51.66/13.98 YES 51.94/14.01 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 51.94/14.01 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 51.94/14.01 51.94/14.01 51.94/14.01 Termination w.r.t. Q of the given QTRS could be proven: 51.94/14.01 51.94/14.01 (0) QTRS 51.94/14.01 (1) QTRS Reverse [EQUIVALENT, 0 ms] 51.94/14.01 (2) QTRS 51.94/14.01 (3) QTRSRRRProof [EQUIVALENT, 161 ms] 51.94/14.01 (4) QTRS 51.94/14.01 (5) DependencyPairsProof [EQUIVALENT, 512 ms] 51.94/14.01 (6) QDP 51.94/14.01 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 51.94/14.01 (8) QDP 51.94/14.01 (9) QDPOrderProof [EQUIVALENT, 624 ms] 51.94/14.01 (10) QDP 51.94/14.01 (11) DependencyGraphProof [EQUIVALENT, 0 ms] 51.94/14.01 (12) TRUE 51.94/14.01 51.94/14.01 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (0) 51.94/14.01 Obligation: 51.94/14.01 Q restricted rewrite system: 51.94/14.01 The TRS R consists of the following rules: 51.94/14.01 51.94/14.01 0(0(1(0(x1)))) -> 2(3(4(x1))) 51.94/14.01 3(5(1(1(2(1(x1)))))) -> 3(3(3(1(3(1(x1)))))) 51.94/14.01 0(0(3(3(5(5(4(x1))))))) -> 2(3(3(0(3(4(x1)))))) 51.94/14.01 0(4(0(0(4(4(5(x1))))))) -> 3(5(4(1(2(4(x1)))))) 51.94/14.01 5(5(5(2(5(2(4(4(3(x1))))))))) -> 5(0(1(5(0(4(5(2(x1)))))))) 51.94/14.01 0(4(3(0(1(1(1(4(1(0(x1)))))))))) -> 2(5(0(2(2(1(0(5(1(3(x1)))))))))) 51.94/14.01 0(4(5(2(1(5(3(0(1(1(x1)))))))))) -> 5(3(0(2(3(0(5(0(0(0(x1)))))))))) 51.94/14.01 3(3(1(4(2(0(3(5(0(0(x1)))))))))) -> 0(1(1(2(5(3(1(2(2(2(x1)))))))))) 51.94/14.01 4(5(2(2(1(5(2(4(5(0(x1)))))))))) -> 4(2(5(4(1(4(5(5(5(0(x1)))))))))) 51.94/14.01 0(1(1(3(4(4(0(4(1(5(5(x1))))))))))) -> 0(2(4(4(5(5(5(3(2(4(0(x1))))))))))) 51.94/14.01 2(1(1(3(5(5(4(1(0(4(4(1(x1)))))))))))) -> 2(5(5(3(4(2(0(4(0(1(2(0(x1)))))))))))) 51.94/14.01 4(4(5(1(1(1(3(2(5(5(4(1(x1)))))))))))) -> 4(2(1(0(2(0(0(0(4(3(3(1(x1)))))))))))) 51.94/14.01 4(5(2(1(0(5(2(0(2(5(0(4(x1)))))))))))) -> 3(0(0(5(3(2(0(0(2(0(0(4(x1)))))))))))) 51.94/14.01 5(2(2(4(2(5(1(4(5(4(0(4(x1)))))))))))) -> 2(4(5(5(5(4(3(2(5(3(1(4(x1)))))))))))) 51.94/14.01 0(4(1(5(4(3(5(5(0(0(5(1(2(x1))))))))))))) -> 0(3(5(4(5(0(5(2(0(4(2(4(x1)))))))))))) 51.94/14.01 2(2(2(1(0(2(2(5(1(0(1(5(1(x1))))))))))))) -> 5(4(0(3(2(5(0(1(2(4(3(3(x1)))))))))))) 51.94/14.01 0(2(5(5(1(2(2(5(5(0(5(2(1(0(x1)))))))))))))) -> 2(0(5(5(5(0(1(2(3(4(0(1(1(x1))))))))))))) 51.94/14.01 2(4(1(3(4(1(0(0(3(2(4(4(1(2(x1)))))))))))))) -> 3(4(5(1(4(4(4(5(4(5(1(4(3(1(x1)))))))))))))) 51.94/14.01 0(3(3(2(0(2(2(3(4(0(5(1(2(5(1(2(x1)))))))))))))))) -> 0(1(0(1(3(0(1(1(2(2(4(0(3(4(4(x1))))))))))))))) 51.94/14.01 2(2(0(0(2(0(5(2(4(0(4(3(2(5(2(0(x1)))))))))))))))) -> 4(5(4(1(3(5(1(3(0(2(5(0(2(5(3(x1))))))))))))))) 51.94/14.01 1(4(4(3(4(5(3(5(1(2(5(0(4(4(4(0(4(x1))))))))))))))))) -> 1(2(3(3(1(0(1(1(1(0(3(3(3(3(5(3(4(x1))))))))))))))))) 51.94/14.01 3(0(2(0(3(2(3(3(0(4(3(0(0(2(0(2(0(x1))))))))))))))))) -> 3(5(5(3(2(1(2(2(2(0(3(0(4(5(1(1(x1)))))))))))))))) 51.94/14.01 4(0(4(3(3(5(2(1(3(5(5(3(2(4(5(1(0(x1))))))))))))))))) -> 4(4(5(5(4(2(2(0(2(1(5(2(1(5(4(5(0(x1))))))))))))))))) 51.94/14.01 1(2(4(3(4(4(2(2(1(4(2(1(3(1(5(1(5(3(x1)))))))))))))))))) -> 1(0(3(2(0(0(1(3(0(3(4(0(0(0(3(5(3(x1))))))))))))))))) 51.94/14.01 4(5(5(5(4(0(0(3(3(4(4(3(3(5(5(3(1(0(x1)))))))))))))))))) -> 3(3(2(5(1(1(5(4(1(5(1(2(5(4(1(2(1(x1))))))))))))))))) 51.94/14.01 1(1(1(3(0(3(5(0(5(1(1(4(2(2(0(3(2(3(3(x1))))))))))))))))))) -> 3(5(2(2(4(4(1(2(4(3(0(5(5(0(0(1(2(2(3(x1))))))))))))))))))) 51.94/14.01 0(2(1(3(1(2(0(3(4(2(2(5(3(0(1(3(3(5(3(2(x1)))))))))))))))))))) -> 1(3(1(0(2(5(3(1(1(3(1(5(0(1(1(0(3(0(3(x1))))))))))))))))))) 51.94/14.01 1(0(0(3(2(0(4(5(1(1(2(5(0(1(0(2(1(4(3(2(x1)))))))))))))))))))) -> 3(1(1(4(4(5(4(3(1(0(3(0(4(0(1(0(2(2(2(1(x1)))))))))))))))))))) 51.94/14.01 0(0(3(3(3(1(1(0(0(2(5(0(4(5(1(4(2(4(1(0(5(x1))))))))))))))))))))) -> 1(2(3(0(5(2(3(0(3(5(4(1(4(4(5(0(1(1(1(5(x1)))))))))))))))))))) 51.94/14.01 0(5(3(1(0(2(1(4(5(1(1(0(1(1(3(2(5(4(3(0(4(x1))))))))))))))))))))) -> 1(1(5(5(4(2(3(5(3(1(0(0(5(3(5(5(4(1(3(4(x1)))))))))))))))))))) 51.94/14.01 51.94/14.01 Q is empty. 51.94/14.01 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (1) QTRS Reverse (EQUIVALENT) 51.94/14.01 We applied the QTRS Reverse Processor [REVERSE]. 