))))))))))))))))) 15.32/4.79 0(2(1(4(1(4(2(2(1(4(1(1(x1)))))))))))) -> 2(3(3(5(5(4(3(5(5(2(3(0(2(0(0(0(x1)))))))))))))))) 15.32/4.79 0(2(3(3(2(0(1(4(4(4(0(4(x1)))))))))))) -> 5(1(3(5(5(0(3(2(1(4(5(5(5(5(1(5(3(3(x1)))))))))))))))))) 15.32/4.79 0(2(4(0(3(5(1(3(0(2(2(0(x1)))))))))))) -> 0(4(0(5(5(5(5(5(4(1(3(3(5(5(2(5(0(x1))))))))))))))))) 15.32/4.79 0(3(3(1(1(1(4(1(0(2(1(2(x1)))))))))))) -> 5(1(2(5(2(5(1(5(0(0(1(5(4(3(5(5(x1)))))))))))))))) 15.32/4.79 0(4(1(1(2(2(2(2(0(1(4(4(x1)))))))))))) -> 4(0(0(5(0(0(5(1(5(0(2(3(0(5(2(2(3(x1))))))))))))))))) 15.32/4.79 0(4(1(3(1(4(4(4(4(1(0(2(x1)))))))))))) -> 4(4(2(3(0(1(1(0(3(5(3(1(0(2(x1)))))))))))))) 15.32/4.79 0(4(4(4(4(0(0(1(2(5(2(5(x1)))))))))))) -> 5(5(5(3(0(4(0(0(1(5(5(2(4(3(3(5(5(1(x1)))))))))))))))))) 15.32/4.79 0(4(5(2(0(3(0(1(4(5(1(1(x1)))))))))))) -> 0(1(0(5(3(3(0(3(5(5(5(0(0(3(3(5(x1)))))))))))))))) 15.32/4.79 0(5(1(2(5(4(4(2(0(1(1(2(x1)))))))))))) -> 0(5(4(5(3(4(5(4(3(3(3(2(3(3(5(4(2(x1))))))))))))))))) 15.32/4.79 0(5(3(4(4(4(0(2(4(0(2(1(x1)))))))))))) -> 3(5(3(3(5(4(4(3(5(5(2(3(5(3(5(0(x1)))))))))))))))) 15.32/4.79 0(5(4(1(2(0(0(2(0(4(2(3(x1)))))))))))) -> 5(5(4(5(3(5(2(2(3(3(3(3(5(5(0(2(x1)))))))))))))))) 15.32/4.79 0(5(4(2(2(1(3(1(1(1(3(1(x1)))))))))))) -> 4(3(5(0(2(0(1(5(0(2(5(3(3(5(4(5(5(3(x1)))))))))))))))))) 15.32/4.79 1(0(0(4(4(4(0(1(2(1(5(0(x1)))))))))))) -> 3(5(0(2(1(0(5(3(5(3(3(2(1(5(5(x1))))))))))))))) 15.32/4.79 1(0(1(5(0(1(0(4(2(0(1(2(x1)))))))))))) -> 3(2(5(5(3(4(3(5(4(5(5(3(1(0(2(x1))))))))))))))) 15.32/4.79 1(2(1(4(1(2(1(3(4(3(4(4(x1)))))))))))) -> 2(2(4(0(0(0(0(5(3(0(1(2(4(5(x1)))))))))))))) 15.32/4.79 1(3(2(2(5(1(1(2(1(2(5(0(x1)))))))))))) -> 5(5(5(1(5(4(5(1(4(5(5(5(3(4(5(3(5(0(x1)))))))))))))))))) 15.32/4.79 1(3(3(2(2(3(1(5(1(4(0(2(x1)))))))))))) -> 4(3(3(5(5(4(5(1(5(5(5(0(5(3(2(x1))))))))))))))) 15.32/4.79 1(3(4(4(0(2(2(0(2(1(2(2(x1)))))))))))) -> 1(3(1(5(3(3(5(5(5(5(0(4(3(2(4(x1))))))))))))))) 15.32/4.79 1(4(0(2(4(0(2(1(0(1(1(4(x1)))))))))))) -> 5(0(5(3(0(3(5(5(3(3(0(2(3(4(x1)))))))))))))) 15.32/4.79 1(4(1(4(4(4(4(1(4(1(5(2(x1)))))))))))) -> 3(5(0(4(3(5(4(5(0(5(3(2(1(5(0(5(5(x1))))))))))))))))) 15.32/4.79 1(4(3(2(0(2(4(3(1(1(1(1(x1)))))))))))) -> 4(4(5(3(4(5(5(4(0(4(5(0(5(5(x1)))))))))))))) 15.32/4.79 1(4(4(4(0(2(2(3(2(4(2(2(x1)))))))))))) -> 1(4(5(5(5(5(3(5(1(5(0(0(5(2(5(3(5(x1))))))))))))))))) 15.32/4.79 2(0(0(1(4(1(5(3(1(3(2(5(x1)))))))))))) -> 3(4(4(0(5(1(0(4(5(3(3(0(0(0(0(5(x1)))))))))))))))) 15.32/4.79 2(0(1(3(2(0(5(0(4(4(1(4(x1)))))))))))) -> 4(5(5(3(5(0(4(3(5(5(5(0(1(3(2(3(3(0(x1)))))))))))))))))) 15.32/4.79 2(0(2(0(1(3(4(1(2(0(1(5(x1)))))))))))) -> 5(5(3(5(2(3(0(3(3(5(3(5(5(3(3(x1))))))))))))))) 15.32/4.79 2(0(2(1(1(1(3(4(4(2(2(0(x1)))))))))))) -> 5(5(0(1(4(0(3(0(5(3(3(5(4(5(4(4(0(3(x1)))))))))))))))))) 15.32/4.79 2(0(2(5(2(2(0(3(1(5(0(4(x1)))))))))))) -> 5(0(5(4(5(2(5(1(2(2(3(5(5(5(3(x1))))))))))))))) 15.32/4.79 2(0(4(1(3(4(2(5(4(1(1(3(x1)))))))))))) -> 2(2(3(5(0(0(4(2(0(4(3(5(5(5(4(5(0(x1))))))))))))))))) 15.32/4.79 2(1(0(0(4(4(5(2(0(2(1(1(x1)))))))))))) -> 3(5(1(0(1(5(5(4(5(0(4(2(5(2(4(5(5(4(x1)))))))))))))))))) 15.32/4.79 2(1(1(1(0(4(1(3(0(4(0(3(x1)))))))))))) -> 4(3(0(2(5(0(5(2(1(3(5(3(5(1(x1)))))))))))))) 15.32/4.79 2(1(1(4(1(4(4(0(3(1(1(0(x1)))))))))))) -> 3(2(5(5(5(4(3(5(3(3(5(5(1(4(1(3(x1)))))))))))))))) 15.32/4.79 2(1(3(5(1(3(1(3(1(3(1(2(x1)))))))))))) -> 0(5(1(5(0(2(5(1(3(4(4(0(5(4(3(5(4(x1))))))))))))))))) 15.32/4.79 2(2(1(1(4(2(5(2(4(2(0(3(x1)))))))))))) -> 3(4(4(4(5(2(2(2(2(4(0(5(4(5(x1)))))))))))))) 15.32/4.79 2(2(1(3(1(1(2(0(1(3(4(4(x1)))))))))))) -> 2(4(4(0(0(0(2(5(5(5(3(5(1(3(5(0(4(x1))))))))))))))))) 15.32/4.79 2(2(1(4(4(0(5(2(0(4(2(4(x1)))))))))))) -> 3(5(0(2(5(1(3(2(3(3(5(5(5(0(0(4(x1)))))))))))))))) 15.32/4.79 2(2(2(1(4(4(3(3(5(1(4(1(x1)))))))))))) -> 1(5(4(5(5(5(3(5(5(5(2(1(0(1(0(5(1(x1))))))))))))))))) 15.32/4.79 2(2(5(2(5(5(0(4(0(1(2(0(x1)))))))))))) -> 1(2(5(4(0(5(4(3(0(5(5(0(5(5(x1)))))))))))))) 15.32/4.79 2(3(1(3(4(1(2(1(2(1(0(1(x1)))))))))))) -> 2(2(4(4(0(3(3(2(4(5(0(1(4(5(5(x1))))))))))))))) 15.32/4.79 2(3(2(1(5(1(1(2(4(1(4(1(x1)))))))))))) -> 3(3(0(5(4(5(5(0(0(0(2(3(3(1(4(5(0(x1))))))))))))))))) 15.32/4.79 2(3(2(3(4(2(2(3(5(2(4(4(x1)))))))))))) -> 5(0(3(0(5(5(1(2(4(3(5(5(5(4(0(5(x1)))))))))))))))) 15.32/4.79 2(3(2(4(0(0(4(1(3(0(4(1(x1)))))))))))) -> 