403.94/111.63 YES 405.72/112.09 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 405.72/112.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 405.72/112.09 405.72/112.09 405.72/112.09 Termination w.r.t. Q of the given QTRS could be proven: 405.72/112.09 405.72/112.09 (0) QTRS 405.72/112.09 (1) QTRSRRRProof [EQUIVALENT, 220 ms] 405.72/112.09 (2) QTRS 405.72/112.09 (3) DependencyPairsProof [EQUIVALENT, 1276 ms] 405.72/112.09 (4) QDP 405.72/112.09 (5) QDPOrderProof [EQUIVALENT, 1842 ms] 405.72/112.09 (6) QDP 405.72/112.09 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 405.72/112.09 (8) AND 405.72/112.09 (9) QDP 405.72/112.09 (10) QDPOrderProof [EQUIVALENT, 0 ms] 405.72/112.09 (11) QDP 405.72/112.09 (12) DependencyGraphProof [EQUIVALENT, 0 ms] 405.72/112.09 (13) QDP 405.72/112.09 (14) QDPOrderProof [EQUIVALENT, 51 ms] 405.72/112.09 (15) QDP 405.72/112.09 (16) QDPOrderProof [EQUIVALENT, 6193 ms] 405.72/112.09 (17) QDP 405.72/112.09 (18) PisEmptyProof [EQUIVALENT, 0 ms] 405.72/112.09 (19) YES 405.72/112.09 (20) QDP 405.72/112.09 (21) QDPOrderProof [EQUIVALENT, 0 ms] 405.72/112.09 (22) QDP 405.72/112.09 (23) QDPOrderProof [EQUIVALENT, 52 ms] 405.72/112.09 (24) QDP 405.72/112.09 (25) PisEmptyProof [EQUIVALENT, 0 ms] 405.72/112.09 (26) YES 405.72/112.09 (27) QDP 405.72/112.09 (28) QDPOrderProof [EQUIVALENT, 0 ms] 405.72/112.09 (29) QDP 405.72/112.09 (30) QDPOrderProof [EQUIVALENT, 34 ms] 405.72/112.09 (31) QDP 405.72/112.09 (32) QDPOrderProof [EQUIVALENT, 44 ms] 405.72/112.09 (33) QDP 405.72/112.09 (34) PisEmptyProof [EQUIVALENT, 0 ms] 405.72/112.09 (35) YES 405.72/112.09 (36) QDP 405.72/112.09 (37) QDPOrderProof [EQUIVALENT, 0 ms] 405.72/112.09 (38) QDP 405.72/112.09 (39) QDPOrderProof [EQUIVALENT, 41 ms] 405.72/112.09 (40) QDP 405.72/112.09 (41) QDPOrderProof [EQUIVALENT, 0 ms] 405.72/112.09 (42) QDP 405.72/112.09 (43) PisEmptyProof [EQUIVALENT, 0 ms] 405.72/112.09 (44) YES 405.72/112.09 (45) QDP 405.72/112.09 (46) QDPOrderProof [EQUIVALENT, 0 ms] 405.72/112.09 (47) QDP 405.72/112.09 (48) QDPOrderProof [EQUIVALENT, 50 ms] 405.72/112.09 (49) QDP 405.72/112.09 (50) QDPOrderProof [EQUIVALENT, 0 ms] 405.72/112.09 (51) QDP 405.72/112.09 (52) QDPOrderProof [EQUIVALENT, 1839 ms] 405.72/112.09 (53) QDP 405.72/112.09 (54) PisEmptyProof [EQUIVALENT, 0 ms] 405.72/112.09 (55) YES 405.72/112.09 405.72/112.09 405.72/112.09 ---------------------------------------- 405.72/112.09 405.72/112.09 (0) 405.72/112.09 Obligation: 405.72/112.09 Q restricted rewrite system: 405.72/112.09 The TRS R consists of the following rules: 405.72/112.09 405.72/112.09 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.09 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.09 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.09 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.09 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.09 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.09 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.09 3(2(3(1(2(2(2(4(3(5(x1)))))))))) -> 5(3(4(4(4(4(0(4(0(x1))))))))) 405.72/112.09 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.09 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.09 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.09 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.09 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.09 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.09 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.10 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.10 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.10 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.10 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.10 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.10 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.10 4(2(3(1(4(3(0(3(1(1(5(0(4(1(3(4(3(1(4(4(x1)))))))))))))))))))) -> 4(1(4(4(2(5(5(1(5(4(5(5(2(0(5(0(2(0(5(x1))))))))))))))))))) 405.72/112.10 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.10 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.10 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.10 405.72/112.10 Q is empty. 405.72/112.10 405.72/112.10 ---------------------------------------- 405.72/112.10 405.72/112.10 (1) QTRSRRRProof (EQUIVALENT) 405.72/112.10 Used ordering: 405.72/112.10 Polynomial interpretation [POLO]: 405.72/112.10 405.72/112.10 POL(0(x_1)) = 1 + x_1 405.72/112.10 POL(1(x_1)) = 1 + x_1 405.72/112.10 POL(2(x_1)) = 1 + x_1 405.72/112.10 POL(3(x_1)) = 1 + x_1 405.72/112.10 POL(4(x_1)) = 1 + x_1 405.72/112.10 POL(5(x_1)) = 1 + x_1 405.72/112.10 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 405.72/112.10 405.72/112.10 3(2(3(1(2(2(2(4(3(5(x1)))))))))) -> 5(3(4(4(4(4(0(4(0(x1))))))))) 405.72/112.10 4(2(3(1(4(3(0(3(1(1(5(0(4(1(3(4(3(1(4(4(x1)))))))))))))))))))) -> 4(1(4(4(2(5(5(1(5(4(5(5(2(0(5(0(2(0(5(x1))))))))))))))))))) 405.72/112.10 405.72/112.10 405.72/112.10 405.72/112.10 405.72/112.10 ---------------------------------------- 405.72/112.10 405.72/112.10 (2) 405.72/112.10 Obligation: 405.72/112.10 Q restricted rewrite system: 405.72/112.10 The TRS R consists of the following rules: 405.72/112.10 405.72/112.10 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.10 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.10 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.10 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.10 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.10 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.10 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.10 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.10 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.10 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.10 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.10 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.10 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.10 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.10 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.10 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.10 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.10 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.10 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.10 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.10 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.10 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.10 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.10 405.72/112.10 Q is empty. 405.72/112.10 405.72/112.10 ---------------------------------------- 405.72/112.10 405.72/112.10 (3) DependencyPairsProof (EQUIVALENT) 405.72/112.10 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 405.72/112.10 ---------------------------------------- 405.72/112.10 405.72/112.10 (4) 405.72/112.10 Obligation: 405.72/112.10 Q DP problem: 405.72/112.10 The TRS P consists of the following rules: 405.72/112.10 405.72/112.10 0^1(0(1(2(x1)))) -> 0^1(3(4(2(x1)))) 405.72/112.10 0^1(0(1(2(x1)))) -> 3^1(4(2(x1))) 405.72/112.10 0^1(0(1(2(x1)))) -> 4^1(2(x1)) 405.72/112.10 2^1(0(1(0(5(3(x1)))))) -> 2^1(0(3(1(3(3(x1)))))) 405.72/112.10 2^1(0(1(0(5(3(x1)))))) -> 0^1(3(1(3(3(x1))))) 405.72/112.10 2^1(0(1(0(5(3(x1)))))) -> 3^1(1(3(3(x1)))) 405.72/112.10 2^1(0(1(0(5(3(x1)))))) -> 1^1(3(3(x1))) 405.72/112.10 2^1(0(1(0(5(3(x1)))))) -> 3^1(3(x1)) 405.72/112.10 4^1(1(1(5(0(4(x1)))))) -> 4^1(4(2(2(0(4(x1)))))) 405.72/112.10 4^1(1(1(5(0(4(x1)))))) -> 4^1(2(2(0(4(x1))))) 405.72/112.10 4^1(1(1(5(0(4(x1)))))) -> 2^1(2(0(4(x1)))) 405.72/112.10 4^1(1(1(5(0(4(x1)))))) -> 2^1(0(4(x1))) 405.72/112.10 2^1(3(2(5(5(0(0(0(x1)))))))) -> 0^1(2(1(4(2(5(3(2(x1)))))))) 405.72/112.10 2^1(3(2(5(5(0(0(0(x1)))))))) -> 2^1(1(4(2(5(3(2(x1))))))) 405.72/112.10 2^1(3(2(5(5(0(0(0(x1)))))))) -> 1^1(4(2(5(3(2(x1)))))) 405.72/112.10 2^1(3(2(5(5(0(0(0(x1)))))))) -> 4^1(2(5(3(2(x1))))) 405.72/112.10 2^1(3(2(5(5(0(0(0(x1)))))))) -> 2^1(5(3(2(x1)))) 405.72/112.10 2^1(3(2(5(5(0(0(0(x1)))))))) -> 5^1(3(2(x1))) 405.72/112.10 2^1(3(2(5(5(0(0(0(x1)))))))) -> 3^1(2(x1)) 405.72/112.10 2^1(3(2(5(5(0(0(0(x1)))))))) -> 2^1(x1) 405.72/112.10 5^1(0(0(5(3(3(4(3(x1)))))))) -> 5^1(3(1(3(0(3(0(3(x1)))))))) 405.72/112.10 5^1(0(0(5(3(3(4(3(x1)))))))) -> 3^1(1(3(0(3(0(3(x1))))))) 405.72/112.10 5^1(0(0(5(3(3(4(3(x1)))))))) -> 1^1(3(0(3(0(3(x1)))))) 405.72/112.10 5^1(0(0(5(3(3(4(3(x1)))))))) -> 3^1(0(3(0(3(x1))))) 405.72/112.10 5^1(0(0(5(3(3(4(3(x1)))))))) -> 0^1(3(0(3(x1)))) 405.72/112.10 5^1(0(0(5(3(3(4(3(x1)))))))) -> 3^1(0(3(x1))) 405.72/112.10 5^1(0(0(5(3(3(4(3(x1)))))))) -> 0^1(3(x1)) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 4^1(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 3^1(1(0(4(1(0(3(3(x1)))))))) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 1^1(0(4(1(0(3(3(x1))))))) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 0^1(4(1(0(3(3(x1)))))) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 4^1(1(0(3(3(x1))))) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 1^1(0(3(3(x1)))) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 0^1(3(3(x1))) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 3^1(3(x1)) 405.72/112.10 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 3^1(x1) 405.72/112.10 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 4^1(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.10 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 4^1(5(3(1(2(3(4(2(x1)))))))) 405.72/112.10 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 5^1(3(1(2(3(4(2(x1))))))) 405.72/112.10 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 3^1(1(2(3(4(2(x1)))))) 405.72/112.10 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 1^1(2(3(4(2(x1))))) 405.72/112.10 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 2^1(3(4(2(x1)))) 405.72/112.10 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 3^1(4(2(x1))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(0(4(1(1(3(5(3(4(2(x1)))))))))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(4(1(1(3(5(3(4(2(x1))))))))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 4^1(1(1(3(5(3(4(2(x1)))))))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 1^1(1(3(5(3(4(2(x1))))))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 1^1(3(5(3(4(2(x1)))))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 3^1(5(3(4(2(x1))))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 5^1(3(4(2(x1)))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 3^1(4(2(x1))) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 4^1(2(x1)) 405.72/112.10 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 2^1(x1) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 2^1(2(3(3(3(3(0(1(1(3(4(x1))))))))))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 2^1(3(3(3(3(0(1(1(3(4(x1)))))))))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(3(3(3(0(1(1(3(4(x1))))))))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(3(3(0(1(1(3(4(x1)))))))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(3(0(1(1(3(4(x1))))))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(0(1(1(3(4(x1)))))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 