16.20/4.90 YES 16.52/4.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 16.52/4.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.52/4.98 16.52/4.98 16.52/4.98 Termination w.r.t. Q of the given QTRS could be proven: 16.52/4.98 16.52/4.98 (0) QTRS 16.52/4.98 (1) QTRSRRRProof [EQUIVALENT, 575 ms] 16.52/4.98 (2) QTRS 16.52/4.98 (3) QTRSRRRProof [EQUIVALENT, 2 ms] 16.52/4.98 (4) QTRS 16.52/4.98 (5) Overlay + Local Confluence [EQUIVALENT, 0 ms] 16.52/4.98 (6) QTRS 16.52/4.98 (7) DependencyPairsProof [EQUIVALENT, 0 ms] 16.52/4.98 (8) QDP 16.52/4.98 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 16.52/4.98 (10) TRUE 16.52/4.98 16.52/4.98 16.52/4.98 ---------------------------------------- 16.52/4.98 16.52/4.98 (0) 16.52/4.98 Obligation: 16.52/4.98 Q restricted rewrite system: 16.52/4.98 The TRS R consists of the following rules: 16.52/4.98 16.52/4.98 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) 16.52/4.98 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(1(3(5(5(5(2(3(4(0(3(4(4(4(2(2(x1)))))))))))))))) 16.52/4.98 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) 16.52/4.98 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.98 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.98 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.98 0(0(4(0(5(1(3(5(1(2(4(0(3(4(3(3(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.98 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(0(4(0(5(1(3(5(1(2(4(0(3(4(3(3(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(1(3(5(5(5(2(3(4(0(3(4(4(4(2(2(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(2(1(4(0(4(0(0(3(0(2(5(1(2(5(3(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(3(5(0(5(0(3(2(1(5(1(2(0(5(5(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(2(4(3(4(2(4(5(1(3(3(5(5(1(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(3(0(2(3(4(5(4(3(4(0(3(2(1(0(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(4(5(5(5(2(5(3(5(4(2(1(2(2(1(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(5(2(5(1(3(1(5(1(3(3(0(0(5(0(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 1(0(0(3(0(4(1(2(4(1(5(5(3(3(4(5(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 1(1(2(2(3(4(5(4(3(0(5(0(4(2(4(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 2(1(1(3(2(4(4(4(4(0(0(4(5(2(4(5(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 2(3(2(2(5(5(5(0(5(0(3(2(2(4(2(1(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 2(5(5(1(5(1(2(3(0(3(5(2(4(1(0(0(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(1(3(5(5(0(0(3(4(3(0(4(4(2(4(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(4(3(3(4(1(4(1(0(0(5(1(5(4(5(2(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(4(3(4(2(4(4(4(2(4(1(4(4(0(1(5(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 4(0(5(2(3(5(3(3(4(2(3(5(5(4(0(3(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 4(2(0(1(0(5(5(4(3(2(0(2(3(3(1(5(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 4(2(3(1(5(3(5(2(5(0(5(5(1(4(1(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(0(0(1(2(5(5(2(0(5(5(0(3(0(2(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(1(5(0(3(0(5(4(2(0(4(0(2(4(5(2(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(2(3(4(3(3(2(5(1(4(3(2(3(5(2(0(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(2(4(0(2(5(3(2(3(5(0(0(0(5(1(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(2(4(0(3(2(5(1(2(0(5(4(1(0(2(2(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(4(0(4(3(1(2(5(3(2(0(0(2(2(4(0(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(4(5(0(5(1(5(3(0(2(2(3(3(4(1(4(x1)))))))))))))))) 