4(5(5(1(0(0(1(0(5(1(5(5(3(3(5(5(5(0(x1)))))))))))))))))) 15.32/4.79 2(3(3(4(1(3(2(1(4(1(4(3(x1)))))))))))) -> 5(1(1(5(0(0(0(5(1(0(3(5(2(2(x1)))))))))))))) 15.32/4.79 2(4(2(0(4(4(2(2(3(3(1(0(x1)))))))))))) -> 5(5(5(0(2(5(1(5(3(5(2(4(4(1(4(5(3(x1))))))))))))))))) 15.32/4.79 2(4(3(4(1(0(4(2(0(1(5(2(x1)))))))))))) -> 0(0(5(3(4(5(3(4(5(4(0(3(0(2(x1)))))))))))))) 15.32/4.79 2(4(5(4(1(2(0(5(4(1(0(3(x1)))))))))))) -> 5(3(5(3(3(3(5(5(4(3(2(1(5(1(0(x1))))))))))))))) 15.32/4.79 2(5(1(4(4(1(3(4(1(3(2(0(x1)))))))))))) -> 2(5(0(5(3(4(5(3(3(2(1(3(0(4(4(x1))))))))))))))) 15.32/4.79 3(0(4(1(4(2(0(4(1(1(0(0(x1)))))))))))) -> 5(5(5(0(3(2(3(2(1(0(4(3(5(5(0(5(5(2(x1)))))))))))))))))) 15.32/4.79 3(0(4(3(5(2(1(4(4(0(0(1(x1)))))))))))) -> 5(5(3(0(0(5(4(0(5(1(3(2(5(3(x1)))))))))))))) 15.32/4.79 3(1(4(5(1(1(4(1(5(1(3(1(x1)))))))))))) -> 3(5(3(0(3(5(5(3(4(3(5(5(3(0(1(0(x1)))))))))))))))) 15.32/4.79 3(2(0(3(1(4(1(2(1(1(4(4(x1)))))))))))) -> 1(5(2(0(5(1(3(5(4(3(5(3(0(5(2(5(2(x1))))))))))))))))) 15.32/4.79 3(2(0(4(2(3(0(3(3(0(4(4(x1)))))))))))) -> 3(4(4(0(2(5(5(0(5(3(2(3(4(5(3(3(x1)))))))))))))))) 15.32/4.79 3(2(2(2(0(4(5(2(2(5(3(4(x1)))))))))))) -> 1(5(2(3(1(1(0(1(0(4(3(1(5(3(x1)))))))))))))) 15.32/4.79 3(2(4(2(5(0(3(2(0(2(2(5(x1)))))))))))) -> 4(5(0(0(2(2(5(0(5(0(5(1(0(2(5(x1))))))))))))))) 15.32/4.79 3(3(1(2(3(4(4(5(4(1(3(1(x1)))))))))))) -> 4(0(4(5(2(1(5(5(0(4(3(1(5(3(5(5(x1)))))))))))))))) 15.32/4.79 3(3(3(4(0(0(1(4(3(2(0(3(x1)))))))))))) -> 3(5(3(5(1(0(2(5(5(5(2(3(3(4(3(x1))))))))))))))) 15.32/4.79 3(4(1(0(3(4(2(2(3(2(1(3(x1)))))))))))) -> 5(4(5(0(5(5(1(3(0(0(2(4(1(1(x1)))))))))))))) 15.32/4.79 3(4(2(1(1(4(4(1(3(3(4(2(x1)))))))))))) -> 4(0(4(2(1(1(5(5(4(4(5(0(5(0(x1)))))))))))))) 15.32/4.79 3(4(2(2(0(4(2(2(1(2(4(2(x1)))))))))))) -> 2(2(0(1(4(5(2(2(3(5(5(3(3(4(x1)))))))))))))) 15.32/4.79 3(4(4(4(2(1(5(2(4(1(5(2(x1)))))))))))) -> 3(0(0(1(5(5(3(4(0(5(1(0(5(3(5(4(5(5(x1)))))))))))))))))) 15.32/4.79 4(0(0(1(0(4(1(3(1(2(2(4(x1)))))))))))) -> 4(5(0(2(0(0(5(2(5(0(5(0(3(3(0(x1))))))))))))))) 15.32/4.79 4(0(2(1(1(1(4(3(0(3(4(4(x1)))))))))))) -> 1(5(5(1(0(2(4(5(5(4(0(5(2(3(5(x1))))))))))))))) 15.32/4.79 4(0(2(2(2(2(5(4(4(2(4(0(x1)))))))))))) -> 5(0(3(3(5(5(2(4(5(0(4(0(2(5(2(5(x1)))))))))))))))) 15.32/4.79 4(0(4(1(2(4(5(4(0(1(4(3(x1)))))))))))) -> 5(2(3(3(5(0(1(3(4(5(4(5(4(5(4(5(x1)))))))))))))))) 15.32/4.79 4(1(1(2(0(2(3(0(3(4(5(4(x1)))))))))))) -> 4(1(5(3(5(1(5(5(4(2(3(3(5(3(5(3(3(x1))))))))))))))))) 15.32/4.79 4(1(1(2(3(2(4(2(4(3(4(3(x1)))))))))))) -> 1(5(2(5(3(5(0(2(5(0(4(3(5(2(3(4(5(5(x1)))))))))))))))))) 15.32/4.79 4(1(1(3(4(4(1(2(1(3(1(2(x1)))))))))))) -> 2(5(5(5(3(3(0(0(2(3(3(0(3(5(2(4(5(3(x1)))))))))))))))))) 15.32/4.79 4(1(2(1(4(2(4(2(1(2(0(1(x1)))))))))))) -> 4(1(4(5(2(1(1(4(2(4(5(1(5(5(0(x1))))))))))))))) 15.32/4.79 4(1(3(4(4(4(3(3(3(4(2(2(x1)))))))))))) -> 4(4(3(4(0(2(4(5(5(0(3(3(5(2(3(0(x1)))))))))))))))) 15.32/4.79 4(1(4(2(2(0(4(5(2(0(4(5(x1)))))))))))) -> 0(4(2(2(4(5(5(5(3(3(3(5(1(4(x1)))))))))))))) 15.32/4.79 4(1(4(2(3(1(3(4(3(2(5(2(x1)))))))))))) -> 3(3(4(5(5(4(3(3(3(3(0(4(2(1(5(x1))))))))))))))) 15.32/4.79 4(2(0(0(5(3(2(0(4(1(3(5(x1)))))))))))) -> 2(5(3(3(4(3(1(3(0(3(3(5(5(5(5(5(x1)))))))))))))))) 15.32/4.79 4(2(0(2(4(2(0(0(0(1(2(5(x1)))))))))))) -> 5(2(1(3(2(3(5(3(2(4(5(4(3(4(5(5(x1)))))))))))))))) 15.32/4.79 4(2(0(3(2(2(0(3(2(4(2(3(x1)))))))))))) -> 2(1(5(2(2(1(5(5(4(5(0(0(0(2(x1)))))))))))))) 15.32/4.79 4(2(1(0(4(3(2(1(2(4(2(3(x1)))))))))))) -> 0(3(5(0(5(5(5(5(3(5(4(0(3(5(5(3(4(x1))))))))))))))))) 15.32/4.79 4(2(1(1(2(2(0(2(2(0(3(1(x1)))))))))))) -> 1(2(5(5(3(1(0(5(4(0(5(0(2(3(0(4(0(5(x1)))))))))))))))))) 15.32/4.79 4(2(2(0(2(2(0(5(2(1(0(5(x1)))))))))))) -> 3(4(5(5(5(4(0(3(4(3(4(5(5(0(2(5(3(3(x1)))))))))))))))))) 15.32/4.79 4(2(2(3(1(4(1(1(2(3(4(4(x1)))))))))))) -> 1(0(0(4(3(4(0(1(4(5(3(2(4(0(x1)))))))))))))) 15.32/4.79 4(2(4(0(3(1(3(1(3(2(2(3(x1)))))))))))) -> 4(5(1(0(1(3(4(5(5(4(5(2(4(4(5(5(5(2(x1)))))))))))))))))) 15.32/4.79 4(3(1(1(2(4(0(3(1(4(3(0(x1)))))))))))) -> 2(5(3(5(5(2(3(0(3(5(5(2(3(4(1(x1))))))))))))))) 15.32/4.79 4(4(2(2(0(4(2(0(3(1(4(2(x1)))))))))))) -> 2(4(5(1(5(3(3(3(1(0(1(0(1(4(5(5(x1)))))))))))))))) 15.32/4.79 4(4(4(4(1(0(4(1(3(2(3(2(x1)))))))))))) -> 1(3(0(4(0(0(5(5(5(1(3(5(5(1(0(1(4(5(x1)))))))))))))))))) 15.32/4.79 