66.01/17.62 YES 71.96/19.06 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 71.96/19.06 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 71.96/19.06 71.96/19.06 71.96/19.06 Termination w.r.t. Q of the given QTRS could be proven: 71.96/19.06 71.96/19.06 (0) QTRS 71.96/19.06 (1) QTRSRRRProof [EQUIVALENT, 177 ms] 71.96/19.06 (2) QTRS 71.96/19.06 (3) DependencyPairsProof [EQUIVALENT, 322 ms] 71.96/19.06 (4) QDP 71.96/19.06 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 71.96/19.06 (6) AND 71.96/19.06 (7) QDP 71.96/19.06 (8) QDPOrderProof [EQUIVALENT, 271 ms] 71.96/19.06 (9) QDP 71.96/19.06 (10) QDPOrderProof [EQUIVALENT, 85 ms] 71.96/19.06 (11) QDP 71.96/19.06 (12) QDPOrderProof [EQUIVALENT, 65 ms] 71.96/19.06 (13) QDP 71.96/19.06 (14) DependencyGraphProof [EQUIVALENT, 0 ms] 71.96/19.06 (15) QDP 71.96/19.06 (16) QDPOrderProof [EQUIVALENT, 51 ms] 71.96/19.06 (17) QDP 71.96/19.06 (18) PisEmptyProof [EQUIVALENT, 0 ms] 71.96/19.06 (19) YES 71.96/19.06 (20) QDP 71.96/19.06 (21) UsableRulesProof [EQUIVALENT, 0 ms] 71.96/19.06 (22) QDP 71.96/19.06 (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] 71.96/19.06 (24) YES 71.96/19.06 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (0) 71.96/19.06 Obligation: 71.96/19.06 Q restricted rewrite system: 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 0(5(2(4(2(0(0(5(2(x1))))))))) -> 1(5(2(0(2(3(5(2(x1)))))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 5(0(3(5(1(4(2(1(0(2(x1)))))))))) -> 5(2(0(1(3(1(1(0(2(x1))))))))) 71.96/19.06 2(4(5(2(4(3(4(3(1(2(3(x1))))))))))) -> 5(3(1(3(3(3(2(2(4(1(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 3(3(3(2(3(3(1(2(2(4(3(3(x1)))))))))))) -> 1(2(2(1(3(2(3(5(2(5(5(x1))))))))))) 71.96/19.06 5(5(4(0(3(0(2(3(3(2(3(3(x1)))))))))))) -> 5(2(2(3(0(1(1(3(4(4(5(x1))))))))))) 71.96/19.06 0(0(3(1(0(2(2(3(2(5(3(0(1(x1))))))))))))) -> 0(1(3(4(3(1(0(0(3(3(4(0(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 2(4(2(3(3(5(0(4(5(5(2(5(5(x1))))))))))))) -> 3(5(4(3(3(2(0(1(1(4(3(5(x1)))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 2(5(3(5(2(4(2(1(3(0(5(0(3(1(3(x1))))))))))))))) -> 5(3(2(3(5(1(5(3(5(3(5(1(5(x1))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 3(3(2(0(1(5(4(5(4(2(4(2(3(4(4(3(x1)))))))))))))))) -> 5(2(5(5(5(5(2(3(3(1(2(5(0(4(0(x1))))))))))))))) 71.96/19.06 3(0(0(2(0(3(5(3(0(2(5(3(5(5(2(3(4(x1))))))))))))))))) -> 5(3(4(3(0(4(2(2(1(0(4(1(0(0(3(4(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(0(3(2(0(2(4(1(3(2(5(0(0(4(5(0(3(4(3(x1))))))))))))))))))) -> 4(2(2(0(0(0(0(4(1(4(0(5(3(5(0(2(4(3(x1)))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 3(3(5(4(1(1(3(2(1(4(4(0(1(1(0(4(3(1(0(x1))))))))))))))))))) -> 3(4(0(2(3(1(3(0(4(4(3(4(4(4(3(2(1(0(x1)))))))))))))))))) 71.96/19.06 2(5(0(4(0(3(4(3(4(0(0(2(4(2(4(1(0(1(2(3(x1)))))))))))))))))))) -> 0(1(2(0(5(4(3(2(0(2(3(3(3(0(1(5(5(5(1(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 4(3(1(4(3(3(3(3(4(4(2(5(1(4(5(1(4(3(2(3(3(x1))))))))))))))))))))) -> 2(5(5(1(1(1(4(5(3(2(3(3(0(4(2(3(1(5(4(5(x1)))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (1) QTRSRRRProof (EQUIVALENT) 71.96/19.06 Used ordering: 71.96/19.06 Polynomial interpretation [POLO]: 71.96/19.06 71.96/19.06 POL(0(x_1)) = 1 + x_1 71.96/19.06 POL(1(x_1)) = 1 + x_1 71.96/19.06 POL(2(x_1)) = 1 + x_1 71.96/19.06 POL(3(x_1)) = 1 + x_1 71.96/19.06 POL(4(x_1)) = 1 + x_1 71.96/19.06 POL(5(x_1)) = 1 + x_1 71.96/19.06 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 71.96/19.06 71.96/19.06 0(5(2(4(2(0(0(5(2(x1))))))))) -> 1(5(2(0(2(3(5(2(x1)))))))) 71.96/19.06 5(0(3(5(1(4(2(1(0(2(x1)))))))))) -> 5(2(0(1(3(1(1(0(2(x1))))))))) 71.96/19.06 2(4(5(2(4(3(4(3(1(2(3(x1))))))))))) -> 5(3(1(3(3(3(2(2(4(1(x1)))))))))) 71.96/19.06 3(3(3(2(3(3(1(2(2(4(3(3(x1)))))))))))) -> 1(2(2(1(3(2(3(5(2(5(5(x1))))))))))) 71.96/19.06 5(5(4(0(3(0(2(3(3(2(3(3(x1)))))))))))) -> 5(2(2(3(0(1(1(3(4(4(5(x1))))))))))) 71.96/19.06 0(0(3(1(0(2(2(3(2(5(3(0(1(x1))))))))))))) -> 0(1(3(4(3(1(0(0(3(3(4(0(x1)))))))))))) 71.96/19.06 