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (2) 51.94/14.01 Obligation: 51.94/14.01 Q restricted rewrite system: 51.94/14.01 The TRS R consists of the following rules: 51.94/14.01 51.94/14.01 0(1(0(0(x1)))) -> 4(3(2(x1))) 51.94/14.01 1(2(1(1(5(3(x1)))))) -> 1(3(1(3(3(3(x1)))))) 51.94/14.01 4(5(5(3(3(0(0(x1))))))) -> 4(3(0(3(3(2(x1)))))) 51.94/14.01 5(4(4(0(0(4(0(x1))))))) -> 4(2(1(4(5(3(x1)))))) 51.94/14.01 3(4(4(2(5(2(5(5(5(x1))))))))) -> 2(5(4(0(5(1(0(5(x1)))))))) 51.94/14.01 0(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 3(1(5(0(1(2(2(0(5(2(x1)))))))))) 51.94/14.01 1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 0(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 0(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 5(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0(2(1(0(4(0(2(4(3(5(5(2(x1)))))))))))) 51.94/14.01 1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 1(3(3(4(0(0(0(2(0(1(2(4(x1)))))))))))) 51.94/14.01 4(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 4(0(0(2(0(0(2(3(5(0(0(3(x1)))))))))))) 51.94/14.01 4(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4(1(3(5(2(3(4(5(5(5(4(2(x1)))))))))))) 51.94/14.01 2(1(5(0(0(5(5(3(4(5(1(4(0(x1))))))))))))) -> 4(2(4(0(2(5(0(5(4(5(3(0(x1)))))))))))) 51.94/14.01 1(5(1(0(1(5(2(2(0(1(2(2(2(x1))))))))))))) -> 3(3(4(2(1(0(5(2(3(0(4(5(x1)))))))))))) 51.94/14.01 0(1(2(5(0(5(5(2(2(1(5(5(2(0(x1)))))))))))))) -> 1(1(0(4(3(2(1(0(5(5(5(0(2(x1))))))))))))) 51.94/14.01 2(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1(3(4(1(5(4(5(4(4(4(1(5(4(3(x1)))))))))))))) 51.94/14.01 2(1(5(2(1(5(0(4(3(2(2(0(2(3(3(0(x1)))))))))))))))) -> 4(4(3(0(4(2(2(1(1(0(3(1(0(1(0(x1))))))))))))))) 51.94/14.01 0(2(5(2(3(4(0(4(2(5(0(2(0(0(2(2(x1)))))))))))))))) -> 3(5(2(0(5(2(0(3(1(5(3(1(4(5(4(x1))))))))))))))) 51.94/14.01 4(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 4(3(5(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))))))) 51.94/14.01 0(2(0(2(0(0(3(4(0(3(3(2(3(0(2(0(3(x1))))))))))))))))) -> 1(1(5(4(0(3(0(2(2(2(1(2(3(5(5(3(x1)))))))))))))))) 51.94/14.01 0(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 3(5(1(5(1(3(1(2(4(1(2(2(4(4(3(4(2(1(x1)))))))))))))))))) -> 3(5(3(0(0(0(4(3(0(3(1(0(0(2(3(0(1(x1))))))))))))))))) 51.94/14.01 0(1(3(5(5(3(3(4(4(3(3(0(0(4(5(5(5(4(x1)))))))))))))))))) -> 1(2(1(4(5(2(1(5(1(4(5(1(1(5(2(3(3(x1))))))))))))))))) 51.94/14.01 3(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3(2(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))))) 51.94/14.01 2(3(5(3(3(1(0(3(5(2(2(4(3(0(2(1(3(1(2(0(x1)))))))))))))))))))) -> 3(0(3(0(1(1(0(5(1(3(1(1(3(5(2(0(1(3(1(x1))))))))))))))))))) 51.94/14.01 2(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1(2(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))))) 51.94/14.01 5(0(1(4(2(4(1(5(4(0(5(2(0(0(1(1(3(3(3(0(0(x1))))))))))))))))))))) -> 5(1(1(1(0(5(4(4(1(4(5(3(0(3(2(5(0(3(2(1(x1)))))))))))))))))))) 51.94/14.01 4(0(3(4(5(2(3(1(1(0(1(1(5(4(1(2(0(1(3(5(0(x1))))))))))))))))))))) -> 4(3(1(4(5(5(3(5(0(0(1(3(5(3(2(4(5(5(1(1(x1)))))))))))))))))))) 51.94/14.01 51.94/14.01 Q is empty. 51.94/14.01 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (3) QTRSRRRProof (EQUIVALENT) 51.94/14.01 Used ordering: 51.94/14.01 Polynomial interpretation [POLO]: 51.94/14.01 51.94/14.01 POL(0(x_1)) = 1 + x_1 51.94/14.01 POL(1(x_1)) = 1 + x_1 51.94/14.01 POL(2(x_1)) = 1 + x_1 51.94/14.01 POL(3(x_1)) = 1 + x_1 51.94/14.01 POL(4(x_1)) = 1 + x_1 51.94/14.01 POL(5(x_1)) = 1 + x_1 51.94/14.01 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 51.94/14.01 51.94/14.01 0(1(0(0(x1)))) -> 4(3(2(x1))) 51.94/14.01 4(5(5(3(3(0(0(x1))))))) -> 4(3(0(3(3(2(x1)))))) 51.94/14.01 5(4(4(0(0(4(0(x1))))))) -> 4(2(1(4(5(3(x1)))))) 51.94/14.01 3(4(4(2(5(2(5(5(5(x1))))))))) -> 2(5(4(0(5(1(0(5(x1)))))))) 51.94/14.01 2(1(5(0(0(5(5(3(4(5(1(4(0(x1))))))))))))) -> 4(2(4(0(2(5(0(5(4(5(3(0(x1)))))))))))) 51.94/14.01 1(5(1(0(1(5(2(2(0(1(2(2(2(x1))))))))))))) -> 3(3(4(2(1(0(5(2(3(0(4(5(x1)))))))))))) 51.94/14.01 0(1(2(5(0(5(5(2(2(1(5(5(2(0(x1)))))))))))))) -> 1(1(0(4(3(2(1(0(5(5(5(0(2(x1))))))))))))) 51.94/14.01 2(1(5(2(1(5(0(4(3(2(2(0(2(3(3(0(x1)))))))))))))))) -> 4(4(3(0(4(2(2(1(1(0(3(1(0(1(0(x1))))))))))))))) 51.94/14.01 0(2(5(2(3(4(0(4(2(5(0(2(0(0(2(2(x1)))))))))))))))) -> 3(5(2(0(5(2(0(3(1(5(3(1(4(5(4(x1))))))))))))))) 51.94/14.01 0(2(0(2(0(0(3(4(0(3(3(2(3(0(2(0(3(x1))))))))))))))))) -> 1(1(5(4(0(3(0(2(2(2(1(2(3(5(5(3(x1)))))))))))))))) 51.94/14.01 3(5(1(5(1(3(1(2(4(1(2(2(4(4(3(4(2(1(x1)))))))))))))))))) -> 3(5(3(0(0(0(4(3(0(3(1(0(0(2(3(0(1(x1))))))))))))))))) 51.94/14.01 0(1(3(5(5(3(3(4(4(3(3(0(0(4(5(5(5(4(x1)))))))))))))))))) -> 1(2(1(4(5(2(1(5(1(4(5(1(1(5(2(3(3(x1))))))))))))))))) 51.94/14.01 2(3(5(3(3(1(0(3(5(2(2(4(3(0(2(1(3(1(2(0(x1)))))))))))))))))))) -> 3(0(3(0(1(1(0(5(1(3(1(1(3(5(2(0(1(3(1(x1))))))))))))))))))) 51.94/14.01 5(0(1(4(2(4(1(5(4(0(5(2(0(0(1(1(3(3(3(0(0(x1))))))))))))))))))))) -> 5(1(1(1(0(5(4(4(1(4(5(3(0(3(2(5(0(3(2(1(x1)))))))))))))))))))) 51.94/14.01 4(0(3(4(5(2(3(1(1(0(1(1(5(4(1(2(0(1(3(5(0(x1))))))))))))))))))))) -> 4(3(1(4(5(5(3(5(0(0(1(3(5(3(2(4(5(5(1(1(x1)))))))))))))))))))) 51.94/14.01 51.94/14.01 51.94/14.01 51.94/14.01 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (4) 51.94/14.01 Obligation: 51.94/14.01 Q restricted rewrite system: 51.94/14.01 The TRS R consists of the following rules: 51.94/14.01 51.94/14.01 1(2(1(1(5(3(x1)))))) -> 1(3(1(3(3(3(x1)))))) 51.94/14.01 