4(5(0(0(2(2(0(4(3(0(4(4(x1)))))))))))) -> 4(5(5(4(3(4(5(3(0(0(3(4(5(5(5(1(4(x1))))))))))))))))) 15.32/4.79 5(1(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 0(3(2(5(5(4(5(5(3(5(5(4(5(5(4(3(5(x1))))))))))))))))) 15.32/4.79 5(1(5(2(2(1(1(2(0(3(2(2(x1)))))))))))) -> 0(2(5(3(5(5(4(1(0(5(1(5(5(3(3(5(5(5(x1)))))))))))))))))) 15.32/4.79 5(2(0(4(2(2(1(2(5(4(1(2(x1)))))))))))) -> 4(5(5(5(1(3(0(4(0(4(4(5(5(5(0(4(x1)))))))))))))))) 15.32/4.79 5(2(0(5(0(1(2(0(0(2(0(4(x1)))))))))))) -> 0(3(3(4(3(5(1(5(5(2(3(0(1(3(x1)))))))))))))) 15.32/4.79 5(3(0(2(2(4(1(2(4(5(1(0(x1)))))))))))) -> 0(5(1(5(0(2(5(2(5(3(5(1(5(5(x1)))))))))))))) 15.32/4.79 5(3(2(1(4(2(1(2(1(1(4(3(x1)))))))))))) -> 4(5(0(5(3(3(0(5(5(0(5(5(3(5(1(5(1(3(x1)))))))))))))))))) 15.32/4.79 5(4(2(2(2(1(1(5(3(2(2(1(x1)))))))))))) -> 0(4(0(5(5(0(5(3(0(2(5(4(2(5(5(x1))))))))))))))) 15.32/4.79 5(5(1(2(2(0(3(5(1(1(4(3(x1)))))))))))) -> 0(5(0(3(5(4(5(0(1(0(4(0(5(0(x1)))))))))))))) 15.32/4.79 15.32/4.79 Q is empty. 15.32/4.79 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (1) QTRS Reverse (EQUIVALENT) 15.32/4.79 We applied the QTRS Reverse Processor [REVERSE]. 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (2) 15.32/4.79 Obligation: 15.32/4.79 Q restricted rewrite system: 15.32/4.79 The TRS R consists of the following rules: 15.32/4.79 15.32/4.79 1(2(3(1(1(0(2(1(1(1(0(0(x1)))))))))))) -> 1(3(0(4(5(1(4(0(5(0(3(3(4(5(5(3(x1)))))))))))))))) 15.32/4.79 1(3(1(1(4(1(3(1(1(4(0(0(x1)))))))))))) -> 4(0(1(5(0(2(5(2(5(0(5(4(2(5(5(5(3(x1))))))))))))))))) 15.32/4.79 5(1(1(4(3(0(2(2(4(0(1(0(x1)))))))))))) -> 1(0(5(3(5(3(2(1(3(4(5(1(0(4(x1)))))))))))))) 15.32/4.79 0(4(0(3(4(2(2(2(2(2(1(0(x1)))))))))))) -> 2(0(5(5(0(5(3(3(3(5(3(5(4(2(2(5(5(5(x1)))))))))))))))))) 15.32/4.79 1(2(1(2(4(3(5(1(4(2(1(0(x1)))))))))))) -> 5(1(1(3(5(4(0(1(2(5(5(3(2(5(0(x1))))))))))))))) 15.32/4.79 2(0(5(2(4(2(2(1(1(3(1(0(x1)))))))))))) -> 4(5(2(5(5(5(3(3(4(3(1(5(3(5(4(5(2(x1))))))))))))))))) 15.32/4.79 1(1(4(1(2(2(4(1(4(1(2(0(x1)))))))))))) -> 0(0(0(2(0(3(2(5(5(3(4(5(5(3(3(2(x1)))))))))))))))) 15.32/4.79 4(0(4(4(4(1(0(2(3(3(2(0(x1)))))))))))) -> 3(3(5(1(5(5(5(5(4(1(2(3(0(5(5(3(1(5(x1)))))))))))))))))) 15.32/4.79 0(2(2(0(3(1(5(3(0(4(2(0(x1)))))))))))) -> 0(5(2(5(5(3(3(1(4(5(5(5(5(5(0(4(0(x1))))))))))))))))) 15.32/4.79 2(1(2(0(1(4(1(1(1(3(3(0(x1)))))))))))) -> 5(5(3(4(5(1(0(0(5(1(5(2(5(2(1(5(x1)))))))))))))))) 15.32/4.79 4(4(1(0(2(2(2(2(1(1(4(0(x1)))))))))))) -> 3(2(2(5(0(3(2(0(5(1(5(0(0(5(0(0(4(x1))))))))))))))))) 15.32/4.79 2(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 2(0(1(3(5(3(0(1(1(0(3(2(4(4(x1)))))))))))))) 15.32/4.79 5(2(5(2(1(0(0(4(4(4(4(0(x1)))))))))))) -> 1(5(5(3(3(4(2(5(5(1(0(0(4(0(3(5(5(5(x1)))))))))))))))))) 15.32/4.79 1(1(5(4(1(0(3(0(2(5(4(0(x1)))))))))))) -> 5(3(3(0(0(5(5(5(3(0(3(3(5(0(1(0(x1)))))))))))))))) 15.32/4.79 2(1(1(0(2(4(4(5(2(1(5(0(x1)))))))))))) -> 2(4(5(3(3(2(3(3(3(4(5(4(3(5(4(5(0(x1))))))))))))))))) 15.32/4.79 1(2(0(4(2(0(4(4(4(3(5(0(x1)))))))))))) -> 0(5(3(5(3(2(5(5(3(4(4(5(3(3(5(3(x1)))))))))))))))) 15.32/4.79 3(2(4(0(2(0(0(2(1(4(5(0(x1)))))))))))) -> 2(0(5(5(3(3(3(3(2(2(5(3(5(4(5(5(x1)))))))))))))))) 15.32/4.79 1(3(1(1(1(3(1(2(2(4(5(0(x1)))))))))))) -> 3(5(5(4(5(3(3(5(2(0(5(1(0(2(0(5(3(4(x1)))))))))))))))))) 15.32/4.79 0(5(1(2(1(0(4(4(4(0(0(1(x1)))))))))))) -> 5(5(1(2(3(3(5(3(5(0(1(2(0(5(3(x1))))))))))))))) 15.32/4.79 2(1(0(2(4(0(1(0(5(1(0(1(x1)))))))))))) -> 2(0(1(3(5(5(4(5(3(4(3(5(5(2(3(x1))))))))))))))) 15.32/4.79 4(4(3(4(3(1(2(1(4(1(2(1(x1)))))))))))) -> 5(4(2(1(0(3(5(0(0(0(0(4(2(2(x1)))))))))))))) 15.32/4.79 0(5(2(1(2(1(1(5(2(2(3(1(x1)))))))))))) -> 0(5(3(5(4(3(5(5(5(4(1(5(4(5(1(5(5(5(x1)))))))))))))))))) 15.32/4.79 2(0(4(1(5(1(3(2(2(3(3(1(x1)))))))))))) -> 2(3(5(0(5(5(5(1(5(4(5(5(3(3(4(x1))))))))))))))) 15.32/4.79 2(2(1(2(0(2(2(0(4(4(3(1(x1)))))))))))) -> 4(2(3(4(0(5(5(5(5(3(3(5(1(3(1(x1))))))))))))))) 15.32/4.79 4(1(1(0(1(2(0(4(2(0(4(1(x1)))))))))))) -> 4(3(2(0(3(3(5(5(3(0(3(5(0(5(x1)))))))))))))) 15.32/4.79 2(5(1(4(1(4(4(4(4(1(4(1(x1)))))))))))) -> 5(5(0(5(1(2(3(5(0(5(4(5(3(4(0(5(3(x1))))))))))))))))) 15.32/4.79 1(1(1(1(3(4(2(0(2(3(4(1(x1)))))))))))) -> 5(5(0(5(4(0(4(5(5(4(3(5(4(4(x1)))))))))))))) 15.32/4.79 2(2(4(2(3(2(2(0(4(4(4(1(x1)))))))))))) -> 5(3(5(2(5(0(0(5(1(5(3(5(5(5(5(4(1(x1))))))))))))))))) 