236.92/61.08 YES 238.69/61.55 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 238.69/61.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 238.69/61.55 238.69/61.55 238.69/61.55 Termination w.r.t. Q of the given QTRS could be proven: 238.69/61.55 238.69/61.55 (0) QTRS 238.69/61.55 (1) QTRSRRRProof [EQUIVALENT, 160 ms] 238.69/61.55 (2) QTRS 238.69/61.55 (3) DependencyPairsProof [EQUIVALENT, 516 ms] 238.69/61.55 (4) QDP 238.69/61.55 (5) QDPOrderProof [EQUIVALENT, 1343 ms] 238.69/61.55 (6) QDP 238.69/61.55 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 238.69/61.55 (8) AND 238.69/61.55 (9) QDP 238.69/61.55 (10) QDPOrderProof [EQUIVALENT, 63 ms] 238.69/61.55 (11) QDP 238.69/61.55 (12) QDPOrderProof [EQUIVALENT, 39 ms] 238.69/61.55 (13) QDP 238.69/61.55 (14) PisEmptyProof [EQUIVALENT, 0 ms] 238.69/61.55 (15) YES 238.69/61.55 (16) QDP 238.69/61.55 (17) QDPOrderProof [EQUIVALENT, 3100 ms] 238.69/61.55 (18) QDP 238.69/61.55 (19) PisEmptyProof [EQUIVALENT, 0 ms] 238.69/61.55 (20) YES 238.69/61.55 (21) QDP 238.69/61.55 (22) QDPOrderProof [EQUIVALENT, 72 ms] 238.69/61.55 (23) QDP 238.69/61.55 (24) QDPOrderProof [EQUIVALENT, 35 ms] 238.69/61.55 (25) QDP 238.69/61.55 (26) QDPOrderProof [EQUIVALENT, 3660 ms] 238.69/61.55 (27) QDP 238.69/61.55 (28) QDPOrderProof [EQUIVALENT, 3694 ms] 238.69/61.55 (29) QDP 238.69/61.55 (30) PisEmptyProof [EQUIVALENT, 0 ms] 238.69/61.55 (31) YES 238.69/61.55 (32) QDP 238.69/61.55 (33) QDPOrderProof [EQUIVALENT, 81 ms] 238.69/61.55 (34) QDP 238.69/61.55 (35) QDPOrderProof [EQUIVALENT, 68 ms] 238.69/61.55 (36) QDP 238.69/61.55 (37) QDPOrderProof [EQUIVALENT, 0 ms] 238.69/61.55 (38) QDP 238.69/61.55 (39) DependencyGraphProof [EQUIVALENT, 0 ms] 238.69/61.55 (40) QDP 238.69/61.55 (41) QDPOrderProof [EQUIVALENT, 46 ms] 238.69/61.55 (42) QDP 238.69/61.55 (43) QDPOrderProof [EQUIVALENT, 54 ms] 238.69/61.55 (44) QDP 238.69/61.55 (45) PisEmptyProof [EQUIVALENT, 0 ms] 238.69/61.55 (46) YES 238.69/61.55 238.69/61.55 238.69/61.55 ---------------------------------------- 238.69/61.55 238.69/61.55 (0) 238.69/61.55 Obligation: 238.69/61.55 Q restricted rewrite system: 238.69/61.55 The TRS R consists of the following rules: 238.69/61.55 238.69/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.69/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.69/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.69/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.69/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.69/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.69/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.69/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.69/61.55 4(3(0(2(5(3(1(2(3(x1))))))))) -> 4(1(1(0(0(0(5(3(x1)))))))) 238.69/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.69/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.69/61.55 3(0(4(4(4(5(3(1(2(5(0(4(x1)))))))))))) -> 5(3(3(0(3(5(1(0(0(1(0(x1))))))))))) 238.69/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.69/61.55 5(4(2(3(0(4(3(2(2(2(4(1(x1)))))))))))) -> 5(1(0(2(4(4(4(5(1(4(1(x1))))))))))) 238.69/61.55 3(0(0(2(1(1(3(1(5(0(5(1(0(5(x1)))))))))))))) -> 5(1(0(1(2(2(1(3(3(1(0(2(5(x1))))))))))))) 238.69/61.55 0(4(2(4(1(1(5(3(0(2(2(0(5(1(5(x1))))))))))))))) -> 1(1(0(0(3(5(5(1(1(2(5(3(5(5(x1)))))))))))))) 238.69/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.69/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.69/61.55 0(0(0(2(0(3(0(5(1(0(5(0(5(1(0(4(3(x1))))))))))))))))) -> 0(0(1(4(5(0(0(2(0(0(1(1(3(2(5(3(x1)))))))))))))))) 238.69/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.69/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.69/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.69/61.55 2(4(2(1(5(5(0(1(0(4(2(2(2(3(4(1(0(4(x1)))))))))))))))))) -> 2(1(3(2(1(2(2(5(1(1(3(5(4(4(5(5(5(x1))))))))))))))))) 238.69/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.69/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.69/61.55 238.69/61.55 Q is empty. 238.69/61.55 238.69/61.55 ---------------------------------------- 238.69/61.55 238.69/61.55 (1) QTRSRRRProof (EQUIVALENT) 238.69/61.55 Used ordering: 238.69/61.55 Polynomial interpretation [POLO]: 238.69/61.55 238.69/61.55 POL(0(x_1)) = 1 + x_1 238.69/61.55 POL(1(x_1)) = 1 + x_1 238.69/61.55 POL(2(x_1)) = 1 + x_1 238.69/61.55 POL(3(x_1)) = 1 + x_1 238.69/61.55 POL(4(x_1)) = 1 + x_1 238.69/61.55 POL(5(x_1)) = 1 + x_1 238.69/61.55 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 238.69/61.55 238.69/61.55 4(3(0(2(5(3(1(2(3(x1))))))))) -> 4(1(1(0(0(0(5(3(x1)))))))) 238.69/61.55 3(0(4(4(4(5(3(1(2(5(0(4(x1)))))))))))) -> 5(3(3(0(3(5(1(0(0(1(0(x1))))))))))) 238.69/61.55 5(4(2(3(0(4(3(2(2(2(4(1(x1)))))))))))) -> 5(1(0(2(4(4(4(5(1(4(1(x1))))))))))) 238.69/61.55 3(0(0(2(1(1(3(1(5(0(5(1(0(5(x1)))))))))))))) -> 5(1(0(1(2(2(1(3(3(1(0(2(5(x1))))))))))))) 238.69/61.55 0(4(2(4(1(1(5(3(0(2(2(0(5(1(5(x1))))))))))))))) -> 1(1(0(0(3(5(5(1(1(2(5(3(5(5(x1)))))))))))))) 238.69/61.55 0(0(0(2(0(3(0(5(1(0(5(0(5(1(0(4(3(x1))))))))))))))))) -> 0(0(1(4(5(0(0(2(0(0(1(1(3(2(5(3(x1)))))))))))))))) 238.69/61.55 2(4(2(1(5(5(0(1(0(4(2(2(2(3(4(1(0(4(x1)))))))))))))))))) -> 2(1(3(2(1(2(2(5(1(1(3(5(4(4(5(5(5(x1))))))))))))))))) 238.69/61.55 238.69/61.55 238.69/61.55 238.69/61.55 238.69/61.55 ---------------------------------------- 238.69/61.55 238.69/61.55 (2) 238.69/61.55 Obligation: 238.69/61.55 Q restricted rewrite system: 238.69/61.55 The TRS R consists of the following rules: 238.69/61.55 238.69/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.69/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.69/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.69/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.69/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.69/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.69/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.69/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.69/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.69/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.69/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.69/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.69/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.69/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.69/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.69/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.69/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.69/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.69/61.55 238.69/61.55 Q is empty. 