84.62/22.38 YES 85.86/22.62 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 85.86/22.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 85.86/22.62 85.86/22.62 85.86/22.62 Termination w.r.t. Q of the given QTRS could be proven: 85.86/22.62 85.86/22.62 (0) QTRS 85.86/22.62 (1) QTRS Reverse [EQUIVALENT, 0 ms] 85.86/22.62 (2) QTRS 85.86/22.62 (3) QTRSRRRProof [EQUIVALENT, 213 ms] 85.86/22.62 (4) QTRS 85.86/22.62 (5) DependencyPairsProof [EQUIVALENT, 408 ms] 85.86/22.62 (6) QDP 85.86/22.62 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 85.86/22.62 (8) QDP 85.86/22.62 (9) QDPOrderProof [EQUIVALENT, 803 ms] 85.86/22.62 (10) QDP 85.86/22.62 (11) DependencyGraphProof [EQUIVALENT, 0 ms] 85.86/22.62 (12) AND 85.86/22.62 (13) QDP 85.86/22.62 (14) QDPOrderProof [EQUIVALENT, 33 ms] 85.86/22.62 (15) QDP 85.86/22.62 (16) PisEmptyProof [EQUIVALENT, 0 ms] 85.86/22.62 (17) YES 85.86/22.62 (18) QDP 85.86/22.62 (19) QDPOrderProof [EQUIVALENT, 38 ms] 85.86/22.62 (20) QDP 85.86/22.62 (21) PisEmptyProof [EQUIVALENT, 0 ms] 85.86/22.62 (22) YES 85.86/22.62 85.86/22.62 85.86/22.62 ---------------------------------------- 85.86/22.62 85.86/22.62 (0) 85.86/22.62 Obligation: 85.86/22.62 Q restricted rewrite system: 85.86/22.62 The TRS R consists of the following rules: 85.86/22.62 85.86/22.62 0(1(2(3(x1)))) -> 3(2(4(x1))) 85.86/22.62 2(3(3(0(4(x1))))) -> 4(2(1(5(x1)))) 85.86/22.62 0(3(3(1(1(4(x1)))))) -> 3(2(3(0(1(3(x1)))))) 85.86/22.62 5(1(3(0(4(0(x1)))))) -> 3(5(3(3(2(x1))))) 85.86/22.62 0(3(2(1(4(0(1(x1))))))) -> 4(0(5(1(3(0(1(x1))))))) 85.86/22.62 2(2(0(2(5(2(0(x1))))))) -> 2(2(1(2(5(1(3(x1))))))) 85.86/22.62 4(5(3(2(4(4(2(2(x1)))))))) -> 4(0(5(0(0(0(2(2(x1)))))))) 85.86/22.62 1(0(2(5(2(3(0(1(1(x1))))))))) -> 1(5(1(2(0(2(4(4(1(x1))))))))) 85.86/22.62 4(4(0(3(5(1(2(4(4(x1))))))))) -> 1(5(2(0(3(5(0(0(x1)))))))) 85.86/22.62 0(4(1(2(0(5(0(2(2(4(x1)))))))))) -> 2(5(4(0(1(2(5(3(4(x1))))))))) 85.86/22.62 4(5(4(1(2(4(1(0(1(5(x1)))))))))) -> 1(1(0(1(3(1(5(2(5(x1))))))))) 85.86/22.62 5(1(0(3(2(3(4(5(4(3(x1)))))))))) -> 5(2(0(5(3(4(2(5(3(x1))))))))) 85.86/22.62 1(3(0(4(3(0(5(3(2(5(3(x1))))))))))) -> 1(3(0(0(0(3(1(3(3(5(3(x1))))))))))) 85.86/22.62 4(5(0(0(4(4(5(0(5(4(5(x1))))))))))) -> 2(4(2(2(2(4(3(1(4(5(x1)))))))))) 85.86/22.62 2(3(0(0(5(4(1(3(4(0(1(4(x1)))))))))))) -> 4(0(3(3(4(5(1(1(4(2(4(x1))))))))))) 85.86/22.62 5(1(4(3(0(5(1(2(5(5(4(0(x1)))))))))))) -> 2(5(0(0(5(1(4(2(5(1(5(x1))))))))))) 85.86/22.62 5(1(5(2(0(5(5(5(2(2(5(1(x1)))))))))))) -> 2(2(4(0(0(5(3(0(5(1(0(2(x1)))))))))))) 85.86/22.62 4(5(4(5(1(2(0(2(5(4(4(5(5(x1))))))))))))) -> 1(1(3(4(3(3(0(4(2(5(5(3(x1)))))))))))) 85.86/22.62 5(5(0(4(0(2(1(1(0(4(5(0(5(x1))))))))))))) -> 1(1(0(3(4(2(1(1(5(0(2(5(x1)))))))))))) 85.86/22.62 5(0(5(1(0(3(1(3(1(1(3(1(5(1(x1)))))))))))))) -> 5(4(4(1(2(5(5(0(1(0(3(2(2(2(x1)))))))))))))) 85.86/22.62 5(5(3(0(4(4(0(2(1(5(1(4(2(1(x1)))))))))))))) -> 5(4(1(5(2(4(3(3(5(2(4(5(0(x1))))))))))))) 85.86/22.62 0(1(4(2(3(2(2(1(0(3(1(5(2(3(1(x1))))))))))))))) -> 1(5(2(4(2(5(2(4(3(4(1(0(4(2(x1)))))))))))))) 85.86/22.62 0(3(2(0(0(2(2(4(2(4(4(3(3(2(0(x1))))))))))))))) -> 3(2(1(0(4(4(2(1(0(4(3(3(1(0(x1)))))))))))))) 85.86/22.62 2(4(4(3(0(1(0(1(4(0(3(4(1(0(0(5(x1)))))))))))))))) -> 2(5(3(1(2(2(2(2(5(3(3(2(1(4(5(x1))))))))))))))) 85.86/22.62 5(0(3(0(1(1(5(1(1(2(0(3(3(0(4(5(1(x1))))))))))))))))) -> 3(4(5(2(0(1(2(0(1(5(4(1(3(1(5(2(x1)))))))))))))))) 85.86/22.62 0(5(5(2(5(4(5(0(5(2(2(3(1(3(3(4(4(2(x1)))))))))))))))))) -> 5(0(2(4(4(3(2(2(5(1(4(4(1(1(4(3(5(2(x1)))))))))))))))))) 85.86/22.62 1(2(0(1(0(5(0(2(4(4(5(1(4(1(2(0(4(5(x1)))))))))))))))))) -> 1(2(1(5(2(5(1(4(0(3(5(3(1(4(2(3(5(x1))))))))))))))))) 85.86/22.62 1(4(4(3(3(0(0(3(5(2(1(4(4(4(3(0(1(5(x1)))))))))))))))))) -> 3(5(3(3(0(2(5(1(5(4(4(3(1(2(3(4(3(5(x1)))))))))))))))))) 85.86/22.62 3(5(1(4(5(2(4(1(3(2(4(4(0(5(4(1(0(3(x1)))))))))))))))))) -> 3(0(5(5(4(5(1(4(3(0(0(5(5(3(3(1(2(3(x1)))))))))))))))))) 85.86/22.62 4(5(0(4(0(3(4(5(0(1(3(3(0(2(2(3(5(1(x1)))))))))))))))))) -> 1(5(3(0(1(1(2(3(5(0(0(0(2(0(1(0(1(x1))))))))))))))))) 85.86/22.62 5(3(5(3(3(1(5(5(2(2(3(3(4(1(5(1(0(5(x1)))))))))))))))))) -> 3(5(0(4(4(3(4(0(5(2(0(0(2(4(1(5(1(5(x1)))))))))))))))))) 85.86/22.62 5(4(0(1(5(1(2(4(0(4(0(3(2(1(5(3(3(0(x1)))))))))))))))))) -> 4(2(1(0(3(0(1(5(0(1(1(0(5(5(4(2(1(x1))))))))))))))))) 85.86/22.62 3(5(0(2(4(0(3(0(0(1(0(0(4(3(0(4(2(5(1(0(x1)))))))))))))))))))) -> 1(1(4(1(1(3(2(5(3(4(5(2(4(4(0(2(0(0(0(x1))))))))))))))))))) 85.86/22.62 4(1(0(2(0(3(5(5(3(2(1(2(4(5(2(2(3(4(3(0(x1)))))))))))))))))))) -> 0(0(5(5(4(1(2(2(1(0(0(4(4(5(0(5(3(5(3(0(x1)))))))))))))))))))) 85.86/22.62 4(3(0(0(2(1(4(5(1(4(3(5(0(2(2(3(5(1(4(1(4(x1))))))))))))))))))))) -> 4(3(4(1(1(0(4(2(1(5(2(1(1(2(4(1(2(3(1(3(x1)))))))))))))))))))) 85.86/22.62 85.86/22.62 Q is empty. 85.86/22.62 85.86/22.62 ---------------------------------------- 85.86/22.62 85.86/22.62 (1) QTRS Reverse (EQUIVALENT) 85.86/22.62 We applied the QTRS Reverse Processor [REVERSE]. 85.86/22.62 ---------------------------------------- 85.86/22.62 85.86/22.62 (2) 85.86/22.62 Obligation: 85.86/22.62 Q restricted rewrite system: 85.86/22.62 The TRS R consists of the following rules: 85.86/22.62 85.86/22.62 3(2(1(0(x1)))) -> 4(2(3(x1))) 85.86/22.62 4(0(3(3(2(x1))))) -> 5(1(2(4(x1)))) 85.86/22.62 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.62 0(4(0(3(1(5(x1)))))) -> 2(3(3(5(3(x1))))) 85.86/22.62 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.62 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.62 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.62 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.62 4(4(2(1(5(3(0(4(4(x1))))))))) -> 0(0(5(3(0(2(5(1(x1)))))))) 85.86/22.62 4(2(2(0(5(0(2(1(4(0(x1)))))))))) -> 4(3(5(2(1(0(4(5(2(x1))))))))) 85.86/22.62 5(1(0(1(4(2(1(4(5(4(x1)))))))))) -> 5(2(5(1(3(1(0(1(1(x1))))))))) 85.86/22.62 3(4(5(4(3(2(3(0(1(5(x1)))))))))) -> 3(5(2(4(3(5(0(2(5(x1))))))))) 85.86/22.62 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.62 5(4(5(0(5(4(4(0(0(5(4(x1))))))))))) -> 5(4(1(3(4(2(2(2(4(2(x1)))))))))) 85.86/22.62 4(1(0(4(3(1(4(5(0(0(3(2(x1)))))))))))) -> 4(2(4(1(1(5(4(3(3(0(4(x1))))))))))) 85.86/22.62 0(4(5(5(2(1(5(0(3(4(1(5(x1)))))))))))) -> 