0(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 3(1(5(0(1(2(2(0(5(2(x1)))))))))) 51.94/14.01 1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 0(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 0(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 5(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0(2(1(0(4(0(2(4(3(5(5(2(x1)))))))))))) 51.94/14.01 1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 1(3(3(4(0(0(0(2(0(1(2(4(x1)))))))))))) 51.94/14.01 4(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 4(0(0(2(0(0(2(3(5(0(0(3(x1)))))))))))) 51.94/14.01 4(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4(1(3(5(2(3(4(5(5(5(4(2(x1)))))))))))) 51.94/14.01 2(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1(3(4(1(5(4(5(4(4(4(1(5(4(3(x1)))))))))))))) 51.94/14.01 4(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 4(3(5(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))))))) 51.94/14.01 0(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 3(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3(2(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))))) 51.94/14.01 2(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1(2(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))))) 51.94/14.01 51.94/14.01 Q is empty. 51.94/14.01 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (5) DependencyPairsProof (EQUIVALENT) 51.94/14.01 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (6) 51.94/14.01 Obligation: 51.94/14.01 Q DP problem: 51.94/14.01 The TRS P consists of the following rules: 51.94/14.01 51.94/14.01 1^1(2(1(1(5(3(x1)))))) -> 1^1(3(1(3(3(3(x1)))))) 51.94/14.01 1^1(2(1(1(5(3(x1)))))) -> 3^1(1(3(3(3(x1))))) 51.94/14.01 1^1(2(1(1(5(3(x1)))))) -> 1^1(3(3(3(x1)))) 51.94/14.01 1^1(2(1(1(5(3(x1)))))) -> 3^1(3(3(x1))) 51.94/14.01 1^1(2(1(1(5(3(x1)))))) -> 3^1(3(x1)) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 3^1(1(5(0(1(2(2(0(5(2(x1)))))))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 1^1(5(0(1(2(2(0(5(2(x1))))))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 5^1(0(1(2(2(0(5(2(x1)))))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 0^1(1(2(2(0(5(2(x1))))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 1^1(2(2(0(5(2(x1)))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(2(0(5(2(x1))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(0(5(2(x1)))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 0^1(5(2(x1))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 5^1(2(x1)) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(x1) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(0(5(0(3(2(0(3(5(x1))))))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(5(0(3(2(0(3(5(x1)))))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 5^1(0(3(2(0(3(5(x1))))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(3(2(0(3(5(x1)))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 3^1(2(0(3(5(x1))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 2^1(0(3(5(x1)))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(3(5(x1))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 3^1(5(x1)) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 5^1(x1) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(2(1(3(5(2(1(1(0(x1))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(1(3(5(2(1(1(0(x1)))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 1^1(3(5(2(1(1(0(x1))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 3^1(5(2(1(1(0(x1)))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 5^1(2(1(1(0(x1))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(1(1(0(x1)))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 1^1(1(0(x1))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 1^1(0(x1)) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 0^1(x1) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0^1(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 5^1(5(5(4(1(4(5(2(4(x1))))))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 5^1(5(4(1(4(5(2(4(x1)))))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 5^1(4(1(4(5(2(4(x1))))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 4^1(1(4(5(2(4(x1)))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 1^1(4(5(2(4(x1))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 4^1(5(2(4(x1)))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 5^1(2(4(x1))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 2^1(4(x1)) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0^1(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 4^1(2(3(5(5(5(4(4(2(0(x1)))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 2^1(3(5(5(5(4(4(2(0(x1))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 3^1(5(5(5(4(4(2(0(x1)))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 