16.52/4.98 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(0(4(0(5(1(3(5(1(2(4(0(3(4(3(3(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(1(3(5(5(5(2(3(4(0(3(4(4(4(2(2(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(2(1(4(0(4(0(0(3(0(2(5(1(2(5(3(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(3(5(0(5(0(3(2(1(5(1(2(0(5(5(4(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(4(2(4(3(4(2(4(5(1(3(3(5(5(1(4(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 0(4(3(0(2(3(4(5(4(3(4(0(3(2(1(0(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 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0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 2(5(5(1(5(1(2(3(0(3(5(2(4(1(0(0(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 3(1(1(3(2(0(0(5(2(3(4(5(5(5(1(0(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 3(4(3(3(4(1(4(1(0(0(5(1(5(4(5(2(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 3(4(3(4(2(4(4(4(2(4(1(4(4(0(1(5(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 4(0(5(2(3(5(3(3(4(2(3(5(5(4(0(3(x1)))))))))))))))) 16.52/4.98 0(1(3(0(1(2(4(3(0(3(1(1(0(1(4(5(x1)))))))))))))))) -> 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3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 3(2(3(2(3(1(5(3(4(5(4(3(5(0(3(3(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 4(0(5(2(3(5(3(3(4(2(3(5(5(4(0(3(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 3(1(3(5(5(0(0(3(4(3(0(4(4(2(4(4(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.99 3(1(3(5(5(0(0(3(4(3(0(4(4(2(4(4(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 3(2(3(2(3(1(5(3(4(5(4(3(5(0(3(3(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(1(1(3(2(0(0(5(2(3(4(5(5(5(1(0(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(4(3(4(2(4(4(4(2(4(1(4(4(0(1(5(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 4(1(3(3(5(5(1(3(2(2(4(3(1(0(3(3(x1)))))))))))))))) -> 4(0(5(2(3(5(3(3(4(2(3(5(5(4(0(3(x1)))))))))))))))) 16.52/4.99 4(2(1(3(2(5(1(3(3(4(1(0(3(5(3(5(x1)))))))))))))))) -> 4(2(0(1(0(5(5(4(3(2(0(2(3(3(1(5(x1)))))))))))))))) 16.52/4.99 5(0(0(1(2(5(5(2(0(5(5(0(3(0(2(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 3(4(3(4(2(4(4(4(2(4(1(4(4(0(1(5(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 4(2(0(1(0(5(5(4(3(2(0(2(3(3(1(5(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(0(0(1(2(5(5(2(0(5(5(0(3(0(2(4(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(1(5(0(3(0(5(4(2(0(4(0(2(4(5(2(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(2(3(4(3(3(2(5(1(4(3(2(3(5(2(0(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(2(4(0(2(5(3(2(3(5(0(0(0(5(1(4(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(2(4(0(3(2(5(1(2(0(5(4(1(0(2(2(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(2(4(0(2(5(3(2(3(5(0(0(0(5(1(4(x1)))))))))))))))) -> 5(0(0(1(2(5(5(2(0(5(5(0(3(0(2(4(x1)))))))))))))))) 16.52/4.99 5(2(4(0(2(5(3(2(3(5(0(0(0(5(1(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(2(4(0(3(2(5(1(2(0(5(4(1(0(2(2(x1)))))))))))))))) -> 5(1(5(0(3(0(5(4(2(0(4(0(2(4(5(2(x1)))))))))))))))) 16.52/4.99 5(4(0(4(3(1(2(5(3(2(0(0(2(2(4(0(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(4(3(1(5(4(0(5(3(3(5(3(3(2(3(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(4(5(0(5(1(5(3(0(2(2(3(3(4(1(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 16.52/4.99 Q is empty. 