15.32/4.79 5(2(3(1(3(5(1(4(1(0(0(2(x1)))))))))))) -> 5(0(0(0(0(3(3(5(4(0(1(5(0(4(4(3(x1)))))))))))))))) 15.32/4.79 4(1(4(4(0(5(0(2(3(1(0(2(x1)))))))))))) -> 0(3(3(2(3(1(0(5(5(5(3(4(0(5(3(5(5(4(x1)))))))))))))))))) 15.32/4.79 5(1(0(2(1(4(3(1(0(2(0(2(x1)))))))))))) -> 3(3(5(5(3(5(3(3(0(3(2(5(3(5(5(x1))))))))))))))) 15.32/4.79 0(2(2(4(4(3(1(1(1(2(0(2(x1)))))))))))) -> 3(0(4(4(5(4(5(3(3(5(0(3(0(4(1(0(5(5(x1)))))))))))))))))) 15.32/4.79 4(0(5(1(3(0(2(2(5(2(0(2(x1)))))))))))) -> 3(5(5(5(3(2(2(1(5(2(5(4(5(0(5(x1))))))))))))))) 15.32/4.79 3(1(1(4(5(2(4(3(1(4(0(2(x1)))))))))))) -> 0(5(4(5(5(5(3(4(0(2(4(0(0(5(3(2(2(x1))))))))))))))))) 15.32/4.79 1(1(2(0(2(5(4(4(0(0(1(2(x1)))))))))))) -> 4(5(5(4(2(5(2(4(0(5(4(5(5(1(0(1(5(3(x1)))))))))))))))))) 15.32/4.79 3(0(4(0(3(1(4(0(1(1(1(2(x1)))))))))))) -> 1(5(3(5(3(1(2(5(0(5(2(0(3(4(x1)))))))))))))) 15.32/4.79 0(1(1(3(0(4(4(1(4(1(1(2(x1)))))))))))) -> 3(1(4(1(5(5(3(3(5(3(4(5(5(5(2(3(x1)))))))))))))))) 15.32/4.79 2(1(3(1(3(1(3(1(5(3(1(2(x1)))))))))))) -> 4(5(3(4(5(0(4(4(3(1(5(2(0(5(1(5(0(x1))))))))))))))))) 15.32/4.79 3(0(2(4(2(5(2(4(1(1(2(2(x1)))))))))))) -> 5(4(5(0(4(2(2(2(2(5(4(4(4(3(x1)))))))))))))) 15.32/4.79 4(4(3(1(0(2(1(1(3(1(2(2(x1)))))))))))) -> 4(0(5(3(1(5(3(5(5(5(2(0(0(0(4(4(2(x1))))))))))))))))) 15.32/4.79 4(2(4(0(2(5(0(4(4(1(2(2(x1)))))))))))) -> 4(0(0(5(5(5(3(3(2(3(1(5(2(0(5(3(x1)))))))))))))))) 15.32/4.79 1(4(1(5(3(3(4(4(1(2(2(2(x1)))))))))))) -> 1(5(0(1(0(1(2(5(5(5(3(5(5(5(4(5(1(x1))))))))))))))))) 15.32/4.79 0(2(1(0(4(0(5(5(2(5(2(2(x1)))))))))))) -> 5(5(0(5(5(0(3(4(5(0(4(5(2(1(x1)))))))))))))) 15.32/4.79 1(0(1(2(1(2(1(4(3(1(3(2(x1)))))))))))) -> 5(5(4(1(0(5(4(2(3(3(0(4(4(2(2(x1))))))))))))))) 15.32/4.79 1(4(1(4(2(1(1(5(1(2(3(2(x1)))))))))))) -> 0(5(4(1(3(3(2(0(0(0(5(5(4(5(0(3(3(x1))))))))))))))))) 15.32/4.79 4(4(2(5(3(2(2(4(3(2(3(2(x1)))))))))))) -> 5(0(4(5(5(5(3(4(2(1(5(5(0(3(0(5(x1)))))))))))))))) 15.32/4.79 1(4(0(3(1(4(0(0(4(2(3(2(x1)))))))))))) -> 0(5(5(5(3(3(5(5(1(5(0(1(0(0(1(5(5(4(x1)))))))))))))))))) 15.32/4.79 3(4(1(4(1(2(3(1(4(3(3(2(x1)))))))))))) -> 2(2(5(3(0(1(5(0(0(0(5(1(1(5(x1)))))))))))))) 15.32/4.79 0(1(3(3(2(2(4(4(0(2(4(2(x1)))))))))))) -> 3(5(4(1(4(4(2(5(3(5(1(5(2(0(5(5(5(x1))))))))))))))))) 15.32/4.79 2(5(1(0(2(4(0(1(4(3(4(2(x1)))))))))))) -> 2(0(3(0(4(5(4(3(5(4(3(5(0(0(x1)))))))))))))) 15.32/4.79 3(0(1(4(5(0(2(1(4(5(4(2(x1)))))))))))) -> 0(1(5(1(2(3(4(5(5(3(3(3(5(3(5(x1))))))))))))))) 15.32/4.79 0(2(3(1(4(3(1(4(4(1(5(2(x1)))))))))))) -> 4(4(0(3(1(2(3(3(5(4(3(5(0(5(2(x1))))))))))))))) 15.32/4.79 0(0(1(1(4(0(2(4(1(4(0(3(x1)))))))))))) -> 2(5(5(0(5(5(3(4(0(1(2(3(2(3(0(5(5(5(x1)))))))))))))))))) 15.32/4.79 1(0(0(4(4(1(2(5(3(4(0(3(x1)))))))))))) -> 3(5(2(3(1(5(0(4(5(0(0(3(5(5(x1)))))))))))))) 15.32/4.79 1(3(1(5(1(4(1(1(5(4(1(3(x1)))))))))))) -> 0(1(0(3(5(5(3(4(3(5(5(3(0(3(5(3(x1)))))))))))))))) 15.32/4.79 4(4(1(1(2(1(4(1(3(0(2(3(x1)))))))))))) -> 2(5(2(5(0(3(5(3(4(5(3(1(5(0(2(5(1(x1))))))))))))))))) 15.32/4.79 4(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 3(3(5(4(3(2(3(5(0(5(5(2(0(4(4(3(x1)))))))))))))))) 15.32/4.79 4(3(5(2(2(5(4(0(2(2(2(3(x1)))))))))))) -> 3(5(1(3(4(0(1(0(1(1(3(2(5(1(x1)))))))))))))) 15.32/4.79 5(2(2(0(2(3(0(5(2(4(2(3(x1)))))))))))) -> 5(2(0(1(5(0(5(0(5(2(2(0(0(5(4(x1))))))))))))))) 15.32/4.79 1(3(1(4(5(4(4(3(2(1(3(3(x1)))))))))))) -> 5(5(3(5(1(3(4(0(5(5(1(2(5(4(0(4(x1)))))))))))))))) 15.32/4.79 3(0(2(3(4(1(0(0(4(3(3(3(x1)))))))))))) -> 3(4(3(3(2(5(5(5(2(0(1(5(3(5(3(x1))))))))))))))) 15.32/4.79 3(1(2(3(2(2(4(3(0(1(4(3(x1)))))))))))) -> 1(1(4(2(0(0(3(1(5(5(0(5(4(5(x1)))))))))))))) 15.32/4.79 2(4(3(3(1(4(4(1(1(2(4(3(x1)))))))))))) -> 0(5(0(5(4(4(5(5(1(1(2(4(0(4(x1)))))))))))))) 15.32/4.79 2(4(2(1(2(2(4(0(2(2(4(3(x1)))))))))))) -> 4(3(3(5(5(3(2(2(5(4(1(0(2(2(x1)))))))))))))) 15.32/4.79 2(5(1(4(2(5(1(2(4(4(4(3(x1)))))))))))) -> 5(5(4(5(3(5(0(1(5(0(4(3(5(5(1(0(0(3(x1)))))))))))))))))) 15.32/4.79 4(2(2(1(3(1(4(0(1(0(0(4(x1)))))))))))) -> 0(3(3(0(5(0(5(2(5(0(0(2(0(5(4(x1))))))))))))))) 15.32/4.79 4(4(3(0(3(4(1(1(1(2(0(4(x1)))))))))))) -> 5(3(2(5(0(4(5(5(4(2(0(1(5(5(1(x1))))))))))))))) 15.32/4.79 0(4(2(4(4(5(2(2(2(2(0(4(x1)))))))))))) -> 5(2(5(2(0(4(0(5(4(2(5(5(3(3(0(5(x1)))))))))))))))) 15.32/4.79 3(4(1(0(4(5(4(2(1(4(0(4(x1)))))))))))) -> 