5^1(5(5(4(4(2(0(x1))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 5^1(5(4(4(2(0(x1)))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 5^1(4(4(2(0(x1))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 4^1(4(2(0(x1)))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 4^1(2(0(x1))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 2^1(0(x1)) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0^1(2(1(0(4(0(2(4(3(5(5(2(x1)))))))))))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 2^1(1(0(4(0(2(4(3(5(5(2(x1))))))))))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 1^1(0(4(0(2(4(3(5(5(2(x1)))))))))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0^1(4(0(2(4(3(5(5(2(x1))))))))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 4^1(0(2(4(3(5(5(2(x1)))))))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0^1(2(4(3(5(5(2(x1))))))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 2^1(4(3(5(5(2(x1)))))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 4^1(3(5(5(2(x1))))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 3^1(5(5(2(x1)))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 5^1(5(2(x1))) 51.94/14.01 1^1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 5^1(2(x1)) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 1^1(3(3(4(0(0(0(2(0(1(2(4(x1)))))))))))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 3^1(3(4(0(0(0(2(0(1(2(4(x1))))))))))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 3^1(4(0(0(0(2(0(1(2(4(x1)))))))))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 4^1(0(0(0(2(0(1(2(4(x1))))))))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 0^1(0(0(2(0(1(2(4(x1)))))))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 0^1(0(2(0(1(2(4(x1))))))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 0^1(2(0(1(2(4(x1)))))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 2^1(0(1(2(4(x1))))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 0^1(1(2(4(x1)))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 1^1(2(4(x1))) 51.94/14.01 1^1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 2^1(4(x1)) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 4^1(0(0(2(0(0(2(3(5(0(0(3(x1)))))))))))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 0^1(0(2(0(0(2(3(5(0(0(3(x1))))))))))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 0^1(2(0(0(2(3(5(0(0(3(x1)))))))))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 2^1(0(0(2(3(5(0(0(3(x1))))))))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 0^1(0(2(3(5(0(0(3(x1)))))))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 0^1(2(3(5(0(0(3(x1))))))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 2^1(3(5(0(0(3(x1)))))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 3^1(5(0(0(3(x1))))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 5^1(0(0(3(x1)))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 0^1(0(3(x1))) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 0^1(3(x1)) 51.94/14.01 4^1(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 3^1(x1) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4^1(1(3(5(2(3(4(5(5(5(4(2(x1)))))))))))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 1^1(3(5(2(3(4(5(5(5(4(2(x1))))))))))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 3^1(5(2(3(4(5(5(5(4(2(x1)))))))))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 5^1(2(3(4(5(5(5(4(2(x1))))))))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 2^1(3(4(5(5(5(4(2(x1)))))))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 3^1(4(5(5(5(4(2(x1))))))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4^1(5(5(5(4(2(x1)))))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 5^1(5(5(4(2(x1))))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 5^1(5(4(2(x1)))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 5^1(4(2(x1))) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4^1(2(x1)) 51.94/14.01 4^1(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 2^1(x1) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1^1(3(4(1(5(4(5(4(4(4(1(5(4(3(x1)))))))))))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 3^1(4(1(5(4(5(4(4(4(1(5(4(3(x1))))))))))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 4^1(1(5(4(5(4(4(4(1(5(4(3(x1)))))))))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1^1(5(4(5(4(4(4(1(5(4(3(x1))))))))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 5^1(4(5(4(4(4(1(5(4(3(x1)))))))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 4^1(5(4(4(4(1(5(4(3(x1))))))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 5^1(4(4(4(1(5(4(3(x1)))))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 4^1(4(4(1(5(4(3(x1))))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 4^1(4(1(5(4(3(x1)))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 