16.52/4.99 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (1) QTRSRRRProof (EQUIVALENT) 16.52/4.99 Used ordering: 16.52/4.99 Polynomial interpretation [POLO]: 16.52/4.99 16.52/4.99 POL(0(x_1)) = 16 + x_1 16.52/4.99 POL(1(x_1)) = 27 + x_1 16.52/4.99 POL(2(x_1)) = 12 + x_1 16.52/4.99 POL(3(x_1)) = 20 + x_1 16.52/4.99 POL(4(x_1)) = 11 + x_1 16.52/4.99 POL(5(x_1)) = x_1 16.52/4.99 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 16.52/4.99 16.52/4.99 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) 16.52/4.99 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(1(3(5(5(5(2(3(4(0(3(4(4(4(2(2(x1)))))))))))))))) 16.52/4.99 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) 16.52/4.99 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.99 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 0(0(4(0(5(1(3(5(1(2(4(0(3(4(3(3(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(0(0(1(2(3(2(2(2(2(0(0(3(4(5(5(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(0(4(0(5(1(3(5(1(2(4(0(3(4(3(3(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(1(3(5(5(5(2(3(4(0(3(4(4(4(2(2(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(2(1(4(0(4(0(0(3(0(2(5(1(2(5(3(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(3(5(0(5(0(3(2(1(5(1(2(0(5(5(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(2(4(3(4(2(4(5(1(3(3(5(5(1(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(3(0(2(3(4(5(4(3(4(0(3(2(1(0(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(4(5(5(5(2(5(3(5(4(2(1(2(2(1(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 0(4(5(2(5(1(3(1(5(1(3(3(0(0(5(0(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 1(0(0(3(0(4(1(2(4(1(5(5(3(3(4(5(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 1(1(2(2(3(4(5(4(3(0(5(0(4(2(4(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 2(1(1(3(2(4(4(4(4(0(0(4(5(2(4(5(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 2(3(2(2(5(5(5(0(5(0(3(2(2(4(2(1(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 2(5(5(1(5(1(2(3(0(3(5(2(4(1(0(0(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(1(3(5(5(0(0(3(4(3(0(4(4(2(4(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(4(3(3(4(1(4(1(0(0(5(1(5(4(5(2(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(4(3(4(2(4(4(4(2(4(1(4(4(0(1(5(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 4(0(5(2(3(5(3(3(4(2(3(5(5(4(0(3(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 4(2(0(1(0(5(5(4(3(2(0(2(3(3(1(5(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 4(2(3(1(5(3(5(2(5(0(5(5(1(4(1(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(0(0(1(2(5(5(2(0(5(5(0(3(0(2(4(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(1(5(0(3(0(5(4(2(0(4(0(2(4(5(2(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 5(2(3(4(3(3(2(5(1(4(3(2(3(5(2(0(x1)))))))))))))))) 16.52/4.99 0(1(2(3(0(4(0(3(3(3(2(3(0(0(1(4(x1)))))))))))))))) -> 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1(5(2(3(4(3(1(4(3(0(3(5(4(4(2(2(x1)))))))))))))))) -> 3(4(3(3(4(1(4(1(0(0(5(1(5(4(5(2(x1)))))))))))))))) 16.52/4.99 1(5(2(3(4(3(1(4(3(0(3(5(4(4(2(2(x1)))))))))))))))) -> 5(1(5(0(3(0(5(4(2(0(4(0(2(4(5(2(x1)))))))))))))))) 16.52/4.99 1(5(2(3(4(3(1(4(3(0(3(5(4(4(2(2(x1)))))))))))))))) -> 5(2(4(0(3(2(5(1(2(0(5(4(1(0(2(2(x1)))))))))))))))) 16.52/4.99 2(2(3(2(0(1(0(1(3(3(2(3(2(0(3(3(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 2(2(3(2(0(1(0(1(3(3(2(3(2(0(3(3(x1)))))))))))))))) -> 4(0(5(2(3(5(3(3(4(2(3(5(5(4(0(3(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 1(0(0(3(0(4(1(2(4(1(5(5(3(3(4(5(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 