5(4(5(4(5(4(5(4(3(1(0(5(3(3(2(5(x1)))))))))))))))) 15.32/4.79 4(5(4(3(0(3(2(0(2(1(1(4(x1)))))))))))) -> 3(3(5(3(5(3(3(2(4(5(5(1(5(3(5(1(4(x1))))))))))))))))) 15.32/4.79 3(4(3(4(2(4(2(3(2(1(1(4(x1)))))))))))) -> 5(5(4(3(2(5(3(4(0(5(2(0(5(3(5(2(5(1(x1)))))))))))))))))) 15.32/4.79 2(1(3(1(2(1(4(4(3(1(1(4(x1)))))))))))) -> 3(5(4(2(5(3(0(3(3(2(0(0(3(3(5(5(5(2(x1)))))))))))))))))) 15.32/4.79 1(0(2(1(2(4(2(4(1(2(1(4(x1)))))))))))) -> 0(5(5(1(5(4(2(4(1(1(2(5(4(1(4(x1))))))))))))))) 15.32/4.79 2(2(4(3(3(3(4(4(4(3(1(4(x1)))))))))))) -> 0(3(2(5(3(3(0(5(5(4(2(0(4(3(4(4(x1)))))))))))))))) 15.32/4.79 5(4(0(2(5(4(0(2(2(4(1(4(x1)))))))))))) -> 4(1(5(3(3(3(5(5(5(4(2(2(4(0(x1)))))))))))))) 15.32/4.79 2(5(2(3(4(3(1(3(2(4(1(4(x1)))))))))))) -> 5(1(2(4(0(3(3(3(3(4(5(5(4(3(3(x1))))))))))))))) 15.32/4.79 5(3(1(4(0(2(3(5(0(0(2(4(x1)))))))))))) -> 5(5(5(5(5(3(3(0(3(1(3(4(3(3(5(2(x1)))))))))))))))) 15.32/4.79 5(2(1(0(0(0(2(4(2(0(2(4(x1)))))))))))) -> 5(5(4(3(4(5(4(2(3(5(3(2(3(1(2(5(x1)))))))))))))))) 15.32/4.79 3(2(4(2(3(0(2(2(3(0(2(4(x1)))))))))))) -> 2(0(0(0(5(4(5(5(1(2(2(5(1(2(x1)))))))))))))) 15.32/4.79 3(2(4(2(1(2(3(4(0(1(2(4(x1)))))))))))) -> 4(3(5(5(3(0(4(5(3(5(5(5(5(0(5(3(0(x1))))))))))))))))) 15.32/4.79 1(3(0(2(2(0(2(2(1(1(2(4(x1)))))))))))) -> 5(0(4(0(3(2(0(5(0(4(5(0(1(3(5(5(2(1(x1)))))))))))))))))) 15.32/4.79 5(0(1(2(5(0(2(2(0(2(2(4(x1)))))))))))) -> 3(3(5(2(0(5(5(4(3(4(3(0(4(5(5(5(4(3(x1)))))))))))))))))) 15.32/4.79 4(4(3(2(1(1(4(1(3(2(2(4(x1)))))))))))) -> 0(4(2(3(5(4(1(0(4(3(4(0(0(1(x1)))))))))))))) 15.32/4.79 3(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 2(5(5(5(4(4(2(5(4(5(5(4(3(1(0(1(5(4(x1)))))))))))))))))) 15.32/4.79 0(3(4(1(3(0(4(2(1(1(3(4(x1)))))))))))) -> 1(4(3(2(5(5(3(0(3(2(5(5(3(5(2(x1))))))))))))))) 15.32/4.79 2(4(1(3(0(2(4(0(2(2(4(4(x1)))))))))))) -> 5(5(4(1(0(1(0(1(3(3(3(5(1(5(4(2(x1)))))))))))))))) 15.32/4.79 2(3(2(3(1(4(0(1(4(4(4(4(x1)))))))))))) -> 5(4(1(0(1(5(5(3(1(5(5(5(0(0(4(0(3(1(x1)))))))))))))))))) 15.32/4.79 4(4(0(3(4(0(2(2(0(0(5(4(x1)))))))))))) -> 4(1(5(5(5(4(3(0(0(3(5(4(3(4(5(5(4(x1))))))))))))))))) 15.32/4.79 4(2(4(0(3(1(3(1(3(2(1(5(x1)))))))))))) -> 5(3(4(5(5(4(5(5(3(5(5(4(5(5(2(3(0(x1))))))))))))))))) 15.32/4.79 2(2(3(0(2(1(1(2(2(5(1(5(x1)))))))))))) -> 5(5(5(3(3(5(5(1(5(0(1(4(5(5(3(5(2(0(x1)))))))))))))))))) 15.32/4.79 2(1(4(5(2(1(2(2(4(0(2(5(x1)))))))))))) -> 4(0(5(5(5(4(4(0(4(0(3(1(5(5(5(4(x1)))))))))))))))) 15.32/4.79 4(0(2(0(0(2(1(0(5(0(2(5(x1)))))))))))) -> 3(1(0(3(2(5(5(1(5(3(4(3(3(0(x1)))))))))))))) 15.32/4.79 0(1(5(4(2(1(4(2(2(0(3(5(x1)))))))))))) -> 5(5(1(5(3(5(2(5(2(0(5(1(5(0(x1)))))))))))))) 15.32/4.79 3(4(1(1(2(1(2(4(1(2(3(5(x1)))))))))))) -> 3(1(5(1(5(3(5(5(0(5(5(0(3(3(5(0(5(4(x1)))))))))))))))))) 15.32/4.79 1(2(2(3(5(1(1(2(2(2(4(5(x1)))))))))))) -> 5(5(2(4(5(2(0(3(5(0(5(5(0(4(0(x1))))))))))))))) 15.32/4.79 3(4(1(1(5(3(0(2(2(1(5(5(x1)))))))))))) -> 0(5(0(4(0(1(0(5(4(5(3(0(5(0(x1)))))))))))))) 15.32/4.79 15.32/4.79 Q is empty. 15.32/4.79 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (3) QTRSRRRProof (EQUIVALENT) 15.32/4.79 Used ordering: 15.32/4.79 Polynomial interpretation [POLO]: 15.32/4.79 15.32/4.79 POL(0(x_1)) = 16 + x_1 15.32/4.79 POL(1(x_1)) = 33 + x_1 15.32/4.79 POL(2(x_1)) = 42 + x_1 15.32/4.79 POL(3(x_1)) = 16 + x_1 15.32/4.79 POL(4(x_1)) = 30 + x_1 15.32/4.79 POL(5(x_1)) = x_1 15.32/4.79 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 15.32/4.79 15.32/4.79 1(2(3(1(1(0(2(1(1(1(0(0(x1)))))))))))) -> 1(3(0(4(5(1(4(0(5(0(3(3(4(5(5(3(x1)))))))))))))))) 15.32/4.79 1(3(1(1(4(1(3(1(1(4(0(0(x1)))))))))))) -> 4(0(1(5(0(2(5(2(5(0(5(4(2(5(5(5(3(x1))))))))))))))))) 15.32/4.79 5(1(1(4(3(0(2(2(4(0(1(0(x1)))))))))))) -> 1(0(5(3(5(3(2(1(3(4(5(1(0(4(x1)))))))))))))) 15.32/4.79 0(4(0(3(4(2(2(2(2(2(1(0(x1)))))))))))) -> 2(0(5(5(0(5(3(3(3(5(3(5(4(2(2(5(5(5(x1)))))))))))))))))) 15.32/4.79 1(2(1(2(4(3(5(1(4(2(1(0(x1)))))))))))) -> 5(1(1(3(5(4(0(1(2(5(5(3(2(5(0(x1))))))))))))))) 15.32/4.79 2(0(5(2(4(2(2(1(1(3(1(0(x1)))))))))))) -> 4(5(2(5(5(5(3(3(4(3(1(5(3(5(4(5(2(x1))))))))))))))))) 15.32/4.79 1(1(4(1(2(2(4(1(4(1(2(0(x1)))))))))))) -> 0(0(0(2(0(3(2(5(5(3(4(5(5(3(3(2(x1)))))))))))))))) 15.32/4.79 4(0(4(4(4(1(0(2(3(3(2(0(x1)))))))))))) -> 3(3(5(1(5(5(5(5(4(1(2(3(0(5(5(3(1(5(x1)))))))))))))))))) 15.32/4.79 