0^1(1(1(3(4(x1))))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(1(3(4(x1)))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(3(4(x1))) 405.72/112.10 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(4(x1)) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5^1(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 4^1(3(2(2(3(3(2(1(2(5(0(5(x1)))))))))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 3^1(2(2(3(3(2(1(2(5(0(5(x1))))))))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 2^1(2(3(3(2(1(2(5(0(5(x1)))))))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 2^1(3(3(2(1(2(5(0(5(x1))))))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 3^1(3(2(1(2(5(0(5(x1)))))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 3^1(2(1(2(5(0(5(x1))))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 2^1(1(2(5(0(5(x1)))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 1^1(2(5(0(5(x1))))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 2^1(5(0(5(x1)))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5^1(0(5(x1))) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 0^1(5(x1)) 405.72/112.10 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5^1(x1) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1^1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(4(0(4(1(4(0(3(2(4(1(0(2(4(x1)))))))))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 0^1(4(1(4(0(3(2(4(1(0(2(4(x1)))))))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(1(4(0(3(2(4(1(0(2(4(x1))))))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1^1(4(0(3(2(4(1(0(2(4(x1)))))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(0(3(2(4(1(0(2(4(x1))))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 0^1(3(2(4(1(0(2(4(x1)))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 3^1(2(4(1(0(2(4(x1))))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 2^1(4(1(0(2(4(x1)))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(1(0(2(4(x1))))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1^1(0(2(4(x1)))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 0^1(2(4(x1))) 405.72/112.10 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 2^1(4(x1)) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(5(4(2(0(1(5(1(1(4(1(0(3(4(x1)))))))))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 5^1(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 4^1(2(0(1(5(1(1(4(1(0(3(4(x1)))))))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(0(1(5(1(1(4(1(0(3(4(x1))))))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 0^1(1(5(1(1(4(1(0(3(4(x1)))))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 1^1(5(1(1(4(1(0(3(4(x1))))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 5^1(1(1(4(1(0(3(4(x1)))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 1^1(1(4(1(0(3(4(x1))))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 1^1(4(1(0(3(4(x1)))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 4^1(1(0(3(4(x1))))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 1^1(0(3(4(x1)))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 0^1(3(4(x1))) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 3^1(4(x1)) 405.72/112.10 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 4^1(x1) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(3(3(1(5(0(3(1(0(4(3(1(3(2(x1)))))))))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 3^1(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 3^1(1(5(0(3(1(0(4(3(1(3(2(x1)))))))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 1^1(5(0(3(1(0(4(3(1(3(2(x1))))))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(0(3(1(0(4(3(1(3(2(x1)))))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 0^1(3(1(0(4(3(1(3(2(x1))))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 3^1(1(0(4(3(1(3(2(x1)))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 1^1(0(4(3(1(3(2(x1))))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 0^1(4(3(1(3(2(x1)))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 4^1(3(1(3(2(x1))))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 3^1(1(3(2(x1)))) 405.72/112.10 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 1^1(3(2(x1))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2^1(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1))))))))))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2^1(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 3^1(3(5(4(3(5(4(5(5(0(0(3(1(x1))))))))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 3^1(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(4(3(5(4(5(5(0(0(3(1(x1))))))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 4^1(3(5(4(5(5(0(0(3(1(x1)))))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 3^1(5(4(5(5(0(0(3(1(x1))))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(4(5(5(0(0(3(1(x1)))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 4^1(5(5(0(0(3(1(x1))))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(5(0(0(3(1(x1)))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(0(0(3(1(x1))))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 0^1(0(3(1(x1)))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 0^1(3(1(x1))) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 3^1(1(x1)) 405.72/112.10 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 1^1(x1) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1)))))))))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 3^1(0(2(5(0(5(4(1(3(5(4(4(1(0(x1)))))))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 2^1(5(0(5(4(1(3(5(4(4(1(0(x1)))))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 5^1(0(5(4(1(3(5(4(4(1(0(x1))))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(5(4(1(3(5(4(4(1(0(x1)))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 5^1(4(1(3(5(4(4(1(0(x1))))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(1(3(5(4(4(1(0(x1)))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 1^1(3(5(4(4(1(0(x1))))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 3^1(5(4(4(1(0(x1)))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 5^1(4(4(1(0(x1))))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(4(1(0(x1)))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(1(0(x1))) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 1^1(0(x1)) 405.72/112.10 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(x1) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1)))))))))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 4^1(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 3^1(2(1(3(2(2(1(4(3(0(2(2(5(5(x1)))))))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 1^1(3(2(2(1(4(3(0(2(2(5(5(x1)))))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 3^1(2(2(1(4(3(0(2(2(5(5(x1))))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(2(1(4(3(0(2(2(5(5(x1)))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(1(4(3(0(2(2(5(5(x1))))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 1^1(4(3(0(2(2(5(5(x1)))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 4^1(3(0(2(2(5(5(x1))))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 3^1(0(2(2(5(5(x1)))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 0^1(2(2(5(5(x1))))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(2(5(5(x1)))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(5(5(x1))) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 5^1(5(x1)) 405.72/112.10 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 5^1(x1) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5^1(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 3^1(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1)))))))))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 1^1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 4^1(4(5(0(5(0(3(1(2(1(1(2(4(3(x1)))))))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 4^1(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5^1(0(5(0(3(1(2(1(1(2(4(3(x1)))))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 0^1(5(0(3(1(2(1(1(2(4(3(x1))))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5^1(0(3(1(2(1(1(2(4(3(x1)))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 0^1(3(1(2(1(1(2(4(3(x1))))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 3^1(1(2(1(1(2(4(3(x1)))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 1^1(2(1(1(2(4(3(x1))))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 2^1(1(1(2(4(3(x1)))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 1^1(1(2(4(3(x1))))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 1^1(2(4(3(x1)))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 2^1(4(3(x1))) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 4^1(3(x1)) 405.72/112.10 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 3^1(x1) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5^1(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5^1(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1))))))))))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 0^1(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 0^1(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1))))))))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(1(0(2(2(2(1(3(2(1(2(2(2(x1))))))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 0^1(2(2(2(1(3(2(1(2(2(2(x1))))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(2(2(1(3(2(1(2(2(2(x1)))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(2(1(3(2(1(2(2(2(x1))))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(1(3(2(1(2(2(2(x1)))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(3(2(1(2(2(2(x1))))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 3^1(2(1(2(2(2(x1)))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(1(2(2(2(x1))))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(2(2(2(x1)))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(2(2(x1))) 405.72/112.10 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(2(x1)) 405.72/112.10 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3^1(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.10 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 1^1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1)))))))))))))))))) 405.72/112.10 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 0^1(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))) 405.72/112.10 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3^1(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1)))))))))))))))) 405.72/112.10 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 4^1(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))) 405.72/112.10 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 2^1(2(1(0(1(5(2(0(5(4(4(2(1(4(x1)))))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 2^1(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 