2(4(2(3(3(5(0(4(5(5(2(5(5(x1))))))))))))) -> 3(5(4(3(3(2(0(1(1(4(3(5(x1)))))))))))) 71.96/19.06 2(5(3(5(2(4(2(1(3(0(5(0(3(1(3(x1))))))))))))))) -> 5(3(2(3(5(1(5(3(5(3(5(1(5(x1))))))))))))) 71.96/19.06 3(3(2(0(1(5(4(5(4(2(4(2(3(4(4(3(x1)))))))))))))))) -> 5(2(5(5(5(5(2(3(3(1(2(5(0(4(0(x1))))))))))))))) 71.96/19.06 3(0(0(2(0(3(5(3(0(2(5(3(5(5(2(3(4(x1))))))))))))))))) -> 5(3(4(3(0(4(2(2(1(0(4(1(0(0(3(4(x1)))))))))))))))) 71.96/19.06 1(0(3(2(0(2(4(1(3(2(5(0(0(4(5(0(3(4(3(x1))))))))))))))))))) -> 4(2(2(0(0(0(0(4(1(4(0(5(3(5(0(2(4(3(x1)))))))))))))))))) 71.96/19.06 3(3(5(4(1(1(3(2(1(4(4(0(1(1(0(4(3(1(0(x1))))))))))))))))))) -> 3(4(0(2(3(1(3(0(4(4(3(4(4(4(3(2(1(0(x1)))))))))))))))))) 71.96/19.06 2(5(0(4(0(3(4(3(4(0(0(2(4(2(4(1(0(1(2(3(x1)))))))))))))))))))) -> 0(1(2(0(5(4(3(2(0(2(3(3(3(0(1(5(5(5(1(x1))))))))))))))))))) 71.96/19.06 4(3(1(4(3(3(3(3(4(4(2(5(1(4(5(1(4(3(2(3(3(x1))))))))))))))))))))) -> 2(5(5(1(1(1(4(5(3(2(3(3(0(4(2(3(1(5(4(5(x1)))))))))))))))))))) 71.96/19.06 71.96/19.06 71.96/19.06 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (2) 71.96/19.06 Obligation: 71.96/19.06 Q restricted rewrite system: 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (3) DependencyPairsProof (EQUIVALENT) 71.96/19.06 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (4) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 The TRS P consists of the following rules: 71.96/19.06 71.96/19.06 0^1(0(1(2(2(x1))))) -> 2^1(3(3(2(2(x1))))) 71.96/19.06 0^1(0(1(2(2(x1))))) -> 3^1(3(2(2(x1)))) 71.96/19.06 0^1(0(1(2(2(x1))))) -> 3^1(2(2(x1))) 71.96/19.06 0^1(4(1(0(4(5(x1)))))) -> 5^1(2(5(3(4(5(x1)))))) 71.96/19.06 0^1(4(1(0(4(5(x1)))))) -> 2^1(5(3(4(5(x1))))) 71.96/19.06 0^1(4(1(0(4(5(x1)))))) -> 5^1(3(4(5(x1)))) 71.96/19.06 0^1(4(1(0(4(5(x1)))))) -> 3^1(4(5(x1))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 3^1(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 1^1(0(3(5(3(3(0(2(x1)))))))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(3(5(3(3(0(2(x1))))))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 3^1(5(3(3(0(2(x1)))))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 5^1(3(3(0(2(x1))))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 3^1(3(0(2(x1)))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 3^1(0(2(x1))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(2(x1)) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3^1(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3^1(3(2(5(0(4(0(5(0(x1))))))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3^1(2(5(0(4(0(5(0(x1)))))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 2^1(5(0(4(0(5(0(x1))))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 5^1(0(4(0(5(0(x1)))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 0^1(4(0(5(0(x1))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 0^1(5(0(x1))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 5^1(0(x1)) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2^1(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2^1(5(4(4(2(3(3(0(3(5(4(x1))))))))))) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 5^1(4(4(2(3(3(0(3(5(4(x1)))))))))) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2^1(3(3(0(3(5(4(x1))))))) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 3^1(3(0(3(5(4(x1)))))) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 3^1(0(3(5(4(x1))))) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 0^1(3(5(4(x1)))) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 3^1(5(4(x1))) 71.96/19.06 0^1(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 5^1(4(x1)) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1^1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 5^1(2(4(0(4(2(0(0(5(0(2(x1))))))))))) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 2^1(4(0(4(2(0(0(5(0(2(x1)))))))))) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 0^1(4(2(0(0(5(0(2(x1)))))))) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 2^1(0(0(5(0(2(x1)))))) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 