5(1(5(2(4(1(5(0(0(5(2(x1))))))))))) 85.86/22.62 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.62 5(5(4(4(5(2(0(2(1(5(4(5(4(x1))))))))))))) -> 3(5(5(2(4(0(3(3(4(3(1(1(x1)))))))))))) 85.86/22.62 5(0(5(4(0(1(1(2(0(4(0(5(5(x1))))))))))))) -> 5(2(0(5(1(1(2(4(3(0(1(1(x1)))))))))))) 85.86/22.62 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.62 1(2(4(1(5(1(2(0(4(4(0(3(5(5(x1)))))))))))))) -> 0(5(4(2(5(3(3(4(2(5(1(4(5(x1))))))))))))) 85.86/22.62 1(3(2(5(1(3(0(1(2(2(3(2(4(1(0(x1))))))))))))))) -> 2(4(0(1(4(3(4(2(5(2(4(2(5(1(x1)))))))))))))) 85.86/22.62 0(2(3(3(4(4(2(4(2(2(0(0(2(3(0(x1))))))))))))))) -> 0(1(3(3(4(0(1(2(4(4(0(1(2(3(x1)))))))))))))) 85.86/22.62 5(0(0(1(4(3(0(4(1(0(1(0(3(4(4(2(x1)))))))))))))))) -> 5(4(1(2(3(3(5(2(2(2(2(1(3(5(2(x1))))))))))))))) 85.86/22.62 1(5(4(0(3(3(0(2(1(1(5(1(1(0(3(0(5(x1))))))))))))))))) -> 2(5(1(3(1(4(5(1(0(2(1(0(2(5(4(3(x1)))))))))))))))) 85.86/22.62 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.62 5(4(0(2(1(4(1(5(4(4(2(0(5(0(1(0(2(1(x1)))))))))))))))))) -> 5(3(2(4(1(3(5(3(0(4(1(5(2(5(1(2(1(x1))))))))))))))))) 85.86/22.62 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.62 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.62 1(5(3(2(2(0(3(3(1(0(5(4(3(0(4(0(5(4(x1)))))))))))))))))) -> 1(0(1(0(2(0(0(0(5(3(2(1(1(0(3(5(1(x1))))))))))))))))) 85.86/22.62 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.62 0(3(3(5(1(2(3(0(4(0(4(2(1(5(1(0(4(5(x1)))))))))))))))))) -> 1(2(4(5(5(0(1(1(0(5(1(0(3(0(1(2(4(x1))))))))))))))))) 85.86/22.62 0(1(5(2(4(0(3(4(0(0(1(0(0(3(0(4(2(0(5(3(x1)))))))))))))))))))) -> 0(0(0(2(0(4(4(2(5(4(3(5(2(3(1(1(4(1(1(x1))))))))))))))))))) 85.86/22.62 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.62 4(1(4(1(5(3(2(2(0(5(3(4(1(5(4(1(2(0(0(3(4(x1))))))))))))))))))))) -> 3(1(3(2(1(4(2(1(1(2(5(1(2(4(0(1(1(4(3(4(x1)))))))))))))))))))) 85.86/22.62 85.86/22.62 Q is empty. 85.86/22.62 85.86/22.62 ---------------------------------------- 85.86/22.62 85.86/22.62 (3) QTRSRRRProof (EQUIVALENT) 85.86/22.62 Used ordering: 85.86/22.62 Polynomial interpretation [POLO]: 85.86/22.62 85.86/22.62 POL(0(x_1)) = 1 + x_1 85.86/22.62 POL(1(x_1)) = 1 + x_1 85.86/22.62 POL(2(x_1)) = 1 + x_1 85.86/22.62 POL(3(x_1)) = 1 + x_1 85.86/22.62 POL(4(x_1)) = 1 + x_1 85.86/22.62 POL(5(x_1)) = 1 + x_1 85.86/22.62 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 85.86/22.62 85.86/22.62 3(2(1(0(x1)))) -> 4(2(3(x1))) 85.86/22.62 4(0(3(3(2(x1))))) -> 5(1(2(4(x1)))) 85.86/22.62 0(4(0(3(1(5(x1)))))) -> 2(3(3(5(3(x1))))) 85.86/22.62 4(4(2(1(5(3(0(4(4(x1))))))))) -> 0(0(5(3(0(2(5(1(x1)))))))) 85.86/22.62 4(2(2(0(5(0(2(1(4(0(x1)))))))))) -> 4(3(5(2(1(0(4(5(2(x1))))))))) 85.86/22.62 5(1(0(1(4(2(1(4(5(4(x1)))))))))) -> 5(2(5(1(3(1(0(1(1(x1))))))))) 85.86/22.62 3(4(5(4(3(2(3(0(1(5(x1)))))))))) -> 3(5(2(4(3(5(0(2(5(x1))))))))) 85.86/22.62 5(4(5(0(5(4(4(0(0(5(4(x1))))))))))) -> 5(4(1(3(4(2(2(2(4(2(x1)))))))))) 85.86/22.62 4(1(0(4(3(1(4(5(0(0(3(2(x1)))))))))))) -> 4(2(4(1(1(5(4(3(3(0(4(x1))))))))))) 85.86/22.62 0(4(5(5(2(1(5(0(3(4(1(5(x1)))))))))))) -> 5(1(5(2(4(1(5(0(0(5(2(x1))))))))))) 85.86/22.62 5(5(4(4(5(2(0(2(1(5(4(5(4(x1))))))))))))) -> 3(5(5(2(4(0(3(3(4(3(1(1(x1)))))))))))) 85.86/22.62 5(0(5(4(0(1(1(2(0(4(0(5(5(x1))))))))))))) -> 5(2(0(5(1(1(2(4(3(0(1(1(x1)))))))))))) 85.86/22.62 1(2(4(1(5(1(2(0(4(4(0(3(5(5(x1)))))))))))))) -> 0(5(4(2(5(3(3(4(2(5(1(4(5(x1))))))))))))) 85.86/22.62 1(3(2(5(1(3(0(1(2(2(3(2(4(1(0(x1))))))))))))))) -> 2(4(0(1(4(3(4(2(5(2(4(2(5(1(x1)))))))))))))) 85.86/22.62 0(2(3(3(4(4(2(4(2(2(0(0(2(3(0(x1))))))))))))))) -> 0(1(3(3(4(0(1(2(4(4(0(1(2(3(x1)))))))))))))) 85.86/22.62 5(0(0(1(4(3(0(4(1(0(1(0(3(4(4(2(x1)))))))))))))))) -> 5(4(1(2(3(3(5(2(2(2(2(1(3(5(2(x1))))))))))))))) 85.86/22.62 1(5(4(0(3(3(0(2(1(1(5(1(1(0(3(0(5(x1))))))))))))))))) -> 2(5(1(3(1(4(5(1(0(2(1(0(2(5(4(3(x1)))))))))))))))) 85.86/22.62 5(4(0(2(1(4(1(5(4(4(2(0(5(0(1(0(2(1(x1)))))))))))))))))) -> 5(3(2(4(1(3(5(3(0(4(1(5(2(5(1(2(1(x1))))))))))))))))) 85.86/22.62 1(5(3(2(2(0(3(3(1(0(5(4(3(0(4(0(5(4(x1)))))))))))))))))) -> 1(0(1(0(2(0(0(0(5(3(2(1(1(0(3(5(1(x1))))))))))))))))) 85.86/22.62 0(3(3(5(1(2(3(0(4(0(4(2(1(5(1(0(4(5(x1)))))))))))))))))) -> 1(2(4(5(5(0(1(1(0(5(1(0(3(0(1(2(4(x1))))))))))))))))) 85.86/22.62 0(1(5(2(4(0(3(4(0(0(1(0(0(3(0(4(2(0(5(3(x1)))))))))))))))))))) -> 0(0(0(2(0(4(4(2(5(4(3(5(2(3(1(1(4(1(1(x1))))))))))))))))))) 85.86/22.62 4(1(4(1(5(3(2(2(0(5(3(4(1(5(4(1(2(0(0(3(4(x1))))))))))))))))))))) -> 3(1(3(2(1(4(2(1(1(2(5(1(2(4(0(1(1(4(3(4(x1)))))))))))))))))))) 85.86/22.62 85.86/22.62 85.86/22.62 85.86/22.62 85.86/22.62 ---------------------------------------- 85.86/22.62 85.86/22.62 (4) 85.86/22.62 Obligation: 85.86/22.62 Q restricted rewrite system: 85.86/22.62 The TRS R consists of the following rules: 85.86/22.62 85.86/22.62 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.62 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.62 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.62 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.62 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.62 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.62 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.62 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.62 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.62 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.62 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.62 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.62 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.62 85.86/22.62 Q is empty. 