1^1(0(1(5(2(0(5(4(4(2(1(4(x1)))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 0^1(1(5(2(0(5(4(4(2(1(4(x1))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 1^1(5(2(0(5(4(4(2(1(4(x1)))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 5^1(2(0(5(4(4(2(1(4(x1))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 2^1(0(5(4(4(2(1(4(x1)))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 0^1(5(4(4(2(1(4(x1))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 5^1(4(4(2(1(4(x1)))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 4^1(4(2(1(4(x1))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 4^1(2(1(4(x1)))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 2^1(1(4(x1))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 1^1(4(x1)) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 3^1(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1))))))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 1^1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 4^1(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1))))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 2^1(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(2(4(5(0(2(3(0(5(2(1(5(1(x1))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 2^1(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 4^1(5(0(2(3(0(5(2(1(5(1(x1))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 5^1(0(2(3(0(5(2(1(5(1(x1)))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(2(3(0(5(2(1(5(1(x1))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 2^1(3(0(5(2(1(5(1(x1)))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 3^1(0(5(2(1(5(1(x1))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(5(2(1(5(1(x1)))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 5^1(2(1(5(1(x1))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 2^1(1(5(1(x1)))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 1^1(5(1(x1))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 0^1(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(5(5(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(2(4(2(0(3(5(1(0(3(2(x1))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 2^1(4(2(0(3(5(1(0(3(2(x1)))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 4^1(2(0(3(5(1(0(3(2(x1))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 2^1(0(3(5(1(0(3(2(x1)))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 0^1(3(5(1(0(3(2(x1))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(5(1(0(3(2(x1)))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(1(0(3(2(x1))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(0(3(2(x1)))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 0^1(3(2(x1))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(2(x1)) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 3^1(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 2^1(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 3^1(0(4(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 2^1(0(5(1(4(2(3(2(3(0(0(x1))))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(5(1(4(2(3(2(3(0(0(x1)))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 5^1(1(4(2(3(2(3(0(0(x1))))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 1^1(4(2(3(2(3(0(0(x1)))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(2(3(2(3(0(0(x1))))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 2^1(3(2(3(0(0(x1)))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 3^1(2(3(0(0(x1))))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 2^1(3(0(0(x1)))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 3^1(0(0(x1))) 405.72/112.11 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(0(x1)) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 1^1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 3^1(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(4(4(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(0(5(0(1(2(5(2(4(5(0(x1))))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 0^1(5(0(1(2(5(2(4(5(0(x1)))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(0(1(2(5(2(4(5(0(x1))))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 0^1(1(2(5(2(4(5(0(x1)))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 1^1(2(5(2(4(5(0(x1))))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(5(2(4(5(0(x1)))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(2(4(5(0(x1))))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(4(5(0(x1)))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(5(0(x1))) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(0(x1)) 405.72/112.11 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 0^1(x1) 405.72/112.11 405.72/112.11 The TRS R consists of the following rules: 405.72/112.11 405.72/112.11 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.11 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.11 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.11 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.11 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.11 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.11 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.11 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.11 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.11 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.11 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.11 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.11 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.11 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.11 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.11 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.11 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.11 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.11 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.11 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.11 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.11 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.11 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.11 405.72/112.11 Q is empty. 405.72/112.11 We have to consider all minimal (P,Q,R)-chains. 405.72/112.11 ---------------------------------------- 405.72/112.11 405.72/112.11 (5) QDPOrderProof (EQUIVALENT) 405.72/112.11 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.11 405.72/112.11 405.72/112.11 The following pairs can be oriented strictly and are deleted. 405.72/112.11 405.72/112.11 0^1(0(1(2(x1)))) -> 4^1(2(x1)) 405.72/112.11 2^1(0(1(0(5(3(x1)))))) -> 0^1(3(1(3(3(x1))))) 405.72/112.11 2^1(0(1(0(5(3(x1)))))) -> 3^1(1(3(3(x1)))) 405.72/112.11 2^1(0(1(0(5(3(x1)))))) -> 1^1(3(3(x1))) 405.72/112.11 2^1(0(1(0(5(3(x1)))))) -> 3^1(3(x1)) 405.72/112.11 4^1(1(1(5(0(4(x1)))))) -> 4^1(2(2(0(4(x1))))) 405.72/112.11 4^1(1(1(5(0(4(x1)))))) -> 2^1(2(0(4(x1)))) 405.72/112.11 4^1(1(1(5(0(4(x1)))))) -> 2^1(0(4(x1))) 405.72/112.11 2^1(3(2(5(5(0(0(0(x1)))))))) -> 0^1(2(1(4(2(5(3(2(x1)))))))) 405.72/112.11 2^1(3(2(5(5(0(0(0(x1)))))))) -> 2^1(1(4(2(5(3(2(x1))))))) 405.72/112.11 2^1(3(2(5(5(0(0(0(x1)))))))) -> 1^1(4(2(5(3(2(x1)))))) 405.72/112.11 2^1(3(2(5(5(0(0(0(x1)))))))) -> 4^1(2(5(3(2(x1))))) 405.72/112.11 2^1(3(2(5(5(0(0(0(x1)))))))) -> 2^1(5(3(2(x1)))) 405.72/112.11 2^1(3(2(5(5(0(0(0(x1)))))))) -> 5^1(3(2(x1))) 405.72/112.11 2^1(3(2(5(5(0(0(0(x1)))))))) -> 3^1(2(x1)) 405.72/112.11 2^1(3(2(5(5(0(0(0(x1)))))))) -> 2^1(x1) 405.72/112.11 5^1(0(0(5(3(3(4(3(x1)))))))) -> 1^1(3(0(3(0(3(x1)))))) 405.72/112.11 5^1(0(0(5(3(3(4(3(x1)))))))) -> 3^1(0(3(0(3(x1))))) 405.72/112.11 5^1(0(0(5(3(3(4(3(x1)))))))) -> 0^1(3(0(3(x1)))) 405.72/112.11 5^1(0(0(5(3(3(4(3(x1)))))))) -> 3^1(0(3(x1))) 405.72/112.11 5^1(0(0(5(3(3(4(3(x1)))))))) -> 0^1(3(x1)) 405.72/112.11 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 3^1(1(0(4(1(0(3(3(x1)))))))) 405.72/112.11 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 1^1(0(4(1(0(3(3(x1))))))) 405.72/112.11 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 0^1(4(1(0(3(3(x1)))))) 405.72/112.11 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 4^1(1(0(3(3(x1))))) 405.72/112.11 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 1^1(0(3(3(x1)))) 405.72/112.11 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 0^1(3(3(x1))) 405.72/112.11 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 3^1(3(x1)) 405.72/112.11 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 3^1(x1) 405.72/112.11 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 4^1(5(3(1(2(3(4(2(x1)))))))) 405.72/112.11 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 5^1(3(1(2(3(4(2(x1))))))) 405.72/112.11 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 3^1(1(2(3(4(2(x1)))))) 405.72/112.11 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 1^1(2(3(4(2(x1))))) 405.72/112.11 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 2^1(3(4(2(x1)))) 405.72/112.11 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 3^1(4(2(x1))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(0(4(1(1(3(5(3(4(2(x1)))))))))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(4(1(1(3(5(3(4(2(x1))))))))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 4^1(1(1(3(5(3(4(2(x1)))))))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 1^1(1(3(5(3(4(2(x1))))))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 1^1(3(5(3(4(2(x1)))))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 3^1(5(3(4(2(x1))))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 5^1(3(4(2(x1)))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 3^1(4(2(x1))) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 4^1(2(x1)) 405.72/112.11 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 2^1(x1) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 2^1(2(3(3(3(3(0(1(1(3(4(x1))))))))))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 2^1(3(3(3(3(0(1(1(3(4(x1)))))))))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(3(3(3(0(1(1(3(4(x1))))))))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(3(3(0(1(1(3(4(x1)))))))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(3(0(1(1(3(4(x1))))))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(0(1(1(3(4(x1)))))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 0^1(1(1(3(4(x1))))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(1(3(4(x1)))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(3(4(x1))) 405.72/112.11 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 3^1(4(x1)) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5^1(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 4^1(3(2(2(3(3(2(1(2(5(0(5(x1)))))))))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 3^1(2(2(3(3(2(1(2(5(0(5(x1))))))))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 2^1(2(3(3(2(1(2(5(0(5(x1)))))))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 2^1(3(3(2(1(2(5(0(5(x1))))))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 3^1(3(2(1(2(5(0(5(x1)))))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 3^1(2(1(2(5(0(5(x1))))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 