0^1(0(5(0(2(x1))))) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 0^1(5(0(2(x1)))) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 5^1(0(2(x1))) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 0^1(2(x1)) 71.96/19.06 3^1(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 2^1(x1) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2^1(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 1^1(3(0(1(3(3(2(1(3(4(4(x1))))))))))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 3^1(0(1(3(3(2(1(3(4(4(x1)))))))))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 0^1(1(3(3(2(1(3(4(4(x1))))))))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 1^1(3(3(2(1(3(4(4(x1)))))))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 3^1(3(2(1(3(4(4(x1))))))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 3^1(2(1(3(4(4(x1)))))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2^1(1(3(4(4(x1))))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 1^1(3(4(4(x1)))) 71.96/19.06 2^1(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 3^1(4(4(x1))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5^1(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 2^1(0(5(4(3(4(3(3(0(5(0(0(x1)))))))))))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 0^1(5(4(3(4(3(3(0(5(0(0(x1))))))))))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5^1(4(3(4(3(3(0(5(0(0(x1)))))))))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 3^1(4(3(3(0(5(0(0(x1)))))))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 3^1(3(0(5(0(0(x1)))))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 3^1(0(5(0(0(x1))))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 0^1(5(0(0(x1)))) 71.96/19.06 5^1(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5^1(0(0(x1))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5^1(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 3^1(1(3(1(4(4(2(5(4(5(4(4(1(0(x1)))))))))))))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 1^1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 3^1(1(4(4(2(5(4(5(4(4(1(0(x1)))))))))))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 1^1(4(4(2(5(4(5(4(4(1(0(x1))))))))))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 2^1(5(4(5(4(4(1(0(x1)))))))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5^1(4(5(4(4(1(0(x1))))))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5^1(4(4(1(0(x1))))) 71.96/19.06 2^1(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 1^1(0(x1)) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0^1(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(2(5(5(2(4(4(3(5(3(4(3(4(1(x1)))))))))))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 2^1(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 5^1(5(2(4(4(3(5(3(4(3(4(1(x1)))))))))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 5^1(2(4(4(3(5(3(4(3(4(1(x1))))))))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 2^1(4(4(3(5(3(4(3(4(1(x1)))))))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(5(3(4(3(4(1(x1))))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 5^1(3(4(3(4(1(x1)))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(3(4(1(x1))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(1(x1))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 1^1(x1) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0^1(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 5^1(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1))))))))))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 1^1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 2^1(4(0(2(0(1(2(4(3(3(3(0(5(x1))))))))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0^1(2(0(1(2(4(3(3(3(0(5(x1))))))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 2^1(0(1(2(4(3(3(3(0(5(x1)))))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0^1(1(2(4(3(3(3(0(5(x1))))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 1^1(2(4(3(3(3(0(5(x1)))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 