4^1(1(5(4(3(x1))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1^1(5(4(3(x1)))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 5^1(4(3(x1))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 4^1(3(x1)) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 3^1(x1) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 4^1(3(5(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 3^1(5(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1)))))))))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 5^1(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 3^1(3(3(3(0(1(1(1(0(1(3(3(2(1(x1)))))))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 3^1(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 3^1(3(0(1(1(1(0(1(3(3(2(1(x1)))))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 3^1(0(1(1(1(0(1(3(3(2(1(x1))))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 0^1(1(1(1(0(1(3(3(2(1(x1)))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 1^1(1(1(0(1(3(3(2(1(x1))))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 1^1(1(0(1(3(3(2(1(x1)))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 1^1(0(1(3(3(2(1(x1))))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 0^1(1(3(3(2(1(x1)))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 1^1(3(3(2(1(x1))))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 3^1(3(2(1(x1)))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 3^1(2(1(x1))) 51.94/14.01 4^1(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 2^1(1(x1)) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0^1(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 5^1(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1)))))))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 4^1(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 5^1(1(2(5(1(2(0(2(2(4(5(5(4(4(x1)))))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 1^1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(5(1(2(0(2(2(4(5(5(4(4(x1)))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 5^1(1(2(0(2(2(4(5(5(4(4(x1))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 1^1(2(0(2(2(4(5(5(4(4(x1)))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(0(2(2(4(5(5(4(4(x1))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0^1(2(2(4(5(5(4(4(x1)))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(2(4(5(5(4(4(x1))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(4(5(5(4(4(x1)))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 4^1(5(5(4(4(x1))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 5^1(5(4(4(x1)))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 5^1(4(4(x1))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 4^1(4(x1)) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3^1(2(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1)))))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 1^1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1)))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(5(5(0(3(4(2(1(4(4(2(2(5(3(x1)))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 5^1(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 5^1(0(3(4(2(1(4(4(2(2(5(3(x1)))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(3(4(2(1(4(4(2(2(5(3(x1))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3^1(4(2(1(4(4(2(2(5(3(x1)))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 4^1(2(1(4(4(2(2(5(3(x1))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(1(4(4(2(2(5(3(x1)))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 1^1(4(4(2(2(5(3(x1))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 4^1(4(2(2(5(3(x1)))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 4^1(2(2(5(3(x1))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(2(5(3(x1)))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(5(3(x1))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 5^1(3(x1)) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3^1(x1) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1^1(2(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1))))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1^1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 4^1(0(3(0(1(3(4(5(4(4(1(1(3(x1))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 3^1(0(1(3(4(5(4(4(1(1(3(x1))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(1(3(4(5(4(4(1(1(3(x1)))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1^1(3(4(5(4(4(1(1(3(x1))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 3^1(4(5(4(4(1(1(3(x1)))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 4^1(5(4(4(1(1(3(x1))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 5^1(4(4(1(1(3(x1)))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 4^1(4(1(1(3(x1))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 