238.69/61.55 238.69/61.55 ---------------------------------------- 238.69/61.55 238.69/61.55 (3) DependencyPairsProof (EQUIVALENT) 238.69/61.55 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 238.69/61.55 ---------------------------------------- 238.69/61.55 238.69/61.55 (4) 238.69/61.55 Obligation: 238.69/61.55 Q DP problem: 238.69/61.55 The TRS P consists of the following rules: 238.69/61.55 238.69/61.55 0^1(0(1(1(x1)))) -> 2^1(2(1(3(x1)))) 238.69/61.55 0^1(0(1(1(x1)))) -> 2^1(1(3(x1))) 238.69/61.55 0^1(0(1(1(x1)))) -> 1^1(3(x1)) 238.69/61.55 0^1(0(1(1(x1)))) -> 3^1(x1) 238.69/61.55 1^1(4(0(4(x1)))) -> 1^1(2(3(1(x1)))) 238.69/61.55 1^1(4(0(4(x1)))) -> 2^1(3(1(x1))) 238.69/61.55 1^1(4(0(4(x1)))) -> 3^1(1(x1)) 238.69/61.55 1^1(4(0(4(x1)))) -> 1^1(x1) 238.69/61.55 3^1(4(3(1(1(x1))))) -> 3^1(4(0(3(1(x1))))) 238.69/61.55 3^1(4(3(1(1(x1))))) -> 4^1(0(3(1(x1)))) 238.69/61.55 3^1(4(3(1(1(x1))))) -> 0^1(3(1(x1))) 238.69/61.55 3^1(4(3(1(1(x1))))) -> 3^1(1(x1)) 238.69/61.55 1^1(3(1(1(0(4(x1)))))) -> 1^1(3(0(2(0(4(x1)))))) 238.69/61.55 1^1(3(1(1(0(4(x1)))))) -> 3^1(0(2(0(4(x1))))) 238.69/61.55 1^1(3(1(1(0(4(x1)))))) -> 0^1(2(0(4(x1)))) 238.69/61.55 1^1(3(1(1(0(4(x1)))))) -> 2^1(0(4(x1))) 238.69/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(4(2(3(4(2(2(x1))))))) 238.69/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 4^1(2(3(4(2(2(x1)))))) 238.69/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(3(4(2(2(x1))))) 238.69/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 3^1(4(2(2(x1)))) 238.69/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 4^1(2(2(x1))) 238.69/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(2(x1)) 238.69/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(x1) 238.69/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 5^1(2(4(1(2(3(3(x1))))))) 238.69/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 2^1(4(1(2(3(3(x1)))))) 238.69/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 4^1(1(2(3(3(x1))))) 238.69/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 1^1(2(3(3(x1)))) 238.69/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 2^1(3(3(x1))) 238.69/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 3^1(3(x1)) 238.69/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(1(5(4(2(5(0(0(x1)))))))) 238.69/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 1^1(5(4(2(5(0(0(x1))))))) 238.69/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 5^1(4(2(5(0(0(x1)))))) 238.69/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 4^1(2(5(0(0(x1))))) 238.69/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 2^1(5(0(0(x1)))) 238.69/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 5^1(0(0(x1))) 238.69/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(0(x1)) 238.69/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(x1) 238.69/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 4^1(1(2(3(4(2(5(3(x1)))))))) 238.69/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 1^1(2(3(4(2(5(3(x1))))))) 238.69/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 2^1(3(4(2(5(3(x1)))))) 238.69/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 3^1(4(2(5(3(x1))))) 238.69/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 4^1(2(5(3(x1)))) 238.69/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 2^1(5(3(x1))) 238.69/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 5^1(3(x1)) 238.69/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1^1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.69/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 4^1(3(3(4(3(3(1(0(0(x1))))))))) 238.69/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 3^1(3(4(3(3(1(0(0(x1)))))))) 238.69/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 3^1(4(3(3(1(0(0(x1))))))) 238.69/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 4^1(3(3(1(0(0(x1)))))) 238.69/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 3^1(3(1(0(0(x1))))) 238.69/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 3^1(1(0(0(x1)))) 238.69/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1^1(0(0(x1))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 1^1(0(2(5(0(5(3(5(4(x1))))))))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(2(5(0(5(3(5(4(x1)))))))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 2^1(5(0(5(3(5(4(x1))))))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 5^1(0(5(3(5(4(x1)))))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(5(3(5(4(x1))))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 5^1(3(5(4(x1)))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 3^1(5(4(x1))) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 5^1(4(x1)) 238.69/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 4^1(x1) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4^1(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 1^1(1(4(3(2(2(3(5(2(1(3(x1))))))))))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 1^1(4(3(2(2(3(5(2(1(3(x1)))))))))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4^1(3(2(2(3(5(2(1(3(x1))))))))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 3^1(2(2(3(5(2(1(3(x1)))))))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 2^1(2(3(5(2(1(3(x1))))))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 2^1(3(5(2(1(3(x1)))))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 3^1(5(2(1(3(x1))))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 5^1(2(1(3(x1)))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 2^1(1(3(x1))) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 1^1(3(x1)) 238.69/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 3^1(x1) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 4^1(0(0(3(4(3(3(5(0(4(3(3(1(3(x1)))))))))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(3(4(3(3(5(0(4(3(3(1(3(x1)))))))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(4(3(3(5(0(4(3(3(1(3(x1))))))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 4^1(3(3(5(0(4(3(3(1(3(x1)))))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(3(5(0(4(3(3(1(3(x1))))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(5(0(4(3(3(1(3(x1)))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 5^1(0(4(3(3(1(3(x1))))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(3(3(1(3(x1)))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 4^1(3(3(1(3(x1))))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(3(1(3(x1)))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(1(3(x1))) 238.69/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 1^1(3(x1)) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3^1(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1))))))))))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3^1(4(1(2(1(0(3(1(2(3(2(1(1(x1))))))))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 4^1(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1^1(2(1(0(3(1(2(3(2(1(1(x1))))))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(1(0(3(1(2(3(2(1(1(x1)))))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1^1(0(3(1(2(3(2(1(1(x1))))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 0^1(3(1(2(3(2(1(1(x1)))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3^1(1(2(3(2(1(1(x1))))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1^1(2(3(2(1(1(x1)))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(3(2(1(1(x1))))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3^1(2(1(1(x1)))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(1(1(x1))) 238.69/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1^1(1(x1)) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1^1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1^1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1)))))))))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 0^1(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 0^1(3(4(4(4(4(4(2(3(3(1(0(4(3(x1)))))))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 