85.86/22.62 85.86/22.62 ---------------------------------------- 85.86/22.62 85.86/22.62 (5) DependencyPairsProof (EQUIVALENT) 85.86/22.62 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 85.86/22.62 ---------------------------------------- 85.86/22.62 85.86/22.62 (6) 85.86/22.62 Obligation: 85.86/22.62 Q DP problem: 85.86/22.62 The TRS P consists of the following rules: 85.86/22.62 85.86/22.62 4^1(1(1(3(3(0(x1)))))) -> 3^1(1(0(3(2(3(x1)))))) 85.86/22.62 4^1(1(1(3(3(0(x1)))))) -> 1^1(0(3(2(3(x1))))) 85.86/22.62 4^1(1(1(3(3(0(x1)))))) -> 0^1(3(2(3(x1)))) 85.86/22.62 4^1(1(1(3(3(0(x1)))))) -> 3^1(2(3(x1))) 85.86/22.62 4^1(1(1(3(3(0(x1)))))) -> 2^1(3(x1)) 85.86/22.62 4^1(1(1(3(3(0(x1)))))) -> 3^1(x1) 85.86/22.62 1^1(0(4(1(2(3(0(x1))))))) -> 1^1(0(3(1(5(0(4(x1))))))) 85.86/22.62 1^1(0(4(1(2(3(0(x1))))))) -> 0^1(3(1(5(0(4(x1)))))) 85.86/22.62 1^1(0(4(1(2(3(0(x1))))))) -> 3^1(1(5(0(4(x1))))) 85.86/22.62 1^1(0(4(1(2(3(0(x1))))))) -> 1^1(5(0(4(x1)))) 85.86/22.62 1^1(0(4(1(2(3(0(x1))))))) -> 5^1(0(4(x1))) 85.86/22.62 1^1(0(4(1(2(3(0(x1))))))) -> 0^1(4(x1)) 85.86/22.62 1^1(0(4(1(2(3(0(x1))))))) -> 4^1(x1) 85.86/22.62 0^1(2(5(2(0(2(2(x1))))))) -> 3^1(1(5(2(1(2(2(x1))))))) 85.86/22.62 0^1(2(5(2(0(2(2(x1))))))) -> 1^1(5(2(1(2(2(x1)))))) 85.86/22.62 0^1(2(5(2(0(2(2(x1))))))) -> 5^1(2(1(2(2(x1))))) 85.86/22.62 0^1(2(5(2(0(2(2(x1))))))) -> 2^1(1(2(2(x1)))) 85.86/22.62 0^1(2(5(2(0(2(2(x1))))))) -> 1^1(2(2(x1))) 85.86/22.62 2^1(2(4(4(2(3(5(4(x1)))))))) -> 2^1(2(0(0(0(5(0(4(x1)))))))) 85.86/22.62 2^1(2(4(4(2(3(5(4(x1)))))))) -> 2^1(0(0(0(5(0(4(x1))))))) 85.86/22.62 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(0(0(5(0(4(x1)))))) 85.86/22.62 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(0(5(0(4(x1))))) 85.86/22.62 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(5(0(4(x1)))) 85.86/22.62 2^1(2(4(4(2(3(5(4(x1)))))))) -> 5^1(0(4(x1))) 85.86/22.62 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(4(x1)) 85.86/22.62 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 1^1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.62 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 4^1(4(2(0(2(1(5(1(x1)))))))) 85.86/22.62 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 4^1(2(0(2(1(5(1(x1))))))) 85.86/22.62 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 2^1(0(2(1(5(1(x1)))))) 85.86/22.62 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 0^1(2(1(5(1(x1))))) 85.86/22.62 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 2^1(1(5(1(x1)))) 85.86/22.62 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 1^1(5(1(x1))) 85.86/22.62 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 5^1(1(x1)) 85.86/22.62 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3^1(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.62 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 5^1(3(3(1(3(0(0(0(3(1(x1)))))))))) 85.86/22.62 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3^1(3(1(3(0(0(0(3(1(x1))))))))) 85.86/22.62 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3^1(1(3(0(0(0(3(1(x1)))))))) 85.86/22.62 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 1^1(3(0(0(0(3(1(x1))))))) 85.86/22.62 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3^1(0(0(0(3(1(x1)))))) 85.86/22.62 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 0^1(0(0(3(1(x1))))) 85.86/22.62 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 0^1(0(3(1(x1)))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2^1(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(1(5(0(3(5(0(0(4(2(2(x1))))))))))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 1^1(5(0(3(5(0(0(4(2(2(x1)))))))))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 5^1(0(3(5(0(0(4(2(2(x1))))))))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(3(5(0(0(4(2(2(x1)))))))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 3^1(5(0(0(4(2(2(x1))))))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 5^1(0(0(4(2(2(x1)))))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(0(4(2(2(x1))))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(4(2(2(x1)))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 4^1(2(2(x1))) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2^1(2(x1)) 85.86/22.62 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2^1(x1) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2^1(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2^1(2(3(0(1(0(5(5(2(1(4(4(5(x1))))))))))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2^1(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 3^1(0(1(0(5(5(2(1(4(4(5(x1))))))))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 0^1(1(0(5(5(2(1(4(4(5(x1)))))))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 1^1(0(5(5(2(1(4(4(5(x1))))))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 0^1(5(5(2(1(4(4(5(x1)))))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 5^1(5(2(1(4(4(5(x1))))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 5^1(2(1(4(4(5(x1)))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2^1(1(4(4(5(x1))))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 1^1(4(4(5(x1)))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 4^1(4(5(x1))) 85.86/22.62 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 4^1(5(x1)) 85.86/22.62 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2^1(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.62 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))))))) 85.86/22.62 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 3^1(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))) 85.86/22.62 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))))) 85.86/22.62 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))) 85.86/22.62 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))) 85.86/22.62 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))) 85.86/22.62 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(1(5(2(2(3(4(4(2(0(5(x1))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(5(2(2(3(4(4(2(0(5(x1)))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(2(2(3(4(4(2(0(5(x1))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2^1(2(3(4(4(2(0(5(x1)))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2^1(3(4(4(2(0(5(x1))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 3^1(4(4(2(0(5(x1)))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(4(2(0(5(x1))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(2(0(5(x1)))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2^1(0(5(x1))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 0^1(5(x1)) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(x1) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 