2(1(1(3(2(4(4(4(4(0(0(4(5(2(4(5(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 2(5(0(2(0(3(3(4(1(2(5(1(5(0(0(2(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 2(5(5(1(5(1(2(3(0(3(5(2(4(1(0(0(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 3(4(3(4(2(4(4(4(2(4(1(4(4(0(1(5(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 2(4(1(3(0(2(4(5(3(2(0(3(3(0(1(5(x1)))))))))))))))) -> 4(2(0(1(0(5(5(4(3(2(0(2(3(3(1(5(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 0(0(5(4(2(2(4(0(2(5(1(0(2(1(0(2(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 0(1(3(5(5(5(2(3(4(0(3(4(4(4(2(2(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 0(2(5(5(5(3(0(4(4(2(2(5(0(5(0(2(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 2(1(1(3(2(4(4(4(4(0(0(4(5(2(4(5(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 2(3(2(2(5(5(5(0(5(0(3(2(2(4(2(1(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 2(5(0(2(0(3(3(4(1(2(5(1(5(0(0(2(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 3(4(3(3(4(1(4(1(0(0(5(1(5(4(5(2(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 5(1(5(0(3(0(5(4(2(0(4(0(2(4(5(2(x1)))))))))))))))) 16.52/4.99 2(4(3(4(5(1(4(2(2(1(2(1(5(3(1(2(x1)))))))))))))))) -> 5(2(4(0(3(2(5(1(2(0(5(4(1(0(2(2(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 3(2(3(2(3(1(5(3(4(5(4(3(5(0(3(3(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 4(0(5(2(3(5(3(3(4(2(3(5(5(4(0(3(x1)))))))))))))))) 16.52/4.99 3(0(1(3(0(2(3(2(0(0(4(4(0(0(3(3(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 3(1(3(5(5(0(0(3(4(3(0(4(4(2(4(4(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.99 3(1(3(5(5(0(0(3(4(3(0(4(4(2(4(4(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 3(2(3(2(3(1(5(3(4(5(4(3(5(0(3(3(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(1(1(3(2(0(0(5(2(3(4(5(5(5(1(0(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(2(4(2(4(4(2(0(4(1(3(4(3(5(0(4(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(4(3(4(2(4(4(4(2(4(1(4(4(0(1(5(x1)))))))))))))))) 16.52/4.99 3(3(5(1(0(1(3(2(2(1(0(4(2(1(4(0(x1)))))))))))))))) -> 3(5(5(0(3(4(5(5(5(1(2(1(5(4(3(4(x1)))))))))))))))) 16.52/4.99 4(1(3(3(5(5(1(3(2(2(4(3(1(0(3(3(x1)))))))))))))))) -> 4(0(5(2(3(5(3(3(4(2(3(5(5(4(0(3(x1)))))))))))))))) 16.52/4.99 4(2(1(3(2(5(1(3(3(4(1(0(3(5(3(5(x1)))))))))))))))) -> 4(2(0(1(0(5(5(4(3(2(0(2(3(3(1(5(x1)))))))))))))))) 16.52/4.99 5(0(0(1(2(5(5(2(0(5(5(0(3(0(2(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 3(0(1(0(4(3(0(5(1(0(4(2(4(5(2(5(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 3(4(3(4(2(4(4(4(2(4(1(4(4(0(1(5(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 4(2(0(1(0(5(5(4(3(2(0(2(3(3(1(5(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(0(0(1(2(5(5(2(0(5(5(0(3(0(2(4(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(1(5(0(3(0(5(4(2(0(4(0(2(4(5(2(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(2(3(4(3(3(2(5(1(4(3(2(3(5(2(0(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(2(4(0(2(5(3(2(3(5(0(0(0(5(1(4(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(2(4(0(3(2(5(1(2(0(5(4(1(0(2(2(x1)))))))))))))))) 16.52/4.99 5(2(2(3(1(2(1(2(1(3(2(2(2(4(2(5(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(2(4(0(2(5(3(2(3(5(0(0(0(5(1(4(x1)))))))))))))))) -> 5(0(0(1(2(5(5(2(0(5(5(0(3(0(2(4(x1)))))))))))))))) 16.52/4.99 5(2(4(0(2(5(3(2(3(5(0(0(0(5(1(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(2(4(0(3(2(5(1(2(0(5(4(1(0(2(2(x1)))))))))))))))) -> 5(1(5(0(3(0(5(4(2(0(4(0(2(4(5(2(x1)))))))))))))))) 