4^1(1(1(3(x1)))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1^1(1(3(x1))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1^1(3(x1)) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 3^1(x1) 51.94/14.01 51.94/14.01 The TRS R consists of the following rules: 51.94/14.01 51.94/14.01 1(2(1(1(5(3(x1)))))) -> 1(3(1(3(3(3(x1)))))) 51.94/14.01 0(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 3(1(5(0(1(2(2(0(5(2(x1)))))))))) 51.94/14.01 1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 0(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 0(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 5(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0(2(1(0(4(0(2(4(3(5(5(2(x1)))))))))))) 51.94/14.01 1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 1(3(3(4(0(0(0(2(0(1(2(4(x1)))))))))))) 51.94/14.01 4(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 4(0(0(2(0(0(2(3(5(0(0(3(x1)))))))))))) 51.94/14.01 4(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4(1(3(5(2(3(4(5(5(5(4(2(x1)))))))))))) 51.94/14.01 2(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1(3(4(1(5(4(5(4(4(4(1(5(4(3(x1)))))))))))))) 51.94/14.01 4(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 4(3(5(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))))))) 51.94/14.01 0(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 3(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3(2(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))))) 51.94/14.01 2(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1(2(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))))) 51.94/14.01 51.94/14.01 Q is empty. 51.94/14.01 We have to consider all minimal (P,Q,R)-chains. 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (7) DependencyGraphProof (EQUIVALENT) 51.94/14.01 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 132 less nodes. 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (8) 51.94/14.01 Obligation: 51.94/14.01 Q DP problem: 51.94/14.01 The TRS P consists of the following rules: 51.94/14.01 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(2(0(5(2(x1))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 3^1(x1) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1)))))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 0^1(1(2(2(0(5(2(x1))))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(0(5(2(x1)))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 0^1(5(2(x1))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(x1) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1))))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(2(1(3(5(2(1(1(0(x1))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(1(3(5(2(1(1(0(x1)))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(1(1(0(x1)))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 1^1(1(0(x1))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 0^1(x1) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0^1(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 5^1(5(5(4(1(4(5(2(4(x1))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0^1(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 2^1(3(5(5(5(4(4(2(0(x1))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 5^1(5(5(4(4(2(0(x1))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 5^1(5(4(4(2(0(x1)))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 2^1(0(x1)) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 5^1(5(4(1(4(5(2(4(x1)))))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 2^1(4(x1)) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0^1(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(5(1(2(0(2(2(4(5(5(4(4(x1)))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(0(2(2(4(5(5(4(4(x1))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0^1(2(2(4(5(5(4(4(x1)))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(2(4(5(5(4(4(x1))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(4(5(5(4(4(x1)))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 5^1(5(4(4(x1)))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(0(5(0(3(2(0(3(5(x1))))))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(5(0(3(2(0(3(5(x1)))))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(3(2(0(3(5(x1)))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 2^1(0(3(5(x1)))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(3(5(x1))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 5^1(x1) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(1(3(4(5(4(4(1(1(3(x1)))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 3^1(x1) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(5(5(0(3(4(2(1(4(4(2(2(5(3(x1)))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 