3^1(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1))))))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 3^1(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1))))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 2^1(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 1^1(3(4(4(5(1(5(2(0(3(3(5(3(x1))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 3^1(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(4(5(1(5(2(0(3(3(5(3(x1))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(5(1(5(2(0(3(3(5(3(x1)))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(1(5(2(0(3(3(5(3(x1))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 1^1(5(2(0(3(3(5(3(x1)))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(2(0(3(3(5(3(x1))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 2^1(0(3(3(5(3(x1)))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 0^1(3(3(5(3(x1))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 3^1(3(5(3(x1)))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 3^1(5(3(x1))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(3(x1)) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 3^1(x1) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3^1(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 2^1(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1))))))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 1^1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3^1(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1))))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3^1(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(5(0(0(3(4(1(5(4(5(5(0(3(x1))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(0(3(4(1(5(4(5(5(0(3(x1))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(3(4(1(5(4(5(5(0(3(x1)))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3^1(4(1(5(4(5(5(0(3(x1))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 4^1(1(5(4(5(5(0(3(x1)))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 1^1(5(4(5(5(0(3(x1))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(4(5(5(0(3(x1)))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 4^1(5(5(0(3(x1))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(5(0(3(x1)))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(0(3(x1))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(3(x1)) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 1^1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1))))))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 1^1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1))))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 2^1(0(0(2(5(0(4(3(4(4(0(5(3(x1))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(2(5(0(4(3(4(4(0(5(3(x1))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 2^1(5(0(4(3(4(4(0(5(3(x1)))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(0(4(3(4(4(0(5(3(x1))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(4(3(4(4(0(5(3(x1)))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(3(4(4(0(5(3(x1))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 3^1(4(4(0(5(3(x1)))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(4(0(5(3(x1))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(0(5(3(x1)))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(5(3(x1))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(3(x1)) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 3^1(x1) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 3^1(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1))))))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 3^1(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1))))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(4(0(0(1(2(2(1(4(5(5(0(0(x1))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(0(1(2(2(1(4(5(5(0(0(x1))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(1(2(2(1(4(5(5(0(0(x1)))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 1^1(2(2(1(4(5(5(0(0(x1))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 2^1(2(1(4(5(5(0(0(x1)))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 2^1(1(4(5(5(0(0(x1))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 1^1(4(5(5(0(0(x1)))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(5(5(0(0(x1))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(5(0(0(x1)))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(0(0(x1))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(0(x1)) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(x1) 85.86/22.64 85.86/22.64 The TRS R consists of the following rules: 85.86/22.64 85.86/22.64 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.64 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.64 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.64 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.64 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.64 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.64 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.64 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.64 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.64 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.64 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.64 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.64 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.64 85.86/22.64 Q is empty. 85.86/22.64 We have to consider all minimal (P,Q,R)-chains. 85.86/22.64 ---------------------------------------- 85.86/22.64 85.86/22.64 (7) DependencyGraphProof (EQUIVALENT) 85.86/22.64 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 52 less nodes. 