2^1(1(2(5(0(5(x1)))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 1^1(2(5(0(5(x1))))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 2^1(5(0(5(x1)))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5^1(0(5(x1))) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 0^1(5(x1)) 405.72/112.11 4^1(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5^1(x1) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(4(0(4(1(4(0(3(2(4(1(0(2(4(x1)))))))))))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 0^1(4(1(4(0(3(2(4(1(0(2(4(x1)))))))))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(1(4(0(3(2(4(1(0(2(4(x1))))))))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1^1(4(0(3(2(4(1(0(2(4(x1)))))))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(0(3(2(4(1(0(2(4(x1))))))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 0^1(3(2(4(1(0(2(4(x1)))))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 3^1(2(4(1(0(2(4(x1))))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 2^1(4(1(0(2(4(x1)))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 4^1(1(0(2(4(x1))))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1^1(0(2(4(x1)))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 0^1(2(4(x1))) 405.72/112.11 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 2^1(4(x1)) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(5(4(2(0(1(5(1(1(4(1(0(3(4(x1)))))))))))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 5^1(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 4^1(2(0(1(5(1(1(4(1(0(3(4(x1)))))))))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(0(1(5(1(1(4(1(0(3(4(x1))))))))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 0^1(1(5(1(1(4(1(0(3(4(x1)))))))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 1^1(5(1(1(4(1(0(3(4(x1))))))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 5^1(1(1(4(1(0(3(4(x1)))))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 1^1(1(4(1(0(3(4(x1))))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 1^1(4(1(0(3(4(x1)))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 4^1(1(0(3(4(x1))))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 1^1(0(3(4(x1)))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 0^1(3(4(x1))) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 3^1(4(x1)) 405.72/112.11 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 4^1(x1) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(3(3(1(5(0(3(1(0(4(3(1(3(2(x1)))))))))))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 3^1(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 3^1(1(5(0(3(1(0(4(3(1(3(2(x1)))))))))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 1^1(5(0(3(1(0(4(3(1(3(2(x1))))))))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(0(3(1(0(4(3(1(3(2(x1)))))))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 0^1(3(1(0(4(3(1(3(2(x1))))))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 3^1(1(0(4(3(1(3(2(x1)))))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 1^1(0(4(3(1(3(2(x1))))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 0^1(4(3(1(3(2(x1)))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 4^1(3(1(3(2(x1))))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 3^1(1(3(2(x1)))) 405.72/112.11 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 1^1(3(2(x1))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1))))))))))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2^1(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 3^1(3(5(4(3(5(4(5(5(0(0(3(1(x1))))))))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 3^1(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(4(3(5(4(5(5(0(0(3(1(x1))))))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 4^1(3(5(4(5(5(0(0(3(1(x1)))))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 3^1(5(4(5(5(0(0(3(1(x1))))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(4(5(5(0(0(3(1(x1)))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 4^1(5(5(0(0(3(1(x1))))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(5(0(0(3(1(x1)))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 5^1(0(0(3(1(x1))))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 0^1(0(3(1(x1)))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 0^1(3(1(x1))) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 3^1(1(x1)) 405.72/112.11 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 1^1(x1) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 3^1(0(2(5(0(5(4(1(3(5(4(4(1(0(x1)))))))))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 2^1(5(0(5(4(1(3(5(4(4(1(0(x1)))))))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 5^1(0(5(4(1(3(5(4(4(1(0(x1))))))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(5(4(1(3(5(4(4(1(0(x1)))))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 5^1(4(1(3(5(4(4(1(0(x1))))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(1(3(5(4(4(1(0(x1)))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 1^1(3(5(4(4(1(0(x1))))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 3^1(5(4(4(1(0(x1)))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 5^1(4(4(1(0(x1))))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(4(1(0(x1)))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(1(0(x1))) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 1^1(0(x1)) 405.72/112.11 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(x1) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1)))))))))))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 4^1(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 3^1(2(1(3(2(2(1(4(3(0(2(2(5(5(x1)))))))))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 1^1(3(2(2(1(4(3(0(2(2(5(5(x1)))))))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 3^1(2(2(1(4(3(0(2(2(5(5(x1))))))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(2(1(4(3(0(2(2(5(5(x1)))))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(1(4(3(0(2(2(5(5(x1))))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 1^1(4(3(0(2(2(5(5(x1)))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 4^1(3(0(2(2(5(5(x1))))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 3^1(0(2(2(5(5(x1)))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 0^1(2(2(5(5(x1))))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(2(5(5(x1)))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(5(5(x1))) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 5^1(5(x1)) 405.72/112.11 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 5^1(x1) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5^1(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 3^1(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1)))))))))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 1^1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 4^1(4(5(0(5(0(3(1(2(1(1(2(4(3(x1)))))))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 4^1(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5^1(0(5(0(3(1(2(1(1(2(4(3(x1)))))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 0^1(5(0(3(1(2(1(1(2(4(3(x1))))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5^1(0(3(1(2(1(1(2(4(3(x1)))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 0^1(3(1(2(1(1(2(4(3(x1))))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 3^1(1(2(1(1(2(4(3(x1)))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 1^1(2(1(1(2(4(3(x1))))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 2^1(1(1(2(4(3(x1)))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 1^1(1(2(4(3(x1))))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 1^1(2(4(3(x1)))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 2^1(4(3(x1))) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 4^1(3(x1)) 405.72/112.11 2^1(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 3^1(x1) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5^1(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1))))))))))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 0^1(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 0^1(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1))))))))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(1(0(2(2(2(1(3(2(1(2(2(2(x1))))))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 0^1(2(2(2(1(3(2(1(2(2(2(x1))))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(2(2(1(3(2(1(2(2(2(x1)))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(2(1(3(2(1(2(2(2(x1))))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(1(3(2(1(2(2(2(x1)))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(3(2(1(2(2(2(x1))))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 3^1(2(1(2(2(2(x1)))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(1(2(2(2(x1))))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 1^1(2(2(2(x1)))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(2(2(x1))) 405.72/112.11 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 2^1(2(x1)) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 1^1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1)))))))))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 0^1(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3^1(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1)))))))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 4^1(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 2^1(2(1(0(1(5(2(0(5(4(4(2(1(4(x1)))))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 2^1(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 1^1(0(1(5(2(0(5(4(4(2(1(4(x1)))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 0^1(1(5(2(0(5(4(4(2(1(4(x1))))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 1^1(5(2(0(5(4(4(2(1(4(x1)))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 5^1(2(0(5(4(4(2(1(4(x1))))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 2^1(0(5(4(4(2(1(4(x1)))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 0^1(5(4(4(2(1(4(x1))))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 5^1(4(4(2(1(4(x1)))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 4^1(4(2(1(4(x1))))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 4^1(2(1(4(x1)))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 2^1(1(4(x1))) 405.72/112.11 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 1^1(4(x1)) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 1^1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 4^1(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1))))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 2^1(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1))))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(2(4(5(0(2(3(0(5(2(1(5(1(x1))))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 2^1(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 4^1(5(0(2(3(0(5(2(1(5(1(x1))))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 5^1(0(2(3(0(5(2(1(5(1(x1)))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(2(3(0(5(2(1(5(1(x1))))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 