0(2(2(0(3(1(5(3(0(4(2(0(x1)))))))))))) -> 0(5(2(5(5(3(3(1(4(5(5(5(5(5(0(4(0(x1))))))))))))))))) 15.32/4.79 2(1(2(0(1(4(1(1(1(3(3(0(x1)))))))))))) -> 5(5(3(4(5(1(0(0(5(1(5(2(5(2(1(5(x1)))))))))))))))) 15.32/4.79 4(4(1(0(2(2(2(2(1(1(4(0(x1)))))))))))) -> 3(2(2(5(0(3(2(0(5(1(5(0(0(5(0(0(4(x1))))))))))))))))) 15.32/4.79 5(2(5(2(1(0(0(4(4(4(4(0(x1)))))))))))) -> 1(5(5(3(3(4(2(5(5(1(0(0(4(0(3(5(5(5(x1)))))))))))))))))) 15.32/4.79 1(1(5(4(1(0(3(0(2(5(4(0(x1)))))))))))) -> 5(3(3(0(0(5(5(5(3(0(3(3(5(0(1(0(x1)))))))))))))))) 15.32/4.79 2(1(1(0(2(4(4(5(2(1(5(0(x1)))))))))))) -> 2(4(5(3(3(2(3(3(3(4(5(4(3(5(4(5(0(x1))))))))))))))))) 15.32/4.79 1(2(0(4(2(0(4(4(4(3(5(0(x1)))))))))))) -> 0(5(3(5(3(2(5(5(3(4(4(5(3(3(5(3(x1)))))))))))))))) 15.32/4.79 3(2(4(0(2(0(0(2(1(4(5(0(x1)))))))))))) -> 2(0(5(5(3(3(3(3(2(2(5(3(5(4(5(5(x1)))))))))))))))) 15.32/4.79 1(3(1(1(1(3(1(2(2(4(5(0(x1)))))))))))) -> 3(5(5(4(5(3(3(5(2(0(5(1(0(2(0(5(3(4(x1)))))))))))))))))) 15.32/4.79 0(5(1(2(1(0(4(4(4(0(0(1(x1)))))))))))) -> 5(5(1(2(3(3(5(3(5(0(1(2(0(5(3(x1))))))))))))))) 15.32/4.79 2(1(0(2(4(0(1(0(5(1(0(1(x1)))))))))))) -> 2(0(1(3(5(5(4(5(3(4(3(5(5(2(3(x1))))))))))))))) 15.32/4.79 4(4(3(4(3(1(2(1(4(1(2(1(x1)))))))))))) -> 5(4(2(1(0(3(5(0(0(0(0(4(2(2(x1)))))))))))))) 15.32/4.79 0(5(2(1(2(1(1(5(2(2(3(1(x1)))))))))))) -> 0(5(3(5(4(3(5(5(5(4(1(5(4(5(1(5(5(5(x1)))))))))))))))))) 15.32/4.79 2(0(4(1(5(1(3(2(2(3(3(1(x1)))))))))))) -> 2(3(5(0(5(5(5(1(5(4(5(5(3(3(4(x1))))))))))))))) 15.32/4.79 2(2(1(2(0(2(2(0(4(4(3(1(x1)))))))))))) -> 4(2(3(4(0(5(5(5(5(3(3(5(1(3(1(x1))))))))))))))) 15.32/4.79 4(1(1(0(1(2(0(4(2(0(4(1(x1)))))))))))) -> 4(3(2(0(3(3(5(5(3(0(3(5(0(5(x1)))))))))))))) 15.32/4.79 2(5(1(4(1(4(4(4(4(1(4(1(x1)))))))))))) -> 5(5(0(5(1(2(3(5(0(5(4(5(3(4(0(5(3(x1))))))))))))))))) 15.32/4.79 1(1(1(1(3(4(2(0(2(3(4(1(x1)))))))))))) -> 5(5(0(5(4(0(4(5(5(4(3(5(4(4(x1)))))))))))))) 15.32/4.79 2(2(4(2(3(2(2(0(4(4(4(1(x1)))))))))))) -> 5(3(5(2(5(0(0(5(1(5(3(5(5(5(5(4(1(x1))))))))))))))))) 15.32/4.79 5(2(3(1(3(5(1(4(1(0(0(2(x1)))))))))))) -> 5(0(0(0(0(3(3(5(4(0(1(5(0(4(4(3(x1)))))))))))))))) 15.32/4.79 4(1(4(4(0(5(0(2(3(1(0(2(x1)))))))))))) -> 0(3(3(2(3(1(0(5(5(5(3(4(0(5(3(5(5(4(x1)))))))))))))))))) 15.32/4.79 5(1(0(2(1(4(3(1(0(2(0(2(x1)))))))))))) -> 3(3(5(5(3(5(3(3(0(3(2(5(3(5(5(x1))))))))))))))) 15.32/4.79 0(2(2(4(4(3(1(1(1(2(0(2(x1)))))))))))) -> 3(0(4(4(5(4(5(3(3(5(0(3(0(4(1(0(5(5(x1)))))))))))))))))) 15.32/4.79 4(0(5(1(3(0(2(2(5(2(0(2(x1)))))))))))) -> 3(5(5(5(3(2(2(1(5(2(5(4(5(0(5(x1))))))))))))))) 15.32/4.79 3(1(1(4(5(2(4(3(1(4(0(2(x1)))))))))))) -> 0(5(4(5(5(5(3(4(0(2(4(0(0(5(3(2(2(x1))))))))))))))))) 15.32/4.79 1(1(2(0(2(5(4(4(0(0(1(2(x1)))))))))))) -> 4(5(5(4(2(5(2(4(0(5(4(5(5(1(0(1(5(3(x1)))))))))))))))))) 15.32/4.79 3(0(4(0(3(1(4(0(1(1(1(2(x1)))))))))))) -> 1(5(3(5(3(1(2(5(0(5(2(0(3(4(x1)))))))))))))) 15.32/4.79 0(1(1(3(0(4(4(1(4(1(1(2(x1)))))))))))) -> 3(1(4(1(5(5(3(3(5(3(4(5(5(5(2(3(x1)))))))))))))))) 15.32/4.79 2(1(3(1(3(1(3(1(5(3(1(2(x1)))))))))))) -> 4(5(3(4(5(0(4(4(3(1(5(2(0(5(1(5(0(x1))))))))))))))))) 15.32/4.79 3(0(2(4(2(5(2(4(1(1(2(2(x1)))))))))))) -> 5(4(5(0(4(2(2(2(2(5(4(4(4(3(x1)))))))))))))) 15.32/4.79 4(4(3(1(0(2(1(1(3(1(2(2(x1)))))))))))) -> 4(0(5(3(1(5(3(5(5(5(2(0(0(0(4(4(2(x1))))))))))))))))) 15.32/4.79 4(2(4(0(2(5(0(4(4(1(2(2(x1)))))))))))) -> 4(0(0(5(5(5(3(3(2(3(1(5(2(0(5(3(x1)))))))))))))))) 15.32/4.79 1(4(1(5(3(3(4(4(1(2(2(2(x1)))))))))))) -> 1(5(0(1(0(1(2(5(5(5(3(5(5(5(4(5(1(x1))))))))))))))))) 15.32/4.79 0(2(1(0(4(0(5(5(2(5(2(2(x1)))))))))))) -> 5(5(0(5(5(0(3(4(5(0(4(5(2(1(x1)))))))))))))) 15.32/4.79 1(0(1(2(1(2(1(4(3(1(3(2(x1)))))))))))) -> 5(5(4(1(0(5(4(2(3(3(0(4(4(2(2(x1))))))))))))))) 15.32/4.79 1(4(1(4(2(1(1(5(1(2(3(2(x1)))))))))))) -> 0(5(4(1(3(3(2(0(0(0(5(5(4(5(0(3(3(x1))))))))))))))))) 15.32/4.79 4(4(2(5(3(2(2(4(3(2(3(2(x1)))))))))))) -> 5(0(4(5(5(5(3(4(2(1(5(5(0(3(0(5(x1)))))))))))))))) 15.32/4.79 1(4(0(3(1(4(0(0(4(2(3(2(x1)))))))))))) -> 0(5(5(5(3(3(5(5(1(5(0(1(0(0(1(5(5(4(x1)))))))))))))))))) 15.32/4.79 3(4(1(4(1(2(3(1(4(3(3(2(x1)))))))))))) -> 2(2(5(3(0(1(5(0(0(0(5(1(1(5(x1)))))))))))))) 15.32/4.79 0(1(3(3(2(2(4(4(0(2(4(2(x1)))))))))))) -> 3(5(4(1(4(4(2(5(3(5(1(5(2(0(5(5(5(x1))))))))))))))))) 15.32/4.79 2(5(1(0(2(4(0(1(4(3(4(2(x1)))))))))))) -> 