3^1(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(4(4(4(4(2(3(3(1(0(4(3(x1)))))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(4(4(4(2(3(3(1(0(4(3(x1))))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(4(4(2(3(3(1(0(4(3(x1)))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(4(2(3(3(1(0(4(3(x1))))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(2(3(3(1(0(4(3(x1)))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 2^1(3(3(1(0(4(3(x1))))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 3^1(3(1(0(4(3(x1)))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 3^1(1(0(4(3(x1))))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1^1(0(4(3(x1)))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 0^1(4(3(x1))) 238.69/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(3(x1)) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1)))))))))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 2^1(3(3(1(1(4(5(3(1(3(2(4(0(2(x1)))))))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 3^1(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 3^1(1(1(4(5(3(1(3(2(4(0(2(x1)))))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(1(4(5(3(1(3(2(4(0(2(x1))))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(4(5(3(1(3(2(4(0(2(x1)))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(5(3(1(3(2(4(0(2(x1))))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 5^1(3(1(3(2(4(0(2(x1)))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 3^1(1(3(2(4(0(2(x1))))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(3(2(4(0(2(x1)))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 3^1(2(4(0(2(x1))))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 2^1(4(0(2(x1)))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(0(2(x1))) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 0^1(2(x1)) 238.69/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 2^1(x1) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1))))))))))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 5^1(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1))))))))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(0(0(4(0(2(5(0(2(5(2(2(2(x1))))))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(4(0(2(5(0(2(5(2(2(2(x1))))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 4^1(0(2(5(0(2(5(2(2(2(x1)))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(2(5(0(2(5(2(2(2(x1))))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(5(0(2(5(2(2(2(x1)))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 5^1(0(2(5(2(2(2(x1))))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(2(5(2(2(2(x1)))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(5(2(2(2(x1))))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 5^1(2(2(2(x1)))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(2(2(x1))) 238.69/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(2(x1)) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1^1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1))))))))))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 2^1(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 2^1(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1))))))))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 3^1(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1^1(5(2(5(1(1(3(4(2(4(0(5(5(x1))))))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 2^1(5(1(1(3(4(2(4(0(5(5(x1))))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(1(1(3(4(2(4(0(5(5(x1)))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1^1(1(3(4(2(4(0(5(5(x1))))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1^1(3(4(2(4(0(5(5(x1)))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 3^1(4(2(4(0(5(5(x1))))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 4^1(2(4(0(5(5(x1)))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 2^1(4(0(5(5(x1))))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 4^1(0(5(5(x1)))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 0^1(5(5(x1))) 238.69/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(5(x1)) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 4^1(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 0^1(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 5^1(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 0^1(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 3^1(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 0^1(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 4^1(1(4(1(5(3(4(1(5(0(2(x1))))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(4(1(5(3(4(1(5(0(2(x1)))))))))) 238.69/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 4^1(1(5(3(4(1(5(0(2(x1))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(5(3(4(1(5(0(2(x1)))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 5^1(3(4(1(5(0(2(x1))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 3^1(4(1(5(0(2(x1)))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 4^1(1(5(0(2(x1))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(5(0(2(x1)))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 5^1(0(2(x1))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 0^1(2(x1)) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(x1) 238.90/61.55 238.90/61.55 The TRS R consists of the following rules: 238.90/61.55 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 238.90/61.55 Q is empty. 238.90/61.55 We have to consider all minimal (P,Q,R)-chains. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (5) QDPOrderProof (EQUIVALENT) 238.90/61.55 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.55 238.90/61.55 238.90/61.55 The following pairs can be oriented strictly and are deleted. 238.90/61.55 238.90/61.55 0^1(0(1(1(x1)))) -> 2^1(1(3(x1))) 238.90/61.55 0^1(0(1(1(x1)))) -> 1^1(3(x1)) 238.90/61.55 0^1(0(1(1(x1)))) -> 3^1(x1) 238.90/61.55 1^1(4(0(4(x1)))) -> 2^1(3(1(x1))) 238.90/61.55 1^1(4(0(4(x1)))) -> 3^1(1(x1)) 238.90/61.55 1^1(4(0(4(x1)))) -> 1^1(x1) 238.90/61.55 3^1(4(3(1(1(x1))))) -> 4^1(0(3(1(x1)))) 238.90/61.55 3^1(4(3(1(1(x1))))) -> 0^1(3(1(x1))) 238.90/61.55 3^1(4(3(1(1(x1))))) -> 3^1(1(x1)) 238.90/61.55 1^1(3(1(1(0(4(x1)))))) -> 3^1(0(2(0(4(x1))))) 238.90/61.55 1^1(3(1(1(0(4(x1)))))) -> 0^1(2(0(4(x1)))) 238.90/61.55 1^1(3(1(1(0(4(x1)))))) -> 2^1(0(4(x1))) 238.90/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 4^1(2(3(4(2(2(x1)))))) 238.90/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(3(4(2(2(x1))))) 238.90/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 3^1(4(2(2(x1)))) 238.90/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 4^1(2(2(x1))) 238.90/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(2(x1)) 238.90/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(x1) 238.90/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 2^1(4(1(2(3(3(x1)))))) 238.90/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 4^1(1(2(3(3(x1))))) 238.90/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 1^1(2(3(3(x1)))) 238.90/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 2^1(3(3(x1))) 238.90/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 3^1(3(x1)) 238.90/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 1^1(5(4(2(5(0(0(x1))))))) 238.90/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 5^1(4(2(5(0(0(x1)))))) 238.90/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 