2^1(3(0(5(2(1(5(1(x1)))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 3^1(0(5(2(1(5(1(x1))))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(5(2(1(5(1(x1)))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 5^1(2(1(5(1(x1))))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 2^1(1(5(1(x1)))) 405.72/112.11 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 1^1(5(1(x1))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 0^1(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(5(5(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(3(2(4(2(0(3(5(1(0(3(2(x1)))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(2(4(2(0(3(5(1(0(3(2(x1))))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 2^1(4(2(0(3(5(1(0(3(2(x1)))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 4^1(2(0(3(5(1(0(3(2(x1))))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 2^1(0(3(5(1(0(3(2(x1)))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 0^1(3(5(1(0(3(2(x1))))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(5(1(0(3(2(x1)))))) 405.72/112.11 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 5^1(1(0(3(2(x1))))) 405.72/112.12 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(0(3(2(x1)))) 405.72/112.12 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 0^1(3(2(x1))) 405.72/112.12 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 3^1(2(x1)) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 3^1(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 2^1(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 3^1(0(4(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(2(0(5(1(4(2(3(2(3(0(0(x1)))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 2^1(0(5(1(4(2(3(2(3(0(0(x1))))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(5(1(4(2(3(2(3(0(0(x1)))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 5^1(1(4(2(3(2(3(0(0(x1))))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 1^1(4(2(3(2(3(0(0(x1)))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(2(3(2(3(0(0(x1))))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 2^1(3(2(3(0(0(x1)))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 3^1(2(3(0(0(x1))))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 2^1(3(0(0(x1)))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 3^1(0(0(x1))) 405.72/112.12 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 0^1(0(x1)) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 1^1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 3^1(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(4(4(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(0(5(0(1(2(5(2(4(5(0(x1)))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(0(5(0(1(2(5(2(4(5(0(x1))))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 0^1(5(0(1(2(5(2(4(5(0(x1)))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(0(1(2(5(2(4(5(0(x1))))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 0^1(1(2(5(2(4(5(0(x1)))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 1^1(2(5(2(4(5(0(x1))))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(5(2(4(5(0(x1)))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(2(4(5(0(x1))))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 2^1(4(5(0(x1)))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(5(0(x1))) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 5^1(0(x1)) 405.72/112.12 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 0^1(x1) 405.72/112.12 The remaining pairs can at least be oriented weakly. 405.72/112.12 Used ordering: Polynomial interpretation [POLO]: 405.72/112.12 405.72/112.12 POL(0(x_1)) = 1 + x_1 405.72/112.12 POL(0^1(x_1)) = x_1 405.72/112.12 POL(1(x_1)) = 1 + x_1 405.72/112.12 POL(1^1(x_1)) = 1 + x_1 405.72/112.12 POL(2(x_1)) = 1 + x_1 405.72/112.12 POL(2^1(x_1)) = 1 + x_1 405.72/112.12 POL(3(x_1)) = 1 + x_1 405.72/112.12 POL(3^1(x_1)) = 1 + x_1 405.72/112.12 POL(4(x_1)) = 1 + x_1 405.72/112.12 POL(4^1(x_1)) = 1 + x_1 405.72/112.12 POL(5(x_1)) = 1 + x_1 405.72/112.12 POL(5^1(x_1)) = x_1 405.72/112.12 405.72/112.12 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.12 405.72/112.12 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.12 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.12 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.12 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.12 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.12 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.12 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.12 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.12 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.12 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.12 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.12 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.12 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.12 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.12 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.12 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.12 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.12 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.12 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.12 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.12 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.12 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.12 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.12 405.72/112.12 405.72/112.12 ---------------------------------------- 405.72/112.12 405.72/112.12 (6) 405.72/112.12 Obligation: 405.72/112.12 Q DP problem: 405.72/112.12 The TRS P consists of the following rules: 405.72/112.12 405.72/112.12 0^1(0(1(2(x1)))) -> 0^1(3(4(2(x1)))) 405.72/112.12 0^1(0(1(2(x1)))) -> 3^1(4(2(x1))) 405.72/112.12 2^1(0(1(0(5(3(x1)))))) -> 2^1(0(3(1(3(3(x1)))))) 405.72/112.12 4^1(1(1(5(0(4(x1)))))) -> 4^1(4(2(2(0(4(x1)))))) 405.72/112.12 5^1(0(0(5(3(3(4(3(x1)))))))) -> 5^1(3(1(3(0(3(0(3(x1)))))))) 405.72/112.12 5^1(0(0(5(3(3(4(3(x1)))))))) -> 3^1(1(3(0(3(0(3(x1))))))) 405.72/112.12 1^1(0(0(1(5(5(4(2(4(x1))))))))) -> 4^1(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.12 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 4^1(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.12 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.12 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.12 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1^1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2^1(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 4^1(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1)))))))))))))))) 405.72/112.13 1^1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2^1(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5^1(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3^1(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 3^1(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1))))))))))))))))))) 405.72/112.13 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2^1(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4^1(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (7) DependencyGraphProof (EQUIVALENT) 405.72/112.13 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 5 SCCs with 7 less nodes. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (8) 405.72/112.13 Complex Obligation (AND) 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (9) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 The TRS P consists of the following rules: 405.72/112.13 405.72/112.13 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3^1(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 4^1(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 4^1(1(1(5(0(4(x1)))))) -> 4^1(4(2(2(0(4(x1)))))) 405.72/112.13 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (10) QDPOrderProof (EQUIVALENT) 405.72/112.13 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.13 405.72/112.13 405.72/112.13 The following pairs can be oriented strictly and are deleted. 405.72/112.13 405.72/112.13 4^1(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3^1(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 The remaining pairs can at least be oriented weakly. 405.72/112.13 Used ordering: Polynomial interpretation [POLO]: 405.72/112.13 405.72/112.13 POL(0(x_1)) = 1 405.72/112.13 POL(1(x_1)) = x_1 405.72/112.13 POL(2(x_1)) = 1 405.72/112.13 POL(3(x_1)) = 0 405.72/112.13 POL(3^1(x_1)) = 0 405.72/112.13 POL(4(x_1)) = x_1 405.72/112.13 POL(4^1(x_1)) = x_1 405.72/112.13 POL(5(x_1)) = x_1 405.72/112.13 405.72/112.13 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.13 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (11) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 The TRS P consists of the following rules: 405.72/112.13 405.72/112.13 3^1(0(0(1(0(4(5(4(2(x1))))))))) -> 4^1(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 4^1(1(1(5(0(4(x1)))))) -> 4^1(4(2(2(0(4(x1)))))) 405.72/112.13 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (12) DependencyGraphProof (EQUIVALENT) 405.72/112.13 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (13) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 The TRS P consists of the following rules: 405.72/112.13 405.72/112.13 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 4^1(1(1(5(0(4(x1)))))) -> 4^1(4(2(2(0(4(x1)))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (14) QDPOrderProof (EQUIVALENT) 405.72/112.13 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.13 405.72/112.13 405.72/112.13 The following pairs can be oriented strictly and are deleted. 405.72/112.13 405.72/112.13 4^1(1(1(5(0(4(x1)))))) -> 4^1(4(2(2(0(4(x1)))))) 405.72/112.13 The remaining pairs can at least be oriented weakly. 405.72/112.13 Used ordering: Polynomial interpretation [POLO]: 405.72/112.13 405.72/112.13 POL(0(x_1)) = 0 405.72/112.13 POL(1(x_1)) = 1 405.72/112.13 POL(2(x_1)) = 0 405.72/112.13 POL(3(x_1)) = 0 405.72/112.13 POL(4(x_1)) = 0 405.72/112.13 POL(4^1(x_1)) = x_1 405.72/112.13 POL(5(x_1)) = 0 405.72/112.13 405.72/112.13 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.13 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (15) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 The TRS P consists of the following rules: 405.72/112.13 405.72/112.13 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (16) QDPOrderProof (EQUIVALENT) 405.72/112.13 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.13 405.72/112.13 405.72/112.13 The following pairs can be oriented strictly and are deleted. 405.72/112.13 405.72/112.13 4^1(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4^1(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 The remaining pairs can at least be oriented weakly. 