85.86/22.64 ---------------------------------------- 85.86/22.64 85.86/22.64 (8) 85.86/22.64 Obligation: 85.86/22.64 Q DP problem: 85.86/22.64 The TRS P consists of the following rules: 85.86/22.64 85.86/22.64 4^1(1(1(3(3(0(x1)))))) -> 1^1(0(3(2(3(x1))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 1^1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 4^1(4(2(0(2(1(5(1(x1)))))))) 85.86/22.64 4^1(1(1(3(3(0(x1)))))) -> 0^1(3(2(3(x1)))) 85.86/22.64 0^1(2(5(2(0(2(2(x1))))))) -> 1^1(5(2(1(2(2(x1)))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 4^1(2(0(2(1(5(1(x1))))))) 85.86/22.64 4^1(1(1(3(3(0(x1)))))) -> 3^1(x1) 85.86/22.64 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 5^1(3(3(1(3(0(0(0(3(1(x1)))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 1^1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1))))))))))))))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 0^1(2(1(5(1(x1))))) 85.86/22.64 0^1(2(5(2(0(2(2(x1))))))) -> 5^1(2(1(2(2(x1))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 1^1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1))))))))))))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 1^1(5(1(x1))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 5^1(1(x1)) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))) 85.86/22.64 0^1(2(5(2(0(2(2(x1))))))) -> 1^1(2(2(x1))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(1(5(0(3(5(0(0(4(2(2(x1))))))))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 1^1(5(0(3(5(0(0(4(2(2(x1)))))))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 5^1(0(3(5(0(0(4(2(2(x1))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(2(5(0(4(3(4(4(0(5(3(x1))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(0(4(3(4(4(0(5(3(x1))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(4(3(4(4(0(5(3(x1)))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(3(4(4(0(5(3(x1))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(4(0(5(3(x1))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(0(5(3(x1)))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(5(3(x1))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(3(x1)) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 3^1(x1) 85.86/22.64 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 1^1(3(0(0(0(3(1(x1))))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(3(5(0(0(4(2(2(x1)))))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 5^1(0(0(4(2(2(x1)))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(0(4(2(2(x1))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(4(2(2(x1)))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 4^1(2(2(x1))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2^1(2(x1)) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(0(0(5(0(4(x1)))))) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(0(5(0(4(x1))))) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(5(0(4(x1)))) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 5^1(0(4(x1))) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(4(x1)) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2^1(x1) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 0^1(1(0(5(5(2(1(4(4(5(x1)))))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 1^1(0(5(5(2(1(4(4(5(x1))))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 0^1(5(5(2(1(4(4(5(x1)))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 5^1(5(2(1(4(4(5(x1))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 5^1(2(1(4(4(5(x1)))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 1^1(4(4(5(x1)))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 4^1(4(5(x1))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 4^1(5(x1)) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(1(5(2(2(3(4(4(2(0(5(x1))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(5(2(2(3(4(4(2(0(5(x1)))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(2(2(3(4(4(2(0(5(x1))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(4(2(0(5(x1))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(2(0(5(x1)))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 0^1(5(x1)) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(x1) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 1^1(3(4(4(5(1(5(2(0(3(3(5(3(x1))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(4(5(1(5(2(0(3(3(5(3(x1))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(5(1(5(2(0(3(3(5(3(x1)))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(1(5(2(0(3(3(5(3(x1))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 1^1(5(2(0(3(3(5(3(x1)))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(2(0(3(3(5(3(x1))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 0^1(3(3(5(3(x1))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(3(x1)) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 3^1(x1) 85.86/22.64 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 0^1(0(0(3(1(x1))))) 85.86/22.64 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 0^1(0(3(1(x1)))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 1^1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(5(0(0(3(4(1(5(4(5(5(0(3(x1))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(0(3(4(1(5(4(5(5(0(3(x1))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(3(4(1(5(4(5(5(0(3(x1)))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 4^1(1(5(4(5(5(0(3(x1)))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 1^1(5(4(5(5(0(3(x1))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(4(5(5(0(3(x1)))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 4^1(5(5(0(3(x1))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(5(0(3(x1)))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(0(3(x1))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(3(x1)) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(4(0(0(1(2(2(1(4(5(5(0(0(x1))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(0(1(2(2(1(4(5(5(0(0(x1))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(1(2(2(1(4(5(5(0(0(x1)))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 1^1(2(2(1(4(5(5(0(0(x1))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 1^1(4(5(5(0(0(x1)))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(5(5(0(0(x1))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(5(0(0(x1)))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(0(0(x1))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(0(x1)) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(x1) 85.86/22.64 85.86/22.64 The TRS R consists of the following rules: 85.86/22.64 85.86/22.64 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.64 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.64 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.64 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.64 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.64 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.64 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.64 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.64 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.64 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.64 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.64 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.64 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.64 85.86/22.64 Q is empty. 