2^1(4(3(3(3(0(5(x1))))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 3^1(3(3(0(5(x1))))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 3^1(3(0(5(x1)))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 3^1(0(5(x1))) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0^1(5(x1)) 71.96/19.06 0^1(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 5^1(x1) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0^1(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 1^1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1))))))))))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 5^1(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 2^1(2(5(0(5(3(3(2(3(4(1(5(2(x1))))))))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 2^1(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 5^1(0(5(3(3(2(3(4(1(5(2(x1))))))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0^1(5(3(3(2(3(4(1(5(2(x1)))))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 5^1(3(3(2(3(4(1(5(2(x1))))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 3^1(3(2(3(4(1(5(2(x1)))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 3^1(2(3(4(1(5(2(x1))))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 2^1(3(4(1(5(2(x1)))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 3^1(4(1(5(2(x1))))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 1^1(5(2(x1))) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 5^1(2(x1)) 71.96/19.06 0^1(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 2^1(x1) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2^1(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 5^1(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 5^1(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1)))))))))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 5^1(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 0^1(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2^1(5(0(5(4(4(5(5(0(5(0(0(x1)))))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 5^1(0(5(4(4(5(5(0(5(0(0(x1))))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 0^1(5(4(4(5(5(0(5(0(0(x1)))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 5^1(4(4(5(5(0(5(0(0(x1))))))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 5^1(5(0(5(0(0(x1)))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 5^1(0(5(0(0(x1))))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 0^1(5(0(0(x1)))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 5^1(0(0(x1))) 71.96/19.06 0^1(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 0^1(0(x1)) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1^1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 5^1(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1)))))))))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 3^1(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 2^1(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1)))))))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 5^1(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 0^1(5(2(3(0(0(3(1(5(3(4(4(3(0(x1)))))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 5^1(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 2^1(3(0(0(3(1(5(3(4(4(3(0(x1)))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 3^1(0(0(3(1(5(3(4(4(3(0(x1))))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 0^1(0(3(1(5(3(4(4(3(0(x1)))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 0^1(3(1(5(3(4(4(3(0(x1))))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 3^1(1(5(3(4(4(3(0(x1)))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1^1(5(3(4(4(3(0(x1))))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 5^1(3(4(4(3(0(x1)))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 3^1(4(4(3(0(x1))))) 71.96/19.06 1^1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 3^1(0(x1)) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2^1(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 