405.72/112.13 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 405.72/112.13 405.72/112.13 POL( 4^1_1(x_1) ) = 2x_1 + 1 405.72/112.13 POL( 0_1(x_1) ) = 2 405.72/112.13 POL( 1_1(x_1) ) = max{0, -2} 405.72/112.13 POL( 2_1(x_1) ) = x_1 405.72/112.13 POL( 5_1(x_1) ) = max{0, 2x_1 - 2} 405.72/112.13 POL( 4_1(x_1) ) = max{0, x_1 - 1} 405.72/112.13 POL( 3_1(x_1) ) = max{0, 2x_1 - 2} 405.72/112.13 405.72/112.13 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.13 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (17) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 P is empty. 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (18) PisEmptyProof (EQUIVALENT) 405.72/112.13 The TRS P is empty. Hence, there is no (P,Q,R) chain. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (19) 405.72/112.13 YES 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (20) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 The TRS P consists of the following rules: 405.72/112.13 405.72/112.13 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 5^1(0(0(5(3(3(4(3(x1)))))))) -> 5^1(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5^1(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (21) QDPOrderProof (EQUIVALENT) 405.72/112.13 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.13 405.72/112.13 405.72/112.13 The following pairs can be oriented strictly and are deleted. 405.72/112.13 405.72/112.13 5^1(0(0(5(3(3(4(3(x1)))))))) -> 5^1(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 5^1(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5^1(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 The remaining pairs can at least be oriented weakly. 405.72/112.13 Used ordering: Polynomial interpretation [POLO]: 405.72/112.13 405.72/112.13 POL(0(x_1)) = 1 405.72/112.13 POL(1(x_1)) = 1 405.72/112.13 POL(2(x_1)) = 0 405.72/112.13 POL(3(x_1)) = 0 405.72/112.13 POL(4(x_1)) = 0 405.72/112.13 POL(5(x_1)) = 0 405.72/112.13 POL(5^1(x_1)) = x_1 405.72/112.13 405.72/112.13 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.13 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (22) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 The TRS P consists of the following rules: 405.72/112.13 405.72/112.13 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (23) QDPOrderProof (EQUIVALENT) 405.72/112.13 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.13 405.72/112.13 405.72/112.13 The following pairs can be oriented strictly and are deleted. 405.72/112.13 405.72/112.13 5^1(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5^1(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 The remaining pairs can at least be oriented weakly. 405.72/112.13 Used ordering: Polynomial interpretation [POLO]: 405.72/112.13 405.72/112.13 POL(0(x_1)) = 0 405.72/112.13 POL(1(x_1)) = 0 405.72/112.13 POL(2(x_1)) = 1 + x_1 405.72/112.13 POL(3(x_1)) = 0 405.72/112.13 POL(4(x_1)) = 0 405.72/112.13 POL(5(x_1)) = 1 405.72/112.13 POL(5^1(x_1)) = x_1 405.72/112.13 405.72/112.13 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.13 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (24) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 P is empty. 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (25) PisEmptyProof (EQUIVALENT) 405.72/112.13 The TRS P is empty. Hence, there is no (P,Q,R) chain. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (26) 405.72/112.13 YES 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (27) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 The TRS P consists of the following rules: 405.72/112.13 405.72/112.13 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 2^1(0(1(0(5(3(x1)))))) -> 2^1(0(3(1(3(3(x1)))))) 405.72/112.13 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2^1(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 Q is empty. 405.72/112.13 We have to consider all minimal (P,Q,R)-chains. 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (28) QDPOrderProof (EQUIVALENT) 405.72/112.13 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.13 405.72/112.13 405.72/112.13 The following pairs can be oriented strictly and are deleted. 405.72/112.13 405.72/112.13 2^1(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2^1(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 The remaining pairs can at least be oriented weakly. 405.72/112.13 Used ordering: Polynomial interpretation [POLO]: 405.72/112.13 405.72/112.13 POL(0(x_1)) = 0 405.72/112.13 POL(1(x_1)) = 1 405.72/112.13 POL(2(x_1)) = 0 405.72/112.13 POL(2^1(x_1)) = x_1 405.72/112.13 POL(3(x_1)) = 0 405.72/112.13 POL(4(x_1)) = 0 405.72/112.13 POL(5(x_1)) = 0 405.72/112.13 405.72/112.13 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.13 405.72/112.13 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.13 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.13 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.13 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.13 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.13 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.13 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.13 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.13 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.13 405.72/112.13 405.72/112.13 ---------------------------------------- 405.72/112.13 405.72/112.13 (29) 405.72/112.13 Obligation: 405.72/112.13 Q DP problem: 405.72/112.13 The TRS P consists of the following rules: 405.72/112.13 405.72/112.13 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.13 2^1(0(1(0(5(3(x1)))))) -> 2^1(0(3(1(3(3(x1)))))) 405.72/112.13 405.72/112.13 The TRS R consists of the following rules: 405.72/112.13 405.72/112.13 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.13 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.13 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.13 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.13 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.14 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.14 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.14 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.14 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.14 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.14 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.14 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.14 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.14 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.14 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.14 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.14 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.14 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.14 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.14 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.14 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.14 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.14 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.14 405.72/112.14 Q is empty. 405.72/112.14 We have to consider all minimal (P,Q,R)-chains. 405.72/112.14 ---------------------------------------- 405.72/112.14 405.72/112.14 (30) QDPOrderProof (EQUIVALENT) 405.72/112.14 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.14 405.72/112.14 405.72/112.14 The following pairs can be oriented strictly and are deleted. 405.72/112.14 405.72/112.14 2^1(0(1(0(5(3(x1)))))) -> 2^1(0(3(1(3(3(x1)))))) 405.72/112.14 The remaining pairs can at least be oriented weakly. 405.72/112.14 Used ordering: Polynomial interpretation [POLO]: 405.72/112.14 405.72/112.14 POL(0(x_1)) = x_1 405.72/112.14 POL(1(x_1)) = 1 405.72/112.14 POL(2(x_1)) = 0 405.72/112.14 POL(2^1(x_1)) = x_1 405.72/112.14 POL(3(x_1)) = 0 405.72/112.14 POL(4(x_1)) = 0 405.72/112.14 POL(5(x_1)) = 0 405.72/112.14 405.72/112.14 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.14 405.72/112.14 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.14 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.14 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.14 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.14 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.14 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.14 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.14 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.14 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.14 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.14 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.14 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.14 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.14 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.14 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.14 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.14 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.14 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.14 405.72/112.14 405.72/112.14 ---------------------------------------- 405.72/112.14 405.72/112.14 (31) 405.72/112.14 Obligation: 405.72/112.14 Q DP problem: 405.72/112.14 The TRS P consists of the following rules: 405.72/112.14 405.72/112.14 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.14 405.72/112.14 The TRS R consists of the following rules: 405.72/112.14 405.72/112.14 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.14 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.14 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.14 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.14 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.14 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.14 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.14 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.14 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.14 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.14 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.14 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.14 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.14 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.14 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.14 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.14 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.14 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.14 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.15 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.15 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.15 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.15 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.15 405.72/112.15 Q is empty. 405.72/112.15 We have to consider all minimal (P,Q,R)-chains. 405.72/112.15 ---------------------------------------- 405.72/112.15 405.72/112.15 (32) QDPOrderProof (EQUIVALENT) 405.72/112.15 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.15 405.72/112.15 405.72/112.15 The following pairs can be oriented strictly and are deleted. 405.72/112.15 405.72/112.15 2^1(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2^1(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.15 The remaining pairs can at least be oriented weakly. 