85.86/22.64 We have to consider all minimal (P,Q,R)-chains. 85.86/22.64 ---------------------------------------- 85.86/22.64 85.86/22.64 (9) QDPOrderProof (EQUIVALENT) 85.86/22.64 We use the reduction pair processor [LPAR04,JAR06]. 85.86/22.64 85.86/22.64 85.86/22.64 The following pairs can be oriented strictly and are deleted. 85.86/22.64 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 4^1(4(2(0(2(1(5(1(x1)))))))) 85.86/22.64 4^1(1(1(3(3(0(x1)))))) -> 0^1(3(2(3(x1)))) 85.86/22.64 0^1(2(5(2(0(2(2(x1))))))) -> 1^1(5(2(1(2(2(x1)))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 4^1(2(0(2(1(5(1(x1))))))) 85.86/22.64 4^1(1(1(3(3(0(x1)))))) -> 3^1(x1) 85.86/22.64 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 5^1(3(3(1(3(0(0(0(3(1(x1)))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 1^1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1))))))))))))))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 0^1(2(1(5(1(x1))))) 85.86/22.64 0^1(2(5(2(0(2(2(x1))))))) -> 5^1(2(1(2(2(x1))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 1^1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1))))))))))))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 1^1(5(1(x1))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 5^1(1(x1)) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))) 85.86/22.64 0^1(2(5(2(0(2(2(x1))))))) -> 1^1(2(2(x1))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(1(5(0(3(5(0(0(4(2(2(x1))))))))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 1^1(5(0(3(5(0(0(4(2(2(x1)))))))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 5^1(0(3(5(0(0(4(2(2(x1))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(2(5(0(4(3(4(4(0(5(3(x1))))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(0(4(3(4(4(0(5(3(x1))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(4(3(4(4(0(5(3(x1)))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(3(4(4(0(5(3(x1))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(4(0(5(3(x1))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 4^1(0(5(3(x1)))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 0^1(5(3(x1))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(3(x1)) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 3^1(x1) 85.86/22.64 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 1^1(3(0(0(0(3(1(x1))))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(3(5(0(0(4(2(2(x1)))))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 5^1(0(0(4(2(2(x1)))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(0(4(2(2(x1))))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 0^1(4(2(2(x1)))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 4^1(2(2(x1))) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2^1(2(x1)) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(0(0(5(0(4(x1)))))) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(0(5(0(4(x1))))) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(5(0(4(x1)))) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 5^1(0(4(x1))) 85.86/22.64 2^1(2(4(4(2(3(5(4(x1)))))))) -> 0^1(4(x1)) 85.86/22.64 1^1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2^1(x1) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 0^1(1(0(5(5(2(1(4(4(5(x1)))))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 1^1(0(5(5(2(1(4(4(5(x1))))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 0^1(5(5(2(1(4(4(5(x1)))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 5^1(5(2(1(4(4(5(x1))))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 5^1(2(1(4(4(5(x1)))))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 1^1(4(4(5(x1)))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 4^1(4(5(x1))) 85.86/22.64 1^1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 4^1(5(x1)) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(1(5(2(2(3(4(4(2(0(5(x1))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 1^1(5(2(2(3(4(4(2(0(5(x1)))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(2(2(3(4(4(2(0(5(x1))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(4(2(0(5(x1))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 4^1(2(0(5(x1)))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 0^1(5(x1)) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(x1) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 1^1(3(4(4(5(1(5(2(0(3(3(5(3(x1))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(4(5(1(5(2(0(3(3(5(3(x1))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 4^1(5(1(5(2(0(3(3(5(3(x1)))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(1(5(2(0(3(3(5(3(x1))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 1^1(5(2(0(3(3(5(3(x1)))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(2(0(3(3(5(3(x1))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 0^1(3(3(5(3(x1))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(3(x1)) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 3^1(x1) 85.86/22.64 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 0^1(0(0(3(1(x1))))) 85.86/22.64 3^1(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 0^1(0(3(1(x1)))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 1^1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(5(0(0(3(4(1(5(4(5(5(0(3(x1))))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(0(3(4(1(5(4(5(5(0(3(x1))))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(3(4(1(5(4(5(5(0(3(x1)))))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 