5^1(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(3(4(2(1(4(4(2(2(5(3(x1))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(1(4(4(2(2(5(3(x1)))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(2(5(3(x1)))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(5(3(x1))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3^1(x1) 51.94/14.01 51.94/14.01 The TRS R consists of the following rules: 51.94/14.01 51.94/14.01 1(2(1(1(5(3(x1)))))) -> 1(3(1(3(3(3(x1)))))) 51.94/14.01 0(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 3(1(5(0(1(2(2(0(5(2(x1)))))))))) 51.94/14.01 1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 0(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 0(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 5(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0(2(1(0(4(0(2(4(3(5(5(2(x1)))))))))))) 51.94/14.01 1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 1(3(3(4(0(0(0(2(0(1(2(4(x1)))))))))))) 51.94/14.01 4(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 4(0(0(2(0(0(2(3(5(0(0(3(x1)))))))))))) 51.94/14.01 4(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4(1(3(5(2(3(4(5(5(5(4(2(x1)))))))))))) 51.94/14.01 2(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1(3(4(1(5(4(5(4(4(4(1(5(4(3(x1)))))))))))))) 51.94/14.01 4(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 4(3(5(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))))))) 51.94/14.01 0(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 3(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3(2(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))))) 51.94/14.01 2(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1(2(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))))) 51.94/14.01 51.94/14.01 Q is empty. 51.94/14.01 We have to consider all minimal (P,Q,R)-chains. 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (9) QDPOrderProof (EQUIVALENT) 51.94/14.01 We use the reduction pair processor [LPAR04,JAR06]. 51.94/14.01 51.94/14.01 51.94/14.01 The following pairs can be oriented strictly and are deleted. 51.94/14.01 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(2(0(5(2(x1))))) 51.94/14.01 2^1(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 3^1(x1) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1)))))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 0^1(1(2(2(0(5(2(x1))))))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(0(5(2(x1)))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 0^1(5(2(x1))) 51.94/14.01 0^1(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 2^1(x1) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1))))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 2^1(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1))))))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(2(1(3(5(2(1(1(0(x1))))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(1(3(5(2(1(1(0(x1)))))))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2^1(1(1(0(x1)))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 1^1(1(0(x1))) 51.94/14.01 0^1(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 0^1(x1) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 5^1(5(5(4(1(4(5(2(4(x1))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 2^1(3(5(5(5(4(4(2(0(x1))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 5^1(5(5(4(4(2(0(x1))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 5^1(5(4(4(2(0(x1)))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 2^1(0(x1)) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 5^1(5(4(1(4(5(2(4(x1)))))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 2^1(4(x1)) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(5(1(2(0(2(2(4(5(5(4(4(x1)))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(0(2(2(4(5(5(4(4(x1))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0^1(2(2(4(5(5(4(4(x1)))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(2(4(5(5(4(4(x1))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 2^1(4(5(5(4(4(x1)))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 5^1(5(4(4(x1)))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(0(5(0(3(2(0(3(5(x1))))))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(5(0(3(2(0(3(5(x1)))))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(3(2(0(3(5(x1)))))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 2^1(0(3(5(x1)))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(3(5(x1))) 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 5^1(x1) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 0^1(1(3(4(5(4(4(1(1(3(x1)))))))))) 51.94/14.01 2^1(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 3^1(x1) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(5(5(0(3(4(2(1(4(4(2(2(5(3(x1)))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 5^1(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 0^1(3(4(2(1(4(4(2(2(5(3(x1))))))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(1(4(4(2(2(5(3(x1)))))))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(2(5(3(x1)))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 2^1(5(3(x1))) 51.94/14.01 3^1(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3^1(x1) 51.94/14.01 The remaining pairs can at least be oriented weakly. 