4^1(2(5(0(0(x1))))) 238.90/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 2^1(5(0(0(x1)))) 238.90/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 5^1(0(0(x1))) 238.90/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(0(x1)) 238.90/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(x1) 238.90/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 1^1(2(3(4(2(5(3(x1))))))) 238.90/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 2^1(3(4(2(5(3(x1)))))) 238.90/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 3^1(4(2(5(3(x1))))) 238.90/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 4^1(2(5(3(x1)))) 238.90/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 2^1(5(3(x1))) 238.90/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 5^1(3(x1)) 238.90/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 4^1(3(3(4(3(3(1(0(0(x1))))))))) 238.90/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 3^1(3(4(3(3(1(0(0(x1)))))))) 238.90/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 3^1(4(3(3(1(0(0(x1))))))) 238.90/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 4^1(3(3(1(0(0(x1)))))) 238.90/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 3^1(3(1(0(0(x1))))) 238.90/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 3^1(1(0(0(x1)))) 238.90/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1^1(0(0(x1))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 1^1(0(2(5(0(5(3(5(4(x1))))))))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(2(5(0(5(3(5(4(x1)))))))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 2^1(5(0(5(3(5(4(x1))))))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 5^1(0(5(3(5(4(x1)))))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(5(3(5(4(x1))))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 5^1(3(5(4(x1)))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 3^1(5(4(x1))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 5^1(4(x1)) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 4^1(x1) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 1^1(1(4(3(2(2(3(5(2(1(3(x1))))))))))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 1^1(4(3(2(2(3(5(2(1(3(x1)))))))))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4^1(3(2(2(3(5(2(1(3(x1))))))))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 3^1(2(2(3(5(2(1(3(x1)))))))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 2^1(2(3(5(2(1(3(x1))))))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 2^1(3(5(2(1(3(x1)))))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 3^1(5(2(1(3(x1))))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 5^1(2(1(3(x1)))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 2^1(1(3(x1))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 1^1(3(x1)) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 3^1(x1) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 4^1(0(0(3(4(3(3(5(0(4(3(3(1(3(x1)))))))))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(3(4(3(3(5(0(4(3(3(1(3(x1)))))))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(4(3(3(5(0(4(3(3(1(3(x1))))))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 4^1(3(3(5(0(4(3(3(1(3(x1)))))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(3(5(0(4(3(3(1(3(x1))))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(5(0(4(3(3(1(3(x1)))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 5^1(0(4(3(3(1(3(x1))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(3(3(1(3(x1)))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 4^1(3(3(1(3(x1))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(3(1(3(x1)))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 3^1(1(3(x1))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 1^1(3(x1)) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1))))))))))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3^1(4(1(2(1(0(3(1(2(3(2(1(1(x1))))))))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 4^1(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1^1(2(1(0(3(1(2(3(2(1(1(x1))))))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(1(0(3(1(2(3(2(1(1(x1)))))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1^1(0(3(1(2(3(2(1(1(x1))))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 0^1(3(1(2(3(2(1(1(x1)))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3^1(1(2(3(2(1(1(x1))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1^1(2(3(2(1(1(x1)))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(3(2(1(1(x1))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3^1(2(1(1(x1)))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 2^1(1(1(x1))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1^1(1(x1)) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1^1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1)))))))))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 0^1(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 0^1(3(4(4(4(4(4(2(3(3(1(0(4(3(x1)))))))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 3^1(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(4(4(4(4(2(3(3(1(0(4(3(x1)))))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(4(4(4(2(3(3(1(0(4(3(x1))))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(4(4(2(3(3(1(0(4(3(x1)))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(4(2(3(3(1(0(4(3(x1))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(2(3(3(1(0(4(3(x1)))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 2^1(3(3(1(0(4(3(x1))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 3^1(3(1(0(4(3(x1)))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 3^1(1(0(4(3(x1))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1^1(0(4(3(x1)))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 0^1(4(3(x1))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 4^1(3(x1)) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1)))))))))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 2^1(3(3(1(1(4(5(3(1(3(2(4(0(2(x1)))))))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 3^1(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 3^1(1(1(4(5(3(1(3(2(4(0(2(x1)))))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(1(4(5(3(1(3(2(4(0(2(x1))))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(4(5(3(1(3(2(4(0(2(x1)))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(5(3(1(3(2(4(0(2(x1))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 5^1(3(1(3(2(4(0(2(x1)))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 3^1(1(3(2(4(0(2(x1))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1^1(3(2(4(0(2(x1)))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 3^1(2(4(0(2(x1))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 2^1(4(0(2(x1)))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(0(2(x1))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 0^1(2(x1)) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 2^1(x1) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1))))))))))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 5^1(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1))))))))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(0(0(4(0(2(5(0(2(5(2(2(2(x1))))))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(4(0(2(5(0(2(5(2(2(2(x1))))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 