4^1(1(5(4(5(5(0(3(x1)))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 1^1(5(4(5(5(0(3(x1))))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(4(5(5(0(3(x1)))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 4^1(5(5(0(3(x1))))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(5(0(3(x1)))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 5^1(0(3(x1))) 85.86/22.64 3^1(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 0^1(3(x1)) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(4(0(0(1(2(2(1(4(5(5(0(0(x1))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(0(1(2(2(1(4(5(5(0(0(x1))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(1(2(2(1(4(5(5(0(0(x1)))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 1^1(2(2(1(4(5(5(0(0(x1))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 1^1(4(5(5(0(0(x1)))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 4^1(5(5(0(0(x1))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(5(0(0(x1)))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 5^1(0(0(x1))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(0(x1)) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(x1) 85.86/22.64 The remaining pairs can at least be oriented weakly. 85.86/22.64 Used ordering: Polynomial interpretation [POLO]: 85.86/22.64 85.86/22.64 POL(0(x_1)) = 1 + x_1 85.86/22.64 POL(0^1(x_1)) = 1 + x_1 85.86/22.64 POL(1(x_1)) = 1 + x_1 85.86/22.64 POL(1^1(x_1)) = 1 + x_1 85.86/22.64 POL(2(x_1)) = 1 + x_1 85.86/22.64 POL(2^1(x_1)) = x_1 85.86/22.64 POL(3(x_1)) = 1 + x_1 85.86/22.64 POL(3^1(x_1)) = 1 + x_1 85.86/22.64 POL(4(x_1)) = 1 + x_1 85.86/22.64 POL(4^1(x_1)) = x_1 85.86/22.64 POL(5(x_1)) = 1 + x_1 85.86/22.64 POL(5^1(x_1)) = 1 + x_1 85.86/22.64 85.86/22.64 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 85.86/22.64 85.86/22.64 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.64 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.64 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.64 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.64 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.64 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.64 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.64 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.64 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.64 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.64 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.64 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.64 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.64 85.86/22.64 85.86/22.64 ---------------------------------------- 85.86/22.64 85.86/22.64 (10) 85.86/22.64 Obligation: 85.86/22.64 Q DP problem: 85.86/22.64 The TRS P consists of the following rules: 85.86/22.64 85.86/22.64 4^1(1(1(3(3(0(x1)))))) -> 1^1(0(3(2(3(x1))))) 85.86/22.64 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 1^1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.64 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.64 5^1(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5^1(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.64 2^1(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 5^1(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1))))))))))))))))) 85.86/22.64 0^1(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0^1(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.64 85.86/22.64 The TRS R consists of the following rules: 85.86/22.64 85.86/22.64 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.64 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.64 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.64 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.64 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.64 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.64 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.64 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.64 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.65 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.65 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.65 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.65 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.65 85.86/22.65 Q is empty. 85.86/22.65 We have to consider all minimal (P,Q,R)-chains. 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (11) DependencyGraphProof (EQUIVALENT) 85.86/22.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 4 less nodes. 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (12) 85.86/22.65 Complex Obligation (AND) 85.86/22.65 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (13) 85.86/22.65 Obligation: 85.86/22.65 Q DP problem: 85.86/22.65 The TRS P consists of the following rules: 85.86/22.65 85.86/22.65 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.65 85.86/22.65 The TRS R consists of the following rules: 85.86/22.65 85.86/22.65 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.65 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.65 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.65 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.65 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.65 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.65 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.65 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.65 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.65 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.65 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.65 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.65 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.65 85.86/22.65 Q is empty. 85.86/22.65 We have to consider all minimal (P,Q,R)-chains. 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (14) QDPOrderProof (EQUIVALENT) 85.86/22.65 We use the reduction pair processor [LPAR04,JAR06]. 85.86/22.65 85.86/22.65 85.86/22.65 The following pairs can be oriented strictly and are deleted. 85.86/22.65 85.86/22.65 5^1(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5^1(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.65 The remaining pairs can at least be oriented weakly. 