51.94/14.01 Used ordering: Polynomial interpretation [POLO]: 51.94/14.01 51.94/14.01 POL(0(x_1)) = 1 + x_1 51.94/14.01 POL(0^1(x_1)) = 1 + x_1 51.94/14.01 POL(1(x_1)) = 1 + x_1 51.94/14.01 POL(1^1(x_1)) = 1 + x_1 51.94/14.01 POL(2(x_1)) = 1 + x_1 51.94/14.01 POL(2^1(x_1)) = x_1 51.94/14.01 POL(3(x_1)) = 1 + x_1 51.94/14.01 POL(3^1(x_1)) = x_1 51.94/14.01 POL(4(x_1)) = 1 + x_1 51.94/14.01 POL(5(x_1)) = 1 + x_1 51.94/14.01 POL(5^1(x_1)) = 1 + x_1 51.94/14.01 51.94/14.01 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 51.94/14.01 51.94/14.01 1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 0(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 2(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1(3(4(1(5(4(5(4(4(4(1(5(4(3(x1)))))))))))))) 51.94/14.01 1(2(1(1(5(3(x1)))))) -> 1(3(1(3(3(3(x1)))))) 51.94/14.01 1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0(2(1(0(4(0(2(4(3(5(5(2(x1)))))))))))) 51.94/14.01 0(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 0(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 1(3(3(4(0(0(0(2(0(1(2(4(x1)))))))))))) 51.94/14.01 2(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1(2(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))))) 51.94/14.01 5(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 0(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 3(1(5(0(1(2(2(0(5(2(x1)))))))))) 51.94/14.01 3(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3(2(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))))) 51.94/14.01 4(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4(1(3(5(2(3(4(5(5(5(4(2(x1)))))))))))) 51.94/14.01 4(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 4(0(0(2(0(0(2(3(5(0(0(3(x1)))))))))))) 51.94/14.01 4(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 4(3(5(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))))))) 51.94/14.01 51.94/14.01 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (10) 51.94/14.01 Obligation: 51.94/14.01 Q DP problem: 51.94/14.01 The TRS P consists of the following rules: 51.94/14.01 51.94/14.01 1^1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0^1(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 0^1(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0^1(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 5^1(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0^1(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 0^1(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0^1(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 51.94/14.01 The TRS R consists of the following rules: 51.94/14.01 51.94/14.01 1(2(1(1(5(3(x1)))))) -> 1(3(1(3(3(3(x1)))))) 51.94/14.01 0(1(4(1(1(1(0(3(4(0(x1)))))))))) -> 3(1(5(0(1(2(2(0(5(2(x1)))))))))) 51.94/14.01 1(1(0(3(5(1(2(5(4(0(x1)))))))))) -> 0(0(0(5(0(3(2(0(3(5(x1)))))))))) 51.94/14.01 0(0(5(3(0(2(4(1(3(3(x1)))))))))) -> 2(2(2(1(3(5(2(1(1(0(x1)))))))))) 51.94/14.01 0(5(4(2(5(1(2(2(5(4(x1)))))))))) -> 0(5(5(5(4(1(4(5(2(4(x1)))))))))) 51.94/14.01 5(5(1(4(0(4(4(3(1(1(0(x1))))))))))) -> 0(4(2(3(5(5(5(4(4(2(0(x1))))))))))) 51.94/14.01 1(4(4(0(1(4(5(5(3(1(1(2(x1)))))))))))) -> 0(2(1(0(4(0(2(4(3(5(5(2(x1)))))))))))) 51.94/14.01 1(4(5(5(2(3(1(1(1(5(4(4(x1)))))))))))) -> 1(3(3(4(0(0(0(2(0(1(2(4(x1)))))))))))) 51.94/14.01 4(0(5(2(0(2(5(0(1(2(5(4(x1)))))))))))) -> 4(0(0(2(0(0(2(3(5(0(0(3(x1)))))))))))) 51.94/14.01 4(0(4(5(4(1(5(2(4(2(2(5(x1)))))))))))) -> 4(1(3(5(2(3(4(5(5(5(4(2(x1)))))))))))) 51.94/14.01 2(1(4(4(2(3(0(0(1(4(3(1(4(2(x1)))))))))))))) -> 1(3(4(1(5(4(5(4(4(4(1(5(4(3(x1)))))))))))))) 51.94/14.01 4(0(4(4(4(0(5(2(1(5(3(5(4(3(4(4(1(x1))))))))))))))))) -> 4(3(5(3(3(3(3(0(1(1(1(0(1(3(3(2(1(x1))))))))))))))))) 51.94/14.01 0(1(5(4(2(3(5(5(3(1(2(5(3(3(4(0(4(x1))))))))))))))))) -> 0(5(4(5(1(2(5(1(2(0(2(2(4(5(5(4(4(x1))))))))))))))))) 51.94/14.01 3(3(2(3(0(2(2(4(1(1(5(0(5(3(0(3(1(1(1(x1))))))))))))))))))) -> 3(2(2(1(0(0(5(5(0(3(4(2(1(4(4(2(2(5(3(x1))))))))))))))))))) 51.94/14.01 2(3(4(1(2(0(1(0(5(2(1(1(5(4(0(2(3(0(0(1(x1)))))))))))))))))))) -> 1(2(2(2(0(1(0(4(0(3(0(1(3(4(5(4(4(1(1(3(x1)))))))))))))))))))) 51.94/14.01 51.94/14.01 Q is empty. 51.94/14.01 We have to consider all minimal (P,Q,R)-chains. 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (11) DependencyGraphProof (EQUIVALENT) 51.94/14.01 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes. 51.94/14.01 ---------------------------------------- 51.94/14.01 51.94/14.01 (12) 51.94/14.01 TRUE 52.20/14.10 EOF