3^1(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1)))))))))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 0^1(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 5^1(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1)))))))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 5^1(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 5^1(5(2(2(0(2(5(1(1(0(1(0(0(1(x1)))))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 5^1(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2^1(2(0(2(5(1(1(0(1(0(0(1(x1)))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2^1(0(2(5(1(1(0(1(0(0(1(x1))))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 0^1(2(5(1(1(0(1(0(0(1(x1)))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2^1(5(1(1(0(1(0(0(1(x1))))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 5^1(1(1(0(1(0(0(1(x1)))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 1^1(1(0(1(0(0(1(x1))))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 1^1(0(1(0(0(1(x1)))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 0^1(1(0(0(1(x1))))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 1^1(0(0(1(x1)))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 0^1(0(1(x1))) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 0^1(1(x1)) 71.96/19.06 0^1(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 1^1(x1) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 0^1(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1)))))))))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 0^1(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1)))))))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 1^1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1)))))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 1^1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1)))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(2(0(5(3(3(2(5(2(2(5(2(x1)))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(0(5(3(3(2(5(2(2(5(2(x1))))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 0^1(5(3(3(2(5(2(2(5(2(x1)))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 5^1(3(3(2(5(2(2(5(2(x1))))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 3^1(3(2(5(2(2(5(2(x1)))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 3^1(2(5(2(2(5(2(x1))))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(5(2(2(5(2(x1)))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 5^1(2(2(5(2(x1))))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(2(5(2(x1)))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(5(2(x1))) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 5^1(2(x1)) 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(x1) 71.96/19.06 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (5) DependencyGraphProof (EQUIVALENT) 71.96/19.06 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 172 less nodes. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (6) 71.96/19.06 Complex Obligation (AND) 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (7) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 The TRS P consists of the following rules: 71.96/19.06 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(3(4(1(x1))))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(3(5(3(3(0(2(x1))))))) 71.96/19.06 0^1(0(1(2(2(x1))))) -> 2^1(3(3(2(2(x1))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(1(x1))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(2(x1)) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 2^1(5(0(4(0(5(0(x1))))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 0^1(5(0(x1))) 71.96/19.06 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (8) QDPOrderProof (EQUIVALENT) 71.96/19.06 We use the reduction pair processor [LPAR04,JAR06]. 71.96/19.06 71.96/19.06 71.96/19.06 The following pairs can be oriented strictly and are deleted. 71.96/19.06 71.96/19.06 0^1(0(1(2(2(x1))))) -> 2^1(3(3(2(2(x1))))) 71.96/19.06 The remaining pairs can at least be oriented weakly. 