2(0(3(0(4(5(4(3(5(4(3(5(0(0(x1)))))))))))))) 15.32/4.79 3(0(1(4(5(0(2(1(4(5(4(2(x1)))))))))))) -> 0(1(5(1(2(3(4(5(5(3(3(3(5(3(5(x1))))))))))))))) 15.32/4.79 0(2(3(1(4(3(1(4(4(1(5(2(x1)))))))))))) -> 4(4(0(3(1(2(3(3(5(4(3(5(0(5(2(x1))))))))))))))) 15.32/4.79 0(0(1(1(4(0(2(4(1(4(0(3(x1)))))))))))) -> 2(5(5(0(5(5(3(4(0(1(2(3(2(3(0(5(5(5(x1)))))))))))))))))) 15.32/4.79 1(0(0(4(4(1(2(5(3(4(0(3(x1)))))))))))) -> 3(5(2(3(1(5(0(4(5(0(0(3(5(5(x1)))))))))))))) 15.32/4.79 1(3(1(5(1(4(1(1(5(4(1(3(x1)))))))))))) -> 0(1(0(3(5(5(3(4(3(5(5(3(0(3(5(3(x1)))))))))))))))) 15.32/4.79 4(4(1(1(2(1(4(1(3(0(2(3(x1)))))))))))) -> 2(5(2(5(0(3(5(3(4(5(3(1(5(0(2(5(1(x1))))))))))))))))) 15.32/4.79 4(3(5(2(2(5(4(0(2(2(2(3(x1)))))))))))) -> 3(5(1(3(4(0(1(0(1(1(3(2(5(1(x1)))))))))))))) 15.32/4.79 5(2(2(0(2(3(0(5(2(4(2(3(x1)))))))))))) -> 5(2(0(1(5(0(5(0(5(2(2(0(0(5(4(x1))))))))))))))) 15.32/4.79 1(3(1(4(5(4(4(3(2(1(3(3(x1)))))))))))) -> 5(5(3(5(1(3(4(0(5(5(1(2(5(4(0(4(x1)))))))))))))))) 15.32/4.79 3(0(2(3(4(1(0(0(4(3(3(3(x1)))))))))))) -> 3(4(3(3(2(5(5(5(2(0(1(5(3(5(3(x1))))))))))))))) 15.32/4.79 3(1(2(3(2(2(4(3(0(1(4(3(x1)))))))))))) -> 1(1(4(2(0(0(3(1(5(5(0(5(4(5(x1)))))))))))))) 15.32/4.79 2(4(3(3(1(4(4(1(1(2(4(3(x1)))))))))))) -> 0(5(0(5(4(4(5(5(1(1(2(4(0(4(x1)))))))))))))) 15.32/4.79 2(4(2(1(2(2(4(0(2(2(4(3(x1)))))))))))) -> 4(3(3(5(5(3(2(2(5(4(1(0(2(2(x1)))))))))))))) 15.32/4.79 2(5(1(4(2(5(1(2(4(4(4(3(x1)))))))))))) -> 5(5(4(5(3(5(0(1(5(0(4(3(5(5(1(0(0(3(x1)))))))))))))))))) 15.32/4.79 4(2(2(1(3(1(4(0(1(0(0(4(x1)))))))))))) -> 0(3(3(0(5(0(5(2(5(0(0(2(0(5(4(x1))))))))))))))) 15.32/4.79 4(4(3(0(3(4(1(1(1(2(0(4(x1)))))))))))) -> 5(3(2(5(0(4(5(5(4(2(0(1(5(5(1(x1))))))))))))))) 15.32/4.79 0(4(2(4(4(5(2(2(2(2(0(4(x1)))))))))))) -> 5(2(5(2(0(4(0(5(4(2(5(5(3(3(0(5(x1)))))))))))))))) 15.32/4.79 3(4(1(0(4(5(4(2(1(4(0(4(x1)))))))))))) -> 5(4(5(4(5(4(5(4(3(1(0(5(3(3(2(5(x1)))))))))))))))) 15.32/4.79 4(5(4(3(0(3(2(0(2(1(1(4(x1)))))))))))) -> 3(3(5(3(5(3(3(2(4(5(5(1(5(3(5(1(4(x1))))))))))))))))) 15.32/4.79 3(4(3(4(2(4(2(3(2(1(1(4(x1)))))))))))) -> 5(5(4(3(2(5(3(4(0(5(2(0(5(3(5(2(5(1(x1)))))))))))))))))) 15.32/4.79 2(1(3(1(2(1(4(4(3(1(1(4(x1)))))))))))) -> 3(5(4(2(5(3(0(3(3(2(0(0(3(3(5(5(5(2(x1)))))))))))))))))) 15.32/4.79 1(0(2(1(2(4(2(4(1(2(1(4(x1)))))))))))) -> 0(5(5(1(5(4(2(4(1(1(2(5(4(1(4(x1))))))))))))))) 15.32/4.79 2(2(4(3(3(3(4(4(4(3(1(4(x1)))))))))))) -> 0(3(2(5(3(3(0(5(5(4(2(0(4(3(4(4(x1)))))))))))))))) 15.32/4.79 5(4(0(2(5(4(0(2(2(4(1(4(x1)))))))))))) -> 4(1(5(3(3(3(5(5(5(4(2(2(4(0(x1)))))))))))))) 15.32/4.79 2(5(2(3(4(3(1(3(2(4(1(4(x1)))))))))))) -> 5(1(2(4(0(3(3(3(3(4(5(5(4(3(3(x1))))))))))))))) 15.32/4.79 5(3(1(4(0(2(3(5(0(0(2(4(x1)))))))))))) -> 5(5(5(5(5(3(3(0(3(1(3(4(3(3(5(2(x1)))))))))))))))) 15.32/4.79 5(2(1(0(0(0(2(4(2(0(2(4(x1)))))))))))) -> 5(5(4(3(4(5(4(2(3(5(3(2(3(1(2(5(x1)))))))))))))))) 15.32/4.79 3(2(4(2(3(0(2(2(3(0(2(4(x1)))))))))))) -> 2(0(0(0(5(4(5(5(1(2(2(5(1(2(x1)))))))))))))) 15.32/4.79 3(2(4(2(1(2(3(4(0(1(2(4(x1)))))))))))) -> 4(3(5(5(3(0(4(5(3(5(5(5(5(0(5(3(0(x1))))))))))))))))) 15.32/4.79 1(3(0(2(2(0(2(2(1(1(2(4(x1)))))))))))) -> 5(0(4(0(3(2(0(5(0(4(5(0(1(3(5(5(2(1(x1)))))))))))))))))) 15.32/4.79 5(0(1(2(5(0(2(2(0(2(2(4(x1)))))))))))) -> 3(3(5(2(0(5(5(4(3(4(3(0(4(5(5(5(4(3(x1)))))))))))))))))) 15.32/4.79 4(4(3(2(1(1(4(1(3(2(2(4(x1)))))))))))) -> 0(4(2(3(5(4(1(0(4(3(4(0(0(1(x1)))))))))))))) 15.32/4.79 0(3(4(1(3(0(4(2(1(1(3(4(x1)))))))))))) -> 1(4(3(2(5(5(3(0(3(2(5(5(3(5(2(x1))))))))))))))) 15.32/4.79 2(4(1(3(0(2(4(0(2(2(4(4(x1)))))))))))) -> 5(5(4(1(0(1(0(1(3(3(3(5(1(5(4(2(x1)))))))))))))))) 15.32/4.79 2(3(2(3(1(4(0(1(4(4(4(4(x1)))))))))))) -> 5(4(1(0(1(5(5(3(1(5(5(5(0(0(4(0(3(1(x1)))))))))))))))))) 15.32/4.79 4(4(0(3(4(0(2(2(0(0(5(4(x1)))))))))))) -> 4(1(5(5(5(4(3(0(0(3(5(4(3(4(5(5(4(x1))))))))))))))))) 15.32/4.79 4(2(4(0(3(1(3(1(3(2(1(5(x1)))))))))))) -> 5(3(4(5(5(4(5(5(3(5(5(4(5(5(2(3(0(x1))))))))))))))))) 15.32/4.79 2(2(3(0(2(1(1(2(2(5(1(5(x1)))))))))))) -> 5(5(5(3(3(5(5(1(5(0(1(4(5(5(3(5(2(0(x1)))))))))))))))))) 15.32/4.79 2(1(4(5(2(1(2(2(4(0(2(5(x1)))))))))))) -> 4(0(5(5(5(4(4(0(4(0(3(1(5(5(5(4(x1)))))))))))))))) 15.32/4.79 4(0(2(0(0(2(1(0(5(0(2(5(x1)))))))))))) -> 3(1(0(3(2(5(5(1(5(3(4(3(3(0(x1)))))))))))))) 15.32/4.79 0(1(5(4(2(1(4(2(2(0(3(5(x1)))))))))))) -> 