4^1(0(2(5(0(2(5(2(2(2(x1)))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(2(5(0(2(5(2(2(2(x1))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(5(0(2(5(2(2(2(x1)))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 5^1(0(2(5(2(2(2(x1))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 0^1(2(5(2(2(2(x1)))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(5(2(2(2(x1))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 5^1(2(2(2(x1)))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(2(2(x1))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 2^1(2(x1)) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1^1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1))))))))))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 2^1(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 2^1(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1))))))))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 3^1(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1^1(5(2(5(1(1(3(4(2(4(0(5(5(x1))))))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 2^1(5(1(1(3(4(2(4(0(5(5(x1))))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(1(1(3(4(2(4(0(5(5(x1)))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1^1(1(3(4(2(4(0(5(5(x1))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1^1(3(4(2(4(0(5(5(x1)))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 3^1(4(2(4(0(5(5(x1))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 4^1(2(4(0(5(5(x1)))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 2^1(4(0(5(5(x1))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 4^1(0(5(5(x1)))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 0^1(5(5(x1))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(5(x1)) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 4^1(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 0^1(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 5^1(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 0^1(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(3(0(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 3^1(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 0^1(4(1(4(1(5(3(4(1(5(0(2(x1)))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 4^1(1(4(1(5(3(4(1(5(0(2(x1))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(4(1(5(3(4(1(5(0(2(x1)))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 4^1(1(5(3(4(1(5(0(2(x1))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(5(3(4(1(5(0(2(x1)))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 5^1(3(4(1(5(0(2(x1))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 3^1(4(1(5(0(2(x1)))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 4^1(1(5(0(2(x1))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 1^1(5(0(2(x1)))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 5^1(0(2(x1))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 0^1(2(x1)) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(x1) 238.90/61.55 The remaining pairs can at least be oriented weakly. 238.90/61.55 Used ordering: Polynomial interpretation [POLO]: 238.90/61.55 238.90/61.55 POL(0(x_1)) = 1 + x_1 238.90/61.55 POL(0^1(x_1)) = x_1 238.90/61.55 POL(1(x_1)) = 1 + x_1 238.90/61.55 POL(1^1(x_1)) = x_1 238.90/61.55 POL(2(x_1)) = 1 + x_1 238.90/61.55 POL(2^1(x_1)) = x_1 238.90/61.55 POL(3(x_1)) = 1 + x_1 238.90/61.55 POL(3^1(x_1)) = x_1 238.90/61.55 POL(4(x_1)) = 1 + x_1 238.90/61.55 POL(4^1(x_1)) = x_1 238.90/61.55 POL(5(x_1)) = 1 + x_1 238.90/61.55 POL(5^1(x_1)) = x_1 238.90/61.55 238.90/61.55 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.55 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.55 238.90/61.55 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (6) 238.90/61.55 Obligation: 238.90/61.55 Q DP problem: 238.90/61.55 The TRS P consists of the following rules: 238.90/61.55 238.90/61.55 0^1(0(1(1(x1)))) -> 2^1(2(1(3(x1)))) 238.90/61.55 1^1(4(0(4(x1)))) -> 1^1(2(3(1(x1)))) 238.90/61.55 3^1(4(3(1(1(x1))))) -> 3^1(4(0(3(1(x1))))) 238.90/61.55 1^1(3(1(1(0(4(x1)))))) -> 1^1(3(0(2(0(4(x1)))))) 238.90/61.55 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(4(2(3(4(2(2(x1))))))) 238.90/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 5^1(2(4(1(2(3(3(x1))))))) 238.90/61.55 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 4^1(4(1(4(0(0(1(3(x1)))))))) -> 4^1(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4^1(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1^1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4^1(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 2^1(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3^1(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1^1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 238.90/61.55 The TRS R consists of the following rules: 238.90/61.55 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 238.90/61.55 Q is empty. 238.90/61.55 We have to consider all minimal (P,Q,R)-chains. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (7) DependencyGraphProof (EQUIVALENT) 238.90/61.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs with 2 less nodes. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (8) 238.90/61.55 Complex Obligation (AND) 238.90/61.55 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (9) 238.90/61.55 Obligation: 238.90/61.55 Q DP problem: 238.90/61.55 The TRS P consists of the following rules: 238.90/61.55 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 5^1(2(4(1(2(3(3(x1))))))) 238.90/61.55 238.90/61.55 The TRS R consists of the following rules: 238.90/61.55 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 238.90/61.55 Q is empty. 238.90/61.55 We have to consider all minimal (P,Q,R)-chains. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (10) QDPOrderProof (EQUIVALENT) 238.90/61.55 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.55 238.90/61.55 238.90/61.55 The following pairs can be oriented strictly and are deleted. 238.90/61.55 238.90/61.55 5^1(5(4(2(0(2(3(x1))))))) -> 5^1(2(4(1(2(3(3(x1))))))) 238.90/61.55 The remaining pairs can at least be oriented weakly. 238.90/61.55 Used ordering: Polynomial interpretation [POLO]: 238.90/61.55 238.90/61.55 POL(0(x_1)) = 0 238.90/61.55 POL(1(x_1)) = 0 238.90/61.55 POL(2(x_1)) = 0 238.90/61.55 POL(3(x_1)) = 0 238.90/61.55 POL(4(x_1)) = 0 238.90/61.55 POL(5(x_1)) = 1 238.90/61.55 POL(5^1(x_1)) = x_1 238.90/61.55 238.90/61.55 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.55 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 238.90/61.55 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (11) 238.90/61.55 Obligation: 238.90/61.55 Q DP problem: 238.90/61.55 The TRS P consists of the following rules: 238.90/61.55 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 238.90/61.55 The TRS R consists of the following rules: 238.90/61.55 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 238.90/61.55 Q is empty. 238.90/61.55 We have to consider all minimal (P,Q,R)-chains. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (12) QDPOrderProof (EQUIVALENT) 238.90/61.55 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.55 238.90/61.55 238.90/61.55 The following pairs can be oriented strictly and are deleted. 