71.96/19.06 Used ordering: Polynomial interpretation [POLO]: 71.96/19.06 71.96/19.06 POL(0(x_1)) = 0 71.96/19.06 POL(0^1(x_1)) = 1 71.96/19.06 POL(1(x_1)) = 0 71.96/19.06 POL(2(x_1)) = 0 71.96/19.06 POL(2^1(x_1)) = x_1 71.96/19.06 POL(3(x_1)) = 0 71.96/19.06 POL(3^1(x_1)) = 1 71.96/19.06 POL(4(x_1)) = 0 71.96/19.06 POL(5(x_1)) = 1 71.96/19.06 71.96/19.06 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 71.96/19.06 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (9) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 The TRS P consists of the following rules: 71.96/19.06 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(3(4(1(x1))))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(3(5(3(3(0(2(x1))))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(1(x1))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(2(x1)) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 2^1(5(0(4(0(5(0(x1))))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 0^1(5(0(x1))) 71.96/19.06 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (10) QDPOrderProof (EQUIVALENT) 71.96/19.06 We use the reduction pair processor [LPAR04,JAR06]. 71.96/19.06 71.96/19.06 71.96/19.06 The following pairs can be oriented strictly and are deleted. 71.96/19.06 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(3(5(3(3(0(2(x1))))))) 71.96/19.06 The remaining pairs can at least be oriented weakly. 71.96/19.06 Used ordering: Polynomial interpretation [POLO]: 71.96/19.06 71.96/19.06 POL(0(x_1)) = 0 71.96/19.06 POL(0^1(x_1)) = x_1 71.96/19.06 POL(1(x_1)) = 0 71.96/19.06 POL(2(x_1)) = 1 71.96/19.06 POL(2^1(x_1)) = 1 71.96/19.06 POL(3(x_1)) = 0 71.96/19.06 POL(3^1(x_1)) = 1 71.96/19.06 POL(4(x_1)) = 0 71.96/19.06 POL(5(x_1)) = 1 71.96/19.06 71.96/19.06 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 71.96/19.06 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (11) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 The TRS P consists of the following rules: 71.96/19.06 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(3(4(1(x1))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(1(x1))) 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(2(x1)) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 2^1(5(0(4(0(5(0(x1))))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 0^1(5(0(x1))) 71.96/19.06 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (12) QDPOrderProof (EQUIVALENT) 71.96/19.06 We use the reduction pair processor [LPAR04,JAR06]. 71.96/19.06 71.96/19.06 71.96/19.06 The following pairs can be oriented strictly and are deleted. 71.96/19.06 71.96/19.06 3^1(4(2(2(1(5(3(3(2(x1))))))))) -> 0^1(2(x1)) 71.96/19.06 The remaining pairs can at least be oriented weakly. 71.96/19.06 Used ordering: Polynomial interpretation [POLO]: 71.96/19.06 71.96/19.06 POL(0(x_1)) = 0 71.96/19.06 POL(0^1(x_1)) = 0 71.96/19.06 POL(1(x_1)) = 0 71.96/19.06 POL(2(x_1)) = 1 71.96/19.06 POL(2^1(x_1)) = 0 71.96/19.06 POL(3(x_1)) = 0 71.96/19.06 POL(3^1(x_1)) = x_1 71.96/19.06 POL(4(x_1)) = x_1 71.96/19.06 POL(5(x_1)) = 0 71.96/19.06 71.96/19.06 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 71.96/19.06 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (13) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 The TRS P consists of the following rules: 71.96/19.06 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(3(4(1(x1))))) 71.96/19.06 2^1(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 3^1(4(1(x1))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 2^1(5(0(4(0(5(0(x1))))))) 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 0^1(5(0(x1))) 71.96/19.06 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (14) DependencyGraphProof (EQUIVALENT) 71.96/19.06 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (15) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 The TRS P consists of the following rules: 71.96/19.06 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 0^1(5(0(x1))) 71.96/19.06 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (16) QDPOrderProof (EQUIVALENT) 71.96/19.06 We use the reduction pair processor [LPAR04,JAR06]. 