405.72/112.15 Used ordering: Polynomial interpretation [POLO]: 405.72/112.15 405.72/112.15 POL(0(x_1)) = x_1 405.72/112.15 POL(1(x_1)) = 1 405.72/112.15 POL(2(x_1)) = 0 405.72/112.15 POL(2^1(x_1)) = x_1 405.72/112.15 POL(3(x_1)) = 0 405.72/112.15 POL(4(x_1)) = 0 405.72/112.15 POL(5(x_1)) = x_1 405.72/112.15 405.72/112.15 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.15 405.72/112.15 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.15 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.15 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.15 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.15 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.15 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.15 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.15 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.15 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.15 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.15 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.15 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.15 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.15 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.15 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.15 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.15 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.15 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.15 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.15 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.15 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.15 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.15 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.15 405.72/112.15 405.72/112.15 ---------------------------------------- 405.72/112.15 405.72/112.15 (33) 405.72/112.15 Obligation: 405.72/112.15 Q DP problem: 405.72/112.15 P is empty. 405.72/112.15 The TRS R consists of the following rules: 405.72/112.15 405.72/112.15 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.15 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.15 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.15 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.15 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.15 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.15 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.15 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.15 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.15 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.15 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.15 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.15 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.15 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.15 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.15 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.15 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.15 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.15 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.15 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.15 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.15 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.15 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.15 405.72/112.15 Q is empty. 405.72/112.15 We have to consider all minimal (P,Q,R)-chains. 405.72/112.15 ---------------------------------------- 405.72/112.15 405.72/112.15 (34) PisEmptyProof (EQUIVALENT) 405.72/112.15 The TRS P is empty. Hence, there is no (P,Q,R) chain. 405.72/112.15 ---------------------------------------- 405.72/112.15 405.72/112.15 (35) 405.72/112.15 YES 405.72/112.15 405.72/112.15 ---------------------------------------- 405.72/112.15 405.72/112.15 (36) 405.72/112.15 Obligation: 405.72/112.15 Q DP problem: 405.72/112.15 The TRS P consists of the following rules: 405.72/112.15 405.72/112.15 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1^1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.15 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.15 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.15 405.72/112.15 The TRS R consists of the following rules: 405.72/112.15 405.72/112.15 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.15 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.15 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.15 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.15 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.15 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.15 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.15 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.15 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.15 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.15 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.15 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.15 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.15 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.15 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.15 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.15 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.15 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.15 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.15 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.15 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.15 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.15 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.15 405.72/112.15 Q is empty. 405.72/112.15 We have to consider all minimal (P,Q,R)-chains. 405.72/112.15 ---------------------------------------- 405.72/112.15 405.72/112.15 (37) QDPOrderProof (EQUIVALENT) 405.72/112.15 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.15 405.72/112.15 405.72/112.15 The following pairs can be oriented strictly and are deleted. 405.72/112.15 405.72/112.15 1^1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1^1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.15 The remaining pairs can at least be oriented weakly. 405.72/112.15 Used ordering: Polynomial interpretation [POLO]: 405.72/112.15 405.72/112.15 POL(0(x_1)) = 1 405.72/112.15 POL(1(x_1)) = x_1 405.72/112.15 POL(1^1(x_1)) = x_1 405.72/112.15 POL(2(x_1)) = 1 405.72/112.15 POL(3(x_1)) = 0 405.72/112.15 POL(4(x_1)) = 0 405.72/112.15 POL(5(x_1)) = x_1 405.72/112.15 405.72/112.15 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.15 405.72/112.15 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.15 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.15 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.15 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.15 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.15 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.15 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.15 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.15 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.15 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.18 405.72/112.18 405.72/112.18 ---------------------------------------- 405.72/112.18 405.72/112.18 (38) 405.72/112.18 Obligation: 405.72/112.18 Q DP problem: 405.72/112.18 The TRS P consists of the following rules: 405.72/112.18 405.72/112.18 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.18 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.18 405.72/112.18 The TRS R consists of the following rules: 405.72/112.18 405.72/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.18 405.72/112.18 Q is empty. 405.72/112.18 We have to consider all minimal (P,Q,R)-chains. 405.72/112.18 ---------------------------------------- 405.72/112.18 405.72/112.18 (39) QDPOrderProof (EQUIVALENT) 405.72/112.18 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.18 405.72/112.18 405.72/112.18 The following pairs can be oriented strictly and are deleted. 405.72/112.18 405.72/112.18 1^1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1^1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.18 The remaining pairs can at least be oriented weakly. 405.72/112.18 Used ordering: Polynomial interpretation [POLO]: 405.72/112.18 405.72/112.18 POL(0(x_1)) = 1 405.72/112.18 POL(1(x_1)) = x_1 405.72/112.18 POL(1^1(x_1)) = x_1 405.72/112.18 POL(2(x_1)) = 1 405.72/112.18 POL(3(x_1)) = 0 405.72/112.18 POL(4(x_1)) = x_1 405.72/112.18 POL(5(x_1)) = x_1 405.72/112.18 405.72/112.18 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.18 405.72/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.18 405.72/112.18 405.72/112.18 ---------------------------------------- 405.72/112.18 405.72/112.18 (40) 405.72/112.18 Obligation: 405.72/112.18 Q DP problem: 405.72/112.18 The TRS P consists of the following rules: 405.72/112.18 405.72/112.18 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.18 405.72/112.18 The TRS R consists of the following rules: 405.72/112.18 405.72/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 405.72/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 405.72/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 405.72/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 405.72/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 405.72/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 405.72/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 405.72/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 405.72/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 405.72/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.18 405.72/112.18 Q is empty. 405.72/112.18 We have to consider all minimal (P,Q,R)-chains. 405.72/112.18 ---------------------------------------- 405.72/112.18 405.72/112.18 (41) QDPOrderProof (EQUIVALENT) 405.72/112.18 We use the reduction pair processor [LPAR04,JAR06]. 405.72/112.18 405.72/112.18 405.72/112.18 The following pairs can be oriented strictly and are deleted. 405.72/112.18 405.72/112.18 1^1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1^1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 405.72/112.18 The remaining pairs can at least be oriented weakly. 405.72/112.18 Used ordering: Polynomial interpretation [POLO]: 405.72/112.18 405.72/112.18 POL(0(x_1)) = 0 405.72/112.18 POL(1(x_1)) = 1 405.72/112.18 POL(1^1(x_1)) = x_1 405.72/112.18 POL(2(x_1)) = x_1 405.72/112.18 POL(3(x_1)) = 0 405.72/112.18 POL(4(x_1)) = 0 405.72/112.18 POL(5(x_1)) = x_1 405.72/112.18 405.72/112.18 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 405.72/112.18 405.72/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 405.72/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 405.72/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 405.72/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 405.72/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 405.72/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 405.72/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 405.72/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 405.72/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 405.72/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 405.72/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 405.72/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 405.72/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 405.72/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 406.06/112.18 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (42) 406.06/112.18 Obligation: 406.06/112.18 Q DP problem: 406.06/112.18 P is empty. 