16.52/4.99 5(4(0(4(3(1(2(5(3(2(0(0(2(2(4(0(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(4(3(1(5(4(0(5(3(3(5(3(3(2(3(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 5(4(5(0(5(1(5(3(0(2(2(3(3(4(1(4(x1)))))))))))))))) -> 5(5(2(0(3(4(2(2(3(3(5(4(0(5(2(4(x1)))))))))))))))) 16.52/4.99 16.52/4.99 16.52/4.99 16.52/4.99 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (2) 16.52/4.99 Obligation: 16.52/4.99 Q restricted rewrite system: 16.52/4.99 The TRS R consists of the following rules: 16.52/4.99 16.52/4.99 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 0(3(5(0(5(0(3(2(1(5(1(2(0(5(5(4(x1)))))))))))))))) -> 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) 16.52/4.99 0(3(5(0(5(0(3(2(1(5(1(2(0(5(5(4(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 16.52/4.99 Q is empty. 16.52/4.99 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (3) QTRSRRRProof (EQUIVALENT) 16.52/4.99 Used ordering: 16.52/4.99 Polynomial interpretation [POLO]: 16.52/4.99 16.52/4.99 POL(0(x_1)) = x_1 16.52/4.99 POL(1(x_1)) = x_1 16.52/4.99 POL(2(x_1)) = 1 + x_1 16.52/4.99 POL(3(x_1)) = x_1 16.52/4.99 POL(4(x_1)) = x_1 16.52/4.99 POL(5(x_1)) = x_1 16.52/4.99 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 16.52/4.99 16.52/4.99 0(3(5(0(5(0(3(2(1(5(1(2(0(5(5(4(x1)))))))))))))))) -> 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) 16.52/4.99 0(3(5(0(5(0(3(2(1(5(1(2(0(5(5(4(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 16.52/4.99 16.52/4.99 16.52/4.99 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (4) 16.52/4.99 Obligation: 16.52/4.99 Q restricted rewrite system: 16.52/4.99 The TRS R consists of the following rules: 16.52/4.99 16.52/4.99 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 16.52/4.99 Q is empty. 16.52/4.99 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (5) Overlay + Local Confluence (EQUIVALENT) 16.52/4.99 The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (6) 16.52/4.99 Obligation: 16.52/4.99 Q restricted rewrite system: 16.52/4.99 The TRS R consists of the following rules: 16.52/4.99 16.52/4.99 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 16.52/4.99 The set Q consists of the following terms: 16.52/4.99 16.52/4.99 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x0)))))))))))))))) 16.52/4.99 16.52/4.99 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (7) DependencyPairsProof (EQUIVALENT) 16.52/4.99 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (8) 16.52/4.99 Obligation: 16.52/4.99 Q DP problem: 16.52/4.99 The TRS P consists of the following rules: 16.52/4.99 16.52/4.99 0^1(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) -> 0^1(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 0^1(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) -> 0^1(4(3(5(4(x1))))) 16.52/4.99 16.52/4.99 The TRS R consists of the following rules: 16.52/4.99 16.52/4.99 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x1)))))))))))))))) -> 0(4(4(1(5(5(5(4(1(3(2(0(4(3(5(4(x1)))))))))))))))) 16.52/4.99 16.52/4.99 The set Q consists of the following terms: 16.52/4.99 16.52/4.99 0(2(4(3(4(1(3(5(5(5(5(4(1(4(0(4(x0)))))))))))))))) 16.52/4.99 16.52/4.99 We have to consider all minimal (P,Q,R)-chains. 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (9) DependencyGraphProof (EQUIVALENT) 16.52/4.99 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes. 16.52/4.99 ---------------------------------------- 16.52/4.99 16.52/4.99 (10) 16.52/4.99 TRUE 16.73/5.13 EOF