71.96/19.06 71.96/19.06 71.96/19.06 The following pairs can be oriented strictly and are deleted. 71.96/19.06 71.96/19.06 0^1(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 0^1(5(0(x1))) 71.96/19.06 The remaining pairs can at least be oriented weakly. 71.96/19.06 Used ordering: Polynomial interpretation [POLO]: 71.96/19.06 71.96/19.06 POL(0(x_1)) = 1 + x_1 71.96/19.06 POL(0^1(x_1)) = x_1 71.96/19.06 POL(1(x_1)) = 1 + x_1 71.96/19.06 POL(2(x_1)) = 1 + x_1 71.96/19.06 POL(3(x_1)) = 1 + x_1 71.96/19.06 POL(4(x_1)) = 1 + x_1 71.96/19.06 POL(5(x_1)) = 1 + x_1 71.96/19.06 71.96/19.06 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (17) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 P is empty. 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (18) PisEmptyProof (EQUIVALENT) 71.96/19.06 The TRS P is empty. Hence, there is no (P,Q,R) chain. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (19) 71.96/19.06 YES 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (20) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 The TRS P consists of the following rules: 71.96/19.06 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(x1) 71.96/19.06 71.96/19.06 The TRS R consists of the following rules: 71.96/19.06 71.96/19.06 0(0(1(2(2(x1))))) -> 2(3(3(2(2(x1))))) 71.96/19.06 0(4(1(0(4(5(x1)))))) -> 5(2(5(3(4(5(x1)))))) 71.96/19.06 3(4(2(2(1(5(3(3(2(x1))))))))) -> 3(1(0(3(5(3(3(0(2(x1))))))))) 71.96/19.06 0(5(5(3(1(3(3(0(2(0(x1)))))))))) -> 3(3(3(2(5(0(4(0(5(0(x1)))))))))) 71.96/19.06 0(2(1(5(3(5(3(0(5(5(5(0(x1)))))))))))) -> 2(2(5(4(4(2(3(3(0(3(5(4(x1)))))))))))) 71.96/19.06 3(2(0(0(4(0(0(0(2(5(1(0(x1)))))))))))) -> 1(5(2(4(0(4(2(0(0(5(0(2(x1)))))))))))) 71.96/19.06 2(1(3(3(4(3(0(2(0(4(0(3(1(x1))))))))))))) -> 2(4(1(3(0(1(3(3(2(1(3(4(4(x1))))))))))))) 71.96/19.06 5(2(3(1(2(1(5(4(5(1(1(0(0(x1))))))))))))) -> 5(2(0(5(4(3(4(3(3(0(5(0(0(x1))))))))))))) 71.96/19.06 2(5(0(2(2(0(3(3(1(4(2(5(0(0(0(x1))))))))))))))) -> 5(3(1(3(1(4(4(2(5(4(5(4(4(1(0(x1))))))))))))))) 71.96/19.06 2(5(1(2(0(0(5(1(2(2(1(0(2(1(5(x1))))))))))))))) -> 0(3(2(5(5(2(4(4(3(5(3(4(3(4(1(x1))))))))))))))) 71.96/19.06 0(3(5(5(0(3(2(4(1(1(4(5(1(5(5(3(x1)))))))))))))))) -> 0(5(1(2(4(0(2(0(1(2(4(3(3(3(0(5(x1)))))))))))))))) 71.96/19.06 0(4(4(1(2(2(1(3(5(3(1(3(4(1(1(0(x1)))))))))))))))) -> 0(1(5(2(2(5(0(5(3(3(2(3(4(1(5(2(x1)))))))))))))))) 71.96/19.06 0(1(1(3(5(1(1(1(3(0(0(4(1(2(2(3(1(5(0(x1))))))))))))))))))) -> 2(4(5(5(5(4(0(2(5(0(5(4(4(5(5(0(5(0(0(x1))))))))))))))))))) 71.96/19.06 1(2(1(3(4(2(4(4(1(2(5(2(3(3(3(5(1(0(0(x1))))))))))))))))))) -> 1(5(3(2(5(0(5(2(3(0(0(3(1(5(3(4(4(3(0(x1))))))))))))))))))) 71.96/19.06 0(3(4(2(2(0(3(4(1(1(5(0(3(5(2(1(3(3(4(1(0(x1))))))))))))))))))))) -> 2(4(4(3(0(5(5(5(5(2(2(0(2(5(1(1(0(1(0(0(1(x1))))))))))))))))))))) 71.96/19.06 2(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(2(2(0(5(3(3(2(5(2(2(5(2(x1))))))))))))))))))))) 71.96/19.06 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (21) UsableRulesProof (EQUIVALENT) 71.96/19.06 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (22) 71.96/19.06 Obligation: 71.96/19.06 Q DP problem: 71.96/19.06 The TRS P consists of the following rules: 71.96/19.06 71.96/19.06 2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(x1) 71.96/19.06 71.96/19.06 R is empty. 71.96/19.06 Q is empty. 71.96/19.06 We have to consider all minimal (P,Q,R)-chains. 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (23) QDPSizeChangeProof (EQUIVALENT) 71.96/19.06 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 71.96/19.06 71.96/19.06 From the DPs we obtained the following set of size-change graphs: 71.96/19.06 *2^1(4(5(2(1(3(5(5(1(1(1(0(0(4(5(0(1(2(0(2(5(x1))))))))))))))))))))) -> 2^1(x1) 71.96/19.06 The graph contains the following edges 1 > 1 71.96/19.06 71.96/19.06 71.96/19.06 ---------------------------------------- 71.96/19.06 71.96/19.06 (24) 71.96/19.06 YES 72.18/19.15 EOF