85.86/22.65 Used ordering: Polynomial interpretation [POLO]: 85.86/22.65 85.86/22.65 POL(0(x_1)) = 1 85.86/22.65 POL(1(x_1)) = 0 85.86/22.65 POL(2(x_1)) = 0 85.86/22.65 POL(3(x_1)) = 0 85.86/22.65 POL(4(x_1)) = 0 85.86/22.65 POL(5(x_1)) = 0 85.86/22.65 POL(5^1(x_1)) = x_1 85.86/22.65 85.86/22.65 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 85.86/22.65 85.86/22.65 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.65 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.65 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.65 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.65 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.65 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.65 85.86/22.65 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (15) 85.86/22.65 Obligation: 85.86/22.65 Q DP problem: 85.86/22.65 P is empty. 85.86/22.65 The TRS R consists of the following rules: 85.86/22.65 85.86/22.65 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.65 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.65 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.65 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.65 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.65 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.65 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.65 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.65 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.65 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.65 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.65 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.65 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.65 85.86/22.65 Q is empty. 85.86/22.65 We have to consider all minimal (P,Q,R)-chains. 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (16) PisEmptyProof (EQUIVALENT) 85.86/22.65 The TRS P is empty. Hence, there is no (P,Q,R) chain. 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (17) 85.86/22.65 YES 85.86/22.65 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (18) 85.86/22.65 Obligation: 85.86/22.65 Q DP problem: 85.86/22.65 The TRS P consists of the following rules: 85.86/22.65 85.86/22.65 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 1^1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.65 85.86/22.65 The TRS R consists of the following rules: 85.86/22.65 85.86/22.65 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.65 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.65 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.65 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.65 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.65 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.65 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.65 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.65 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.65 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.65 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.65 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.65 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.65 85.86/22.65 Q is empty. 85.86/22.65 We have to consider all minimal (P,Q,R)-chains. 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (19) QDPOrderProof (EQUIVALENT) 85.86/22.65 We use the reduction pair processor [LPAR04,JAR06]. 85.86/22.65 85.86/22.65 85.86/22.65 The following pairs can be oriented strictly and are deleted. 85.86/22.65 85.86/22.65 1^1(1(0(3(2(5(2(0(1(x1))))))))) -> 1^1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.65 The remaining pairs can at least be oriented weakly. 85.86/22.65 Used ordering: Polynomial interpretation [POLO]: 85.86/22.65 85.86/22.65 POL(0(x_1)) = 1 + x_1 85.86/22.65 POL(1(x_1)) = 1 + x_1 85.86/22.65 POL(1^1(x_1)) = x_1 85.86/22.65 POL(2(x_1)) = 0 85.86/22.65 POL(3(x_1)) = 0 85.86/22.65 POL(4(x_1)) = 0 85.86/22.65 POL(5(x_1)) = 1 + x_1 85.86/22.65 85.86/22.65 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 85.86/22.65 85.86/22.65 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.65 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.65 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.65 85.86/22.65 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (20) 85.86/22.65 Obligation: 85.86/22.65 Q DP problem: 85.86/22.65 P is empty. 85.86/22.65 The TRS R consists of the following rules: 85.86/22.65 85.86/22.65 4(1(1(3(3(0(x1)))))) -> 3(1(0(3(2(3(x1)))))) 85.86/22.65 1(0(4(1(2(3(0(x1))))))) -> 1(0(3(1(5(0(4(x1))))))) 85.86/22.65 0(2(5(2(0(2(2(x1))))))) -> 3(1(5(2(1(2(2(x1))))))) 85.86/22.65 2(2(4(4(2(3(5(4(x1)))))))) -> 2(2(0(0(0(5(0(4(x1)))))))) 85.86/22.65 1(1(0(3(2(5(2(0(1(x1))))))))) -> 1(4(4(2(0(2(1(5(1(x1))))))))) 85.86/22.65 3(5(2(3(5(0(3(4(0(3(1(x1))))))))))) -> 3(5(3(3(1(3(0(0(0(3(1(x1))))))))))) 85.86/22.65 1(5(2(2(5(5(5(0(2(5(1(5(x1)))))))))))) -> 2(0(1(5(0(3(5(0(0(4(2(2(x1)))))))))))) 85.86/22.65 1(5(1(3(1(1(3(1(3(0(1(5(0(5(x1)))))))))))))) -> 2(2(2(3(0(1(0(5(5(2(1(4(4(5(x1)))))))))))))) 85.86/22.65 2(4(4(3(3(1(3(2(2(5(0(5(4(5(2(5(5(0(x1)))))))))))))))))) -> 2(5(3(4(1(1(4(4(1(5(2(2(3(4(4(2(0(5(x1)))))))))))))))))) 85.86/22.65 5(1(0(3(4(4(4(1(2(5(3(0(0(3(3(4(4(1(x1)))))))))))))))))) -> 5(3(4(3(2(1(3(4(4(5(1(5(2(0(3(3(5(3(x1)))))))))))))))))) 85.86/22.65 3(0(1(4(5(0(4(4(2(3(1(4(2(5(4(1(5(3(x1)))))))))))))))))) -> 3(2(1(3(3(5(5(0(0(3(4(1(5(4(5(5(0(3(x1)))))))))))))))))) 85.86/22.65 5(0(1(5(1(4(3(3(2(2(5(5(1(3(3(5(3(5(x1)))))))))))))))))) -> 5(1(5(1(4(2(0(0(2(5(0(4(3(4(4(0(5(3(x1)))))))))))))))))) 85.86/22.65 0(3(4(3(2(2(5(4(2(1(2(3(5(5(3(0(2(0(1(4(x1)))))))))))))))))))) -> 0(3(5(3(5(0(5(4(4(0(0(1(2(2(1(4(5(5(0(0(x1)))))))))))))))))))) 85.86/22.65 85.86/22.65 Q is empty. 85.86/22.65 We have to consider all minimal (P,Q,R)-chains. 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (21) PisEmptyProof (EQUIVALENT) 85.86/22.65 The TRS P is empty. Hence, there is no (P,Q,R) chain. 85.86/22.65 ---------------------------------------- 85.86/22.65 85.86/22.65 (22) 85.86/22.65 YES 86.05/22.71 EOF