238.90/61.55 238.90/61.55 5^1(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5^1(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 The remaining pairs can at least be oriented weakly. 238.90/61.55 Used ordering: Polynomial interpretation [POLO]: 238.90/61.55 238.90/61.55 POL(0(x_1)) = 0 238.90/61.55 POL(1(x_1)) = 0 238.90/61.55 POL(2(x_1)) = x_1 238.90/61.55 POL(3(x_1)) = 0 238.90/61.55 POL(4(x_1)) = 1 + x_1 238.90/61.55 POL(5(x_1)) = 0 238.90/61.55 POL(5^1(x_1)) = x_1 238.90/61.55 238.90/61.55 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.55 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 238.90/61.55 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (13) 238.90/61.55 Obligation: 238.90/61.55 Q DP problem: 238.90/61.55 P is empty. 238.90/61.55 The TRS R consists of the following rules: 238.90/61.55 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 238.90/61.55 Q is empty. 238.90/61.55 We have to consider all minimal (P,Q,R)-chains. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (14) PisEmptyProof (EQUIVALENT) 238.90/61.55 The TRS P is empty. Hence, there is no (P,Q,R) chain. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (15) 238.90/61.55 YES 238.90/61.55 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (16) 238.90/61.55 Obligation: 238.90/61.55 Q DP problem: 238.90/61.55 The TRS P consists of the following rules: 238.90/61.55 238.90/61.55 3^1(4(3(1(1(x1))))) -> 3^1(4(0(3(1(x1))))) 238.90/61.55 238.90/61.55 The TRS R consists of the following rules: 238.90/61.55 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 238.90/61.55 Q is empty. 238.90/61.55 We have to consider all minimal (P,Q,R)-chains. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (17) QDPOrderProof (EQUIVALENT) 238.90/61.55 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.55 238.90/61.55 238.90/61.55 The following pairs can be oriented strictly and are deleted. 238.90/61.55 238.90/61.55 3^1(4(3(1(1(x1))))) -> 3^1(4(0(3(1(x1))))) 238.90/61.55 The remaining pairs can at least be oriented weakly. 238.90/61.55 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 238.90/61.55 238.90/61.55 POL( 3^1_1(x_1) ) = max{0, 2x_1 - 1} 238.90/61.55 POL( 1_1(x_1) ) = 2 238.90/61.55 POL( 3_1(x_1) ) = 1 238.90/61.55 POL( 0_1(x_1) ) = max{0, 2x_1 - 2} 238.90/61.55 POL( 4_1(x_1) ) = x_1 238.90/61.55 POL( 2_1(x_1) ) = max{0, 2x_1 - 2} 238.90/61.55 POL( 5_1(x_1) ) = 2 238.90/61.55 238.90/61.55 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.55 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 238.90/61.55 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (18) 238.90/61.55 Obligation: 238.90/61.55 Q DP problem: 238.90/61.55 P is empty. 238.90/61.55 The TRS R consists of the following rules: 238.90/61.55 238.90/61.55 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.55 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.55 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.55 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.55 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.55 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.55 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.55 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.55 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.55 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.55 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.55 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.55 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.55 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.55 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.55 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.55 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.55 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.55 238.90/61.55 Q is empty. 238.90/61.55 We have to consider all minimal (P,Q,R)-chains. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (19) PisEmptyProof (EQUIVALENT) 238.90/61.55 The TRS P is empty. Hence, there is no (P,Q,R) chain. 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (20) 238.90/61.55 YES 238.90/61.55 238.90/61.55 ---------------------------------------- 238.90/61.55 238.90/61.55 (21) 238.90/61.55 Obligation: 238.90/61.55 Q DP problem: 238.90/61.55 The TRS P consists of the following rules: 238.90/61.55 238.90/61.55 1^1(3(1(1(0(4(x1)))))) -> 1^1(3(0(2(0(4(x1)))))) 238.90/61.55 1^1(4(0(4(x1)))) -> 1^1(2(3(1(x1)))) 238.90/61.56 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1^1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 238.90/61.56 The TRS R consists of the following rules: 238.90/61.56 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.56 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.56 238.90/61.56 Q is empty. 238.90/61.56 We have to consider all minimal (P,Q,R)-chains. 238.90/61.56 ---------------------------------------- 238.90/61.56 238.90/61.56 (22) QDPOrderProof (EQUIVALENT) 238.90/61.56 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.56 238.90/61.56 238.90/61.56 The following pairs can be oriented strictly and are deleted. 238.90/61.56 238.90/61.56 1^1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1^1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 The remaining pairs can at least be oriented weakly. 238.90/61.56 Used ordering: Polynomial interpretation [POLO]: 238.90/61.56 238.90/61.56 POL(0(x_1)) = 1 238.90/61.56 POL(1(x_1)) = 0 238.90/61.56 POL(1^1(x_1)) = x_1 238.90/61.56 POL(2(x_1)) = 1 238.90/61.56 POL(3(x_1)) = 0 238.90/61.56 POL(4(x_1)) = 1 238.90/61.56 POL(5(x_1)) = 0 238.90/61.56 238.90/61.56 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.56 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 238.90/61.56 238.90/61.56 ---------------------------------------- 238.90/61.56 238.90/61.56 (23) 238.90/61.56 Obligation: 238.90/61.56 Q DP problem: 238.90/61.56 The TRS P consists of the following rules: 238.90/61.56 238.90/61.56 1^1(3(1(1(0(4(x1)))))) -> 1^1(3(0(2(0(4(x1)))))) 238.90/61.56 1^1(4(0(4(x1)))) -> 1^1(2(3(1(x1)))) 238.90/61.56 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 238.90/61.56 The TRS R consists of the following rules: 238.90/61.56 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.56 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.56 238.90/61.56 Q is empty. 238.90/61.56 We have to consider all minimal (P,Q,R)-chains. 238.90/61.56 ---------------------------------------- 238.90/61.56 238.90/61.56 (24) QDPOrderProof (EQUIVALENT) 238.90/61.56 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.56 238.90/61.56 238.90/61.56 The following pairs can be oriented strictly and are deleted. 238.90/61.56 238.90/61.56 1^1(4(0(4(x1)))) -> 1^1(2(3(1(x1)))) 238.90/61.56 The remaining pairs can at least be oriented weakly. 238.90/61.56 Used ordering: Polynomial interpretation [POLO]: 238.90/61.56 238.90/61.56 POL(0(x_1)) = 1 238.90/61.56 POL(1(x_1)) = x_1 238.90/61.56 POL(1^1(x_1)) = x_1 238.90/61.56 POL(2(x_1)) = 0 238.90/61.56 POL(3(x_1)) = 0 238.90/61.56 POL(4(x_1)) = x_1 238.90/61.56 POL(5(x_1)) = 1 238.90/61.56 238.90/61.56 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.56 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 238.90/61.56 238.90/61.56 ---------------------------------------- 238.90/61.56 238.90/61.56 (25) 238.90/61.56 Obligation: 238.90/61.56 Q DP problem: 238.90/61.56 The TRS P consists of the following rules: 238.90/61.56 238.90/61.56 1^1(3(1(1(0(4(x1)))))) -> 1^1(3(0(2(0(4(x1)))))) 238.90/61.56 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 238.90/61.56 The TRS R consists of the following rules: 238.90/61.56 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.56 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.56 238.90/61.56 Q is empty. 