406.06/112.18 The TRS R consists of the following rules: 406.06/112.18 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 406.06/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 406.06/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 406.06/112.18 Q is empty. 406.06/112.18 We have to consider all minimal (P,Q,R)-chains. 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (43) PisEmptyProof (EQUIVALENT) 406.06/112.18 The TRS P is empty. Hence, there is no (P,Q,R) chain. 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (44) 406.06/112.18 YES 406.06/112.18 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (45) 406.06/112.18 Obligation: 406.06/112.18 Q DP problem: 406.06/112.18 The TRS P consists of the following rules: 406.06/112.18 406.06/112.18 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 0^1(0(1(2(x1)))) -> 0^1(3(4(2(x1)))) 406.06/112.18 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 406.06/112.18 The TRS R consists of the following rules: 406.06/112.18 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 406.06/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 406.06/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 406.06/112.18 Q is empty. 406.06/112.18 We have to consider all minimal (P,Q,R)-chains. 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (46) QDPOrderProof (EQUIVALENT) 406.06/112.18 We use the reduction pair processor [LPAR04,JAR06]. 406.06/112.18 406.06/112.18 406.06/112.18 The following pairs can be oriented strictly and are deleted. 406.06/112.18 406.06/112.18 0^1(0(1(2(x1)))) -> 0^1(3(4(2(x1)))) 406.06/112.18 The remaining pairs can at least be oriented weakly. 406.06/112.18 Used ordering: Polynomial interpretation [POLO]: 406.06/112.18 406.06/112.18 POL(0(x_1)) = 1 406.06/112.18 POL(0^1(x_1)) = x_1 406.06/112.18 POL(1(x_1)) = 1 + x_1 406.06/112.18 POL(2(x_1)) = 0 406.06/112.18 POL(3(x_1)) = 0 406.06/112.18 POL(4(x_1)) = 0 406.06/112.18 POL(5(x_1)) = 0 406.06/112.18 406.06/112.18 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 406.06/112.18 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 406.06/112.18 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (47) 406.06/112.18 Obligation: 406.06/112.18 Q DP problem: 406.06/112.18 The TRS P consists of the following rules: 406.06/112.18 406.06/112.18 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 406.06/112.18 The TRS R consists of the following rules: 406.06/112.18 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 406.06/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 406.06/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 406.06/112.18 Q is empty. 406.06/112.18 We have to consider all minimal (P,Q,R)-chains. 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (48) QDPOrderProof (EQUIVALENT) 406.06/112.18 We use the reduction pair processor [LPAR04,JAR06]. 406.06/112.18 406.06/112.18 406.06/112.18 The following pairs can be oriented strictly and are deleted. 406.06/112.18 406.06/112.18 0^1(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0^1(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 The remaining pairs can at least be oriented weakly. 406.06/112.18 Used ordering: Polynomial interpretation [POLO]: 406.06/112.18 406.06/112.18 POL(0(x_1)) = x_1 406.06/112.18 POL(0^1(x_1)) = x_1 406.06/112.18 POL(1(x_1)) = 1 406.06/112.18 POL(2(x_1)) = 0 406.06/112.18 POL(3(x_1)) = 0 406.06/112.18 POL(4(x_1)) = 0 406.06/112.18 POL(5(x_1)) = 0 406.06/112.18 406.06/112.18 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 406.06/112.18 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 406.06/112.18 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (49) 406.06/112.18 Obligation: 406.06/112.18 Q DP problem: 406.06/112.18 The TRS P consists of the following rules: 406.06/112.18 406.06/112.18 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 406.06/112.18 The TRS R consists of the following rules: 406.06/112.18 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 406.06/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 406.06/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 406.06/112.18 Q is empty. 406.06/112.18 We have to consider all minimal (P,Q,R)-chains. 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (50) QDPOrderProof (EQUIVALENT) 406.06/112.18 We use the reduction pair processor [LPAR04,JAR06]. 406.06/112.18 406.06/112.18 406.06/112.18 The following pairs can be oriented strictly and are deleted. 406.06/112.18 406.06/112.18 0^1(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0^1(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 The remaining pairs can at least be oriented weakly. 406.06/112.18 Used ordering: Polynomial interpretation [POLO]: 406.06/112.18 406.06/112.18 POL(0(x_1)) = 1 406.06/112.18 POL(0^1(x_1)) = x_1 406.06/112.18 POL(1(x_1)) = 1 406.06/112.18 POL(2(x_1)) = 1 406.06/112.18 POL(3(x_1)) = 0 406.06/112.18 POL(4(x_1)) = x_1 406.06/112.18 POL(5(x_1)) = x_1 406.06/112.18 406.06/112.18 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 406.06/112.18 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 406.06/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 406.06/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 406.06/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 406.06/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 406.06/112.18 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (51) 406.06/112.18 Obligation: 406.06/112.18 Q DP problem: 406.06/112.18 The TRS P consists of the following rules: 406.06/112.18 406.06/112.18 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 406.06/112.18 The TRS R consists of the following rules: 406.06/112.18 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 406.06/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 406.06/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 406.06/112.18 Q is empty. 406.06/112.18 We have to consider all minimal (P,Q,R)-chains. 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (52) QDPOrderProof (EQUIVALENT) 406.06/112.18 We use the reduction pair processor [LPAR04,JAR06]. 406.06/112.18 406.06/112.18 406.06/112.18 The following pairs can be oriented strictly and are deleted. 406.06/112.18 406.06/112.18 0^1(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0^1(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 The remaining pairs can at least be oriented weakly. 406.06/112.18 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 406.06/112.18 406.06/112.18 POL( 0^1_1(x_1) ) = max{0, 2x_1 - 2} 406.06/112.18 POL( 3_1(x_1) ) = max{0, x_1 - 2} 406.06/112.18 POL( 0_1(x_1) ) = 2 406.06/112.18 POL( 4_1(x_1) ) = max{0, -2} 406.06/112.18 POL( 5_1(x_1) ) = max{0, 2x_1 - 2} 406.06/112.18 POL( 2_1(x_1) ) = 2x_1 406.06/112.18 POL( 1_1(x_1) ) = 1 406.06/112.18 406.06/112.18 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 406.06/112.18 406.06/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 406.06/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 406.06/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 406.06/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 406.06/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 406.06/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 406.06/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 406.06/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 406.06/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 406.06/112.18 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (53) 406.06/112.18 Obligation: 406.06/112.18 Q DP problem: 406.06/112.18 P is empty. 406.06/112.18 The TRS R consists of the following rules: 406.06/112.18 406.06/112.18 0(0(1(2(x1)))) -> 0(3(4(2(x1)))) 406.06/112.18 2(0(1(0(5(3(x1)))))) -> 2(0(3(1(3(3(x1)))))) 406.06/112.18 4(1(1(5(0(4(x1)))))) -> 4(4(2(2(0(4(x1)))))) 406.06/112.18 2(3(2(5(5(0(0(0(x1)))))))) -> 0(2(1(4(2(5(3(2(x1)))))))) 406.06/112.18 5(0(0(5(3(3(4(3(x1)))))))) -> 5(3(1(3(0(3(0(3(x1)))))))) 406.06/112.18 1(0(0(1(5(5(4(2(4(x1))))))))) -> 4(3(1(0(4(1(0(3(3(x1))))))))) 406.06/112.18 3(0(0(1(0(4(5(4(2(x1))))))))) -> 4(4(5(3(1(2(3(4(2(x1))))))))) 406.06/112.18 0(0(1(2(5(1(4(4(5(5(4(x1))))))))))) -> 0(0(0(4(1(1(3(5(3(4(2(x1))))))))))) 406.06/112.18 1(5(2(2(5(1(1(2(4(4(5(4(x1)))))))))))) -> 1(2(2(3(3(3(3(0(1(1(3(4(x1)))))))))))) 406.06/112.18 4(1(5(3(3(5(0(4(5(1(4(4(1(x1))))))))))))) -> 5(4(3(2(2(3(3(2(1(2(5(0(5(x1))))))))))))) 406.06/112.18 1(0(3(0(0(0(0(2(3(1(4(0(2(0(4(x1))))))))))))))) -> 1(4(4(0(4(1(4(0(3(2(4(1(0(2(4(x1))))))))))))))) 406.06/112.18 2(5(0(5(1(5(2(3(5(3(1(3(5(4(5(x1))))))))))))))) -> 2(2(5(4(2(0(1(5(1(1(4(1(0(3(4(x1))))))))))))))) 406.06/112.18 5(2(5(1(1(5(0(0(3(0(5(5(3(3(2(x1))))))))))))))) -> 5(5(3(3(1(5(0(3(1(0(4(3(1(3(2(x1))))))))))))))) 406.06/112.18 2(1(1(5(2(5(5(0(1(3(4(1(4(4(5(3(x1)))))))))))))))) -> 2(5(2(3(3(5(4(3(5(4(5(5(0(0(3(1(x1)))))))))))))))) 406.06/112.18 0(4(4(5(0(4(5(0(5(2(3(0(0(2(4(4(2(x1))))))))))))))))) -> 0(4(4(3(0(2(5(0(5(4(1(3(5(4(4(1(0(x1))))))))))))))))) 406.06/112.18 1(1(0(0(3(1(3(0(2(1(2(5(2(5(0(2(0(x1))))))))))))))))) -> 2(2(4(3(2(1(3(2(2(1(4(3(0(2(2(5(5(x1))))))))))))))))) 406.06/112.18 2(5(4(4(4(2(3(5(4(0(4(0(0(5(4(5(5(x1))))))))))))))))) -> 5(3(1(4(4(5(0(5(0(3(1(2(1(1(2(4(3(x1))))))))))))))))) 406.06/112.18 5(0(0(1(3(3(2(5(3(4(0(3(4(3(5(4(4(2(x1)))))))))))))))))) -> 5(5(0(0(1(1(1(0(2(2(2(1(3(2(1(2(2(2(x1)))))))))))))))))) 406.06/112.18 4(4(0(2(2(1(1(4(1(1(1(0(0(0(2(3(4(4(4(x1))))))))))))))))))) -> 3(1(0(3(4(2(2(1(0(1(5(2(0(5(4(4(2(1(4(x1))))))))))))))))))) 406.06/112.18 0(3(2(2(1(4(5(3(3(5(5(1(5(1(0(5(1(5(5(1(x1)))))))))))))))))))) -> 0(3(1(4(0(2(0(0(2(4(5(0(2(3(0(5(2(1(5(1(x1)))))))))))))))))))) 406.06/112.18 1(4(1(4(2(5(4(5(5(0(5(0(4(0(4(5(0(0(5(4(2(x1))))))))))))))))))))) -> 1(5(5(1(1(3(0(3(5(5(3(2(4(2(0(3(5(1(0(3(2(x1))))))))))))))))))))) 406.06/112.18 2(2(4(0(0(1(4(3(1(4(4(3(1(2(1(1(5(0(4(5(0(x1))))))))))))))))))))) -> 4(3(0(2(4(0(4(3(0(4(2(0(5(1(4(2(3(2(3(0(0(x1))))))))))))))))))))) 406.06/112.18 4(2(4(2(5(5(2(0(2(0(2(0(3(1(5(3(0(1(4(4(2(x1))))))))))))))))))))) -> 4(2(4(5(1(3(5(2(4(4(2(0(5(0(1(2(5(2(4(5(0(x1))))))))))))))))))))) 406.06/112.18 406.06/112.18 Q is empty. 406.06/112.18 We have to consider all minimal (P,Q,R)-chains. 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (54) PisEmptyProof (EQUIVALENT) 406.06/112.18 The TRS P is empty. Hence, there is no (P,Q,R) chain. 406.06/112.18 ---------------------------------------- 406.06/112.18 406.06/112.18 (55) 406.06/112.18 YES 406.13/112.27 EOF