5(5(1(5(3(5(2(5(2(0(5(1(5(0(x1)))))))))))))) 15.32/4.79 3(4(1(1(2(1(2(4(1(2(3(5(x1)))))))))))) -> 3(1(5(1(5(3(5(5(0(5(5(0(3(3(5(0(5(4(x1)))))))))))))))))) 15.32/4.79 1(2(2(3(5(1(1(2(2(2(4(5(x1)))))))))))) -> 5(5(2(4(5(2(0(3(5(0(5(5(0(4(0(x1))))))))))))))) 15.32/4.79 3(4(1(1(5(3(0(2(2(1(5(5(x1)))))))))))) -> 0(5(0(4(0(1(0(5(4(5(3(0(5(0(x1)))))))))))))) 15.32/4.79 15.32/4.79 15.32/4.79 15.32/4.79 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (4) 15.32/4.79 Obligation: 15.32/4.79 Q restricted rewrite system: 15.32/4.79 The TRS R consists of the following rules: 15.32/4.79 15.32/4.79 2(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 2(0(1(3(5(3(0(1(1(0(3(2(4(4(x1)))))))))))))) 15.32/4.79 4(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 3(3(5(4(3(2(3(5(0(5(5(2(0(4(4(3(x1)))))))))))))))) 15.32/4.79 3(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 2(5(5(5(4(4(2(5(4(5(5(4(3(1(0(1(5(4(x1)))))))))))))))))) 15.32/4.79 15.32/4.79 Q is empty. 15.32/4.79 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (5) DependencyPairsProof (EQUIVALENT) 15.32/4.79 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (6) 15.32/4.79 Obligation: 15.32/4.79 Q DP problem: 15.32/4.79 The TRS P consists of the following rules: 15.32/4.79 15.32/4.79 2^1(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 2^1(0(1(3(5(3(0(1(1(0(3(2(4(4(x1)))))))))))))) 15.32/4.79 2^1(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 3^1(5(3(0(1(1(0(3(2(4(4(x1))))))))))) 15.32/4.79 2^1(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 3^1(0(1(1(0(3(2(4(4(x1))))))))) 15.32/4.79 2^1(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 3^1(2(4(4(x1)))) 15.32/4.79 2^1(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 2^1(4(4(x1))) 15.32/4.79 2^1(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 4^1(4(x1)) 15.32/4.79 2^1(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 4^1(x1) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 3^1(3(5(4(3(2(3(5(0(5(5(2(0(4(4(3(x1)))))))))))))))) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 3^1(5(4(3(2(3(5(0(5(5(2(0(4(4(3(x1))))))))))))))) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 4^1(3(2(3(5(0(5(5(2(0(4(4(3(x1))))))))))))) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 3^1(2(3(5(0(5(5(2(0(4(4(3(x1)))))))))))) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 2^1(3(5(0(5(5(2(0(4(4(3(x1))))))))))) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 3^1(5(0(5(5(2(0(4(4(3(x1)))))))))) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 2^1(0(4(4(3(x1))))) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 4^1(4(3(x1))) 15.32/4.79 4^1(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 4^1(3(x1)) 15.32/4.79 3^1(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 2^1(5(5(5(4(4(2(5(4(5(5(4(3(1(0(1(5(4(x1)))))))))))))))))) 15.32/4.79 3^1(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 4^1(4(2(5(4(5(5(4(3(1(0(1(5(4(x1)))))))))))))) 15.32/4.79 3^1(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 4^1(2(5(4(5(5(4(3(1(0(1(5(4(x1))))))))))))) 15.32/4.79 3^1(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 2^1(5(4(5(5(4(3(1(0(1(5(4(x1)))))))))))) 15.32/4.79 3^1(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 4^1(5(5(4(3(1(0(1(5(4(x1)))))))))) 15.32/4.79 3^1(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 4^1(3(1(0(1(5(4(x1))))))) 15.32/4.79 3^1(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 3^1(1(0(1(5(4(x1)))))) 15.32/4.79 15.32/4.79 The TRS R consists of the following rules: 15.32/4.79 15.32/4.79 2(0(1(4(4(4(4(1(3(1(4(0(x1)))))))))))) -> 2(0(1(3(5(3(0(1(1(0(3(2(4(4(x1)))))))))))))) 15.32/4.79 4(4(0(3(3(0(3(2(4(0(2(3(x1)))))))))))) -> 3(3(5(4(3(2(3(5(0(5(5(2(0(4(4(3(x1)))))))))))))))) 15.32/4.79 3(2(2(3(1(3(1(3(0(4(2(4(x1)))))))))))) -> 2(5(5(5(4(4(2(5(4(5(5(4(3(1(0(1(5(4(x1)))))))))))))))))) 15.32/4.79 15.32/4.79 Q is empty. 15.32/4.79 We have to consider all minimal (P,Q,R)-chains. 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (7) DependencyGraphProof (EQUIVALENT) 15.32/4.79 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 23 less nodes. 15.32/4.79 ---------------------------------------- 15.32/4.79 15.32/4.79 (8) 15.32/4.79 TRUE 15.81/6.07 EOF