238.90/61.56 We have to consider all minimal (P,Q,R)-chains. 238.90/61.56 ---------------------------------------- 238.90/61.56 238.90/61.56 (26) QDPOrderProof (EQUIVALENT) 238.90/61.56 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.56 238.90/61.56 238.90/61.56 The following pairs can be oriented strictly and are deleted. 238.90/61.56 238.90/61.56 1^1(3(1(1(0(4(x1)))))) -> 1^1(3(0(2(0(4(x1)))))) 238.90/61.56 The remaining pairs can at least be oriented weakly. 238.90/61.56 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 238.90/61.56 238.90/61.56 POL( 1^1_1(x_1) ) = max{0, 2x_1 - 1} 238.90/61.56 POL( 2_1(x_1) ) = max{0, 2x_1 - 2} 238.90/61.56 POL( 4_1(x_1) ) = 1 238.90/61.56 POL( 5_1(x_1) ) = 2 238.90/61.56 POL( 3_1(x_1) ) = max{0, 2x_1 - 1} 238.90/61.56 POL( 1_1(x_1) ) = 1 238.90/61.56 POL( 0_1(x_1) ) = max{0, -2} 238.90/61.56 238.90/61.56 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.56 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 238.90/61.56 238.90/61.56 ---------------------------------------- 238.90/61.56 238.90/61.56 (27) 238.90/61.56 Obligation: 238.90/61.56 Q DP problem: 238.90/61.56 The TRS P consists of the following rules: 238.90/61.56 238.90/61.56 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 238.90/61.56 The TRS R consists of the following rules: 238.90/61.56 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.56 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.56 238.90/61.56 Q is empty. 238.90/61.56 We have to consider all minimal (P,Q,R)-chains. 238.90/61.56 ---------------------------------------- 238.90/61.56 238.90/61.56 (28) QDPOrderProof (EQUIVALENT) 238.90/61.56 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.56 238.90/61.56 238.90/61.56 The following pairs can be oriented strictly and are deleted. 238.90/61.56 238.90/61.56 1^1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1^1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 The remaining pairs can at least be oriented weakly. 238.90/61.56 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 238.90/61.56 238.90/61.56 POL( 1^1_1(x_1) ) = max{0, x_1 - 2} 238.90/61.56 POL( 2_1(x_1) ) = max{0, x_1 - 1} 238.90/61.56 POL( 4_1(x_1) ) = 1 238.90/61.56 POL( 5_1(x_1) ) = 2x_1 + 1 238.90/61.56 POL( 3_1(x_1) ) = 2x_1 238.90/61.56 POL( 1_1(x_1) ) = 1 238.90/61.56 POL( 0_1(x_1) ) = max{0, x_1 - 1} 238.90/61.56 238.90/61.56 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.56 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.56 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 238.90/61.56 238.90/61.56 ---------------------------------------- 238.90/61.56 238.90/61.56 (29) 238.90/61.56 Obligation: 238.90/61.56 Q DP problem: 238.90/61.56 P is empty. 238.90/61.56 The TRS R consists of the following rules: 238.90/61.56 238.90/61.56 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.56 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.56 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.56 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.56 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.56 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.56 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.56 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.56 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.56 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.56 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.56 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.56 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.56 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.56 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.56 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 Q is empty. 238.90/61.57 We have to consider all minimal (P,Q,R)-chains. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (30) PisEmptyProof (EQUIVALENT) 238.90/61.57 The TRS P is empty. Hence, there is no (P,Q,R) chain. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (31) 238.90/61.57 YES 238.90/61.57 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (32) 238.90/61.57 Obligation: 238.90/61.57 Q DP problem: 238.90/61.57 The TRS P consists of the following rules: 238.90/61.57 238.90/61.57 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(4(2(3(4(2(2(x1))))))) 238.90/61.57 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 4^1(4(1(4(0(0(1(3(x1)))))))) -> 4^1(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 0^1(0(1(1(x1)))) -> 2^1(2(1(3(x1)))) 238.90/61.57 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4^1(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 238.90/61.57 The TRS R consists of the following rules: 238.90/61.57 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 Q is empty. 238.90/61.57 We have to consider all minimal (P,Q,R)-chains. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (33) QDPOrderProof (EQUIVALENT) 238.90/61.57 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.57 238.90/61.57 238.90/61.57 The following pairs can be oriented strictly and are deleted. 238.90/61.57 238.90/61.57 4^1(4(1(4(0(0(1(3(x1)))))))) -> 4^1(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4^1(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4^1(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 The remaining pairs can at least be oriented weakly. 238.90/61.57 Used ordering: Polynomial interpretation [POLO]: 238.90/61.57 238.90/61.57 POL(0(x_1)) = 0 238.90/61.57 POL(0^1(x_1)) = 0 238.90/61.57 POL(1(x_1)) = 0 238.90/61.57 POL(2(x_1)) = 1 + x_1 238.90/61.57 POL(2^1(x_1)) = 0 238.90/61.57 POL(3(x_1)) = 0 238.90/61.57 POL(4(x_1)) = 1 238.90/61.57 POL(4^1(x_1)) = x_1 238.90/61.57 POL(5(x_1)) = x_1 238.90/61.57 238.90/61.57 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.57 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 238.90/61.57 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (34) 238.90/61.57 Obligation: 238.90/61.57 Q DP problem: 238.90/61.57 The TRS P consists of the following rules: 238.90/61.57 238.90/61.57 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(4(2(3(4(2(2(x1))))))) 238.90/61.57 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 0^1(0(1(1(x1)))) -> 2^1(2(1(3(x1)))) 238.90/61.57 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 The TRS R consists of the following rules: 238.90/61.57 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 Q is empty. 238.90/61.57 We have to consider all minimal (P,Q,R)-chains. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (35) QDPOrderProof (EQUIVALENT) 238.90/61.57 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.57 238.90/61.57 238.90/61.57 The following pairs can be oriented strictly and are deleted. 238.90/61.57 238.90/61.57 2^1(4(4(5(4(4(3(x1))))))) -> 2^1(4(2(3(4(2(2(x1))))))) 238.90/61.57 The remaining pairs can at least be oriented weakly. 238.90/61.57 Used ordering: Polynomial interpretation [POLO]: 238.90/61.57 238.90/61.57 POL(0(x_1)) = 0 238.90/61.57 POL(0^1(x_1)) = 0 238.90/61.57 POL(1(x_1)) = 0 238.90/61.57 POL(2(x_1)) = 0 238.90/61.57 POL(2^1(x_1)) = x_1 238.90/61.57 POL(3(x_1)) = 0 238.90/61.57 POL(4(x_1)) = x_1 238.90/61.57 POL(4^1(x_1)) = 0 238.90/61.57 POL(5(x_1)) = 1 238.90/61.57 238.90/61.57 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.57 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 238.90/61.57 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (36) 238.90/61.57 Obligation: 238.90/61.57 Q DP problem: 238.90/61.57 The TRS P consists of the following rules: 238.90/61.57 238.90/61.57 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 0^1(0(1(1(x1)))) -> 2^1(2(1(3(x1)))) 238.90/61.57 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 The TRS R consists of the following rules: 238.90/61.57 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 Q is empty. 238.90/61.57 We have to consider all minimal (P,Q,R)-chains. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (37) QDPOrderProof (EQUIVALENT) 238.90/61.57 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.57 238.90/61.57 238.90/61.57 The following pairs can be oriented strictly and are deleted. 238.90/61.57 238.90/61.57 2^1(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4^1(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 The remaining pairs can at least be oriented weakly. 238.90/61.57 Used ordering: Polynomial interpretation [POLO]: 238.90/61.57 238.90/61.57 POL(0(x_1)) = 0 238.90/61.57 POL(0^1(x_1)) = 0 238.90/61.57 POL(1(x_1)) = 0 238.90/61.57 POL(2(x_1)) = x_1 238.90/61.57 POL(2^1(x_1)) = x_1 238.90/61.57 POL(3(x_1)) = 0 238.90/61.57 POL(4(x_1)) = x_1 238.90/61.57 POL(4^1(x_1)) = 0 238.90/61.57 POL(5(x_1)) = 1 + x_1 238.90/61.57 238.90/61.57 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.57 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 238.90/61.57 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (38) 238.90/61.57 Obligation: 238.90/61.57 Q DP problem: 238.90/61.57 The TRS P consists of the following rules: 238.90/61.57 238.90/61.57 4^1(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0^1(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 0^1(0(1(1(x1)))) -> 2^1(2(1(3(x1)))) 238.90/61.57 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0^1(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2^1(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 The TRS R consists of the following rules: 238.90/61.57 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 Q is empty. 238.90/61.57 We have to consider all minimal (P,Q,R)-chains. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (39) DependencyGraphProof (EQUIVALENT) 238.90/61.57 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (40) 238.90/61.57 Obligation: 238.90/61.57 Q DP problem: 238.90/61.57 The TRS P consists of the following rules: 238.90/61.57 238.90/61.57 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 238.90/61.57 The TRS R consists of the following rules: 238.90/61.57 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 Q is empty. 238.90/61.57 We have to consider all minimal (P,Q,R)-chains. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (41) QDPOrderProof (EQUIVALENT) 238.90/61.57 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.57 238.90/61.57 238.90/61.57 The following pairs can be oriented strictly and are deleted. 238.90/61.57 238.90/61.57 0^1(4(5(2(1(2(0(1(x1)))))))) -> 0^1(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 The remaining pairs can at least be oriented weakly. 238.90/61.57 Used ordering: Polynomial interpretation [POLO]: 238.90/61.57 238.90/61.57 POL(0(x_1)) = 1 238.90/61.57 POL(0^1(x_1)) = x_1 238.90/61.57 POL(1(x_1)) = 0 238.90/61.57 POL(2(x_1)) = 1 238.90/61.57 POL(3(x_1)) = 0 238.90/61.57 POL(4(x_1)) = 1 238.90/61.57 POL(5(x_1)) = 1 238.90/61.57 238.90/61.57 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.57 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 238.90/61.57 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (42) 238.90/61.57 Obligation: 238.90/61.57 Q DP problem: 238.90/61.57 The TRS P consists of the following rules: 238.90/61.57 238.90/61.57 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 238.90/61.57 The TRS R consists of the following rules: 238.90/61.57 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 Q is empty. 238.90/61.57 We have to consider all minimal (P,Q,R)-chains. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (43) QDPOrderProof (EQUIVALENT) 238.90/61.57 We use the reduction pair processor [LPAR04,JAR06]. 238.90/61.57 238.90/61.57 238.90/61.57 The following pairs can be oriented strictly and are deleted. 238.90/61.57 238.90/61.57 0^1(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0^1(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 The remaining pairs can at least be oriented weakly. 238.90/61.57 Used ordering: Polynomial interpretation [POLO]: 238.90/61.57 238.90/61.57 POL(0(x_1)) = 0 238.90/61.57 POL(0^1(x_1)) = x_1 238.90/61.57 POL(1(x_1)) = 0 238.90/61.57 POL(2(x_1)) = 0 238.90/61.57 POL(3(x_1)) = 0 238.90/61.57 POL(4(x_1)) = 0 238.90/61.57 POL(5(x_1)) = 1 238.90/61.57 238.90/61.57 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 238.90/61.57 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 238.90/61.57 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (44) 238.90/61.57 Obligation: 238.90/61.57 Q DP problem: 238.90/61.57 P is empty. 238.90/61.57 The TRS R consists of the following rules: 238.90/61.57 238.90/61.57 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 238.90/61.57 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 238.90/61.57 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 238.90/61.57 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 238.90/61.57 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 238.90/61.57 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) 238.90/61.57 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 238.90/61.57 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 238.90/61.57 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 238.90/61.57 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 238.90/61.57 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 238.90/61.57 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 238.90/61.57 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 238.90/61.57 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 238.90/61.57 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 238.90/61.57 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 238.90/61.57 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 238.90/61.57 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) -> 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 238.90/61.57 238.90/61.57 Q is empty. 238.90/61.57 We have to consider all minimal (P,Q,R)-chains. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (45) PisEmptyProof (EQUIVALENT) 238.90/61.57 The TRS P is empty. Hence, there is no (P,Q,R) chain. 238.90/61.57 ---------------------------------------- 238.90/61.57 238.90/61.57 (46) 238.90/61.57 YES 238.90/61.64 EOF