219.60/56.69 YES 221.85/57.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 221.85/57.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 221.85/57.25 221.85/57.25 221.85/57.25 Termination w.r.t. Q of the given QTRS could be proven: 221.85/57.25 221.85/57.25 (0) QTRS 221.85/57.25 (1) QTRSRRRProof [EQUIVALENT, 213 ms] 221.85/57.25 (2) QTRS 221.85/57.25 (3) DependencyPairsProof [EQUIVALENT, 1170 ms] 221.85/57.25 (4) QDP 221.85/57.25 (5) QDPOrderProof [EQUIVALENT, 1665 ms] 221.85/57.25 (6) QDP 221.85/57.25 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 221.85/57.25 (8) AND 221.85/57.25 (9) QDP 221.85/57.25 (10) QDPOrderProof [EQUIVALENT, 60 ms] 221.85/57.25 (11) QDP 221.85/57.25 (12) QDPOrderProof [EQUIVALENT, 5457 ms] 221.85/57.25 (13) QDP 221.85/57.25 (14) PisEmptyProof [EQUIVALENT, 0 ms] 221.85/57.25 (15) YES 221.85/57.25 (16) QDP 221.85/57.25 (17) QDPOrderProof [EQUIVALENT, 1 ms] 221.85/57.25 (18) QDP 221.85/57.25 (19) QDPOrderProof [EQUIVALENT, 47 ms] 221.85/57.25 (20) QDP 221.85/57.25 (21) PisEmptyProof [EQUIVALENT, 0 ms] 221.85/57.25 (22) YES 221.85/57.25 (23) QDP 221.85/57.25 (24) QDPOrderProof [EQUIVALENT, 56 ms] 221.85/57.25 (25) QDP 221.85/57.25 (26) QDPOrderProof [EQUIVALENT, 52 ms] 221.85/57.25 (27) QDP 221.85/57.25 (28) QDPOrderProof [EQUIVALENT, 73 ms] 221.85/57.25 (29) QDP 221.85/57.25 (30) PisEmptyProof [EQUIVALENT, 0 ms] 221.85/57.25 (31) YES 221.85/57.25 (32) QDP 221.85/57.25 (33) QDPOrderProof [EQUIVALENT, 48 ms] 221.85/57.25 (34) QDP 221.85/57.25 (35) QDPOrderProof [EQUIVALENT, 0 ms] 221.85/57.25 (36) QDP 221.85/57.25 (37) PisEmptyProof [EQUIVALENT, 0 ms] 221.85/57.25 (38) YES 221.85/57.25 (39) QDP 221.85/57.25 (40) QDPOrderProof [EQUIVALENT, 54 ms] 221.85/57.25 (41) QDP 221.85/57.25 (42) QDPOrderProof [EQUIVALENT, 45 ms] 221.85/57.25 (43) QDP 221.85/57.25 (44) QDPOrderProof [EQUIVALENT, 41 ms] 221.85/57.25 (45) QDP 221.85/57.25 (46) PisEmptyProof [EQUIVALENT, 0 ms] 221.85/57.25 (47) YES 221.85/57.25 (48) QDP 221.85/57.25 (49) QDPOrderProof [EQUIVALENT, 52 ms] 221.85/57.25 (50) QDP 221.85/57.25 (51) QDPOrderProof [EQUIVALENT, 46 ms] 221.85/57.25 (52) QDP 221.85/57.25 (53) PisEmptyProof [EQUIVALENT, 0 ms] 221.85/57.25 (54) YES 221.85/57.25 221.85/57.25 221.85/57.25 ---------------------------------------- 221.85/57.25 221.85/57.25 (0) 221.85/57.25 Obligation: 221.85/57.25 Q restricted rewrite system: 221.85/57.25 The TRS R consists of the following rules: 221.85/57.25 221.85/57.25 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.85/57.25 2(1(4(3(1(x1))))) -> 4(1(5(3(x1)))) 221.85/57.25 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.85/57.25 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.85/57.25 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.85/57.25 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.85/57.25 0(1(1(3(2(3(1(3(2(x1))))))))) -> 0(0(5(3(3(1(1(0(x1)))))))) 221.85/57.25 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.85/57.25 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.85/57.25 0(1(1(1(2(2(4(1(1(1(x1)))))))))) -> 2(1(2(4(0(2(2(5(0(x1))))))))) 221.85/57.25 2(2(2(1(4(1(1(3(0(2(x1)))))))))) -> 0(2(0(4(2(3(5(4(0(x1))))))))) 221.85/57.25 2(2(4(2(1(2(3(2(1(4(x1)))))))))) -> 3(3(3(0(4(5(0(2(4(x1))))))))) 221.85/57.25 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.85/57.25 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.85/57.25 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.85/57.25 3(2(1(1(4(2(4(5(2(5(3(3(x1)))))))))))) -> 5(1(3(1(2(4(1(2(2(1(0(x1))))))))))) 221.85/57.25 5(1(3(3(0(3(5(2(1(4(1(5(x1)))))))))))) -> 3(5(5(5(5(0(1(5(4(2(5(x1))))))))))) 221.85/57.25 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.85/57.25 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.85/57.25 1(2(5(2(4(4(0(3(4(0(3(3(2(x1))))))))))))) -> 1(2(4(2(5(3(5(2(1(3(2(0(x1)))))))))))) 221.85/57.25 5(5(0(2(4(4(2(4(2(2(0(3(4(x1))))))))))))) -> 5(3(5(2(0(0(4(4(5(5(5(2(x1)))))))))))) 221.85/57.25 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.85/57.25 2(2(4(0(2(2(4(3(5(0(2(3(3(5(3(x1))))))))))))))) -> 2(1(5(1(3(5(5(5(5(0(0(2(5(x1))))))))))))) 221.85/57.25 5(0(2(2(0(2(4(3(2(2(4(5(0(2(3(x1))))))))))))))) -> 5(4(1(1(5(4(5(0(2(3(0(3(3(3(x1)))))))))))))) 221.85/57.25 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.85/57.25 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.85/57.25 3(3(3(4(0(3(1(4(4(4(4(1(3(3(1(4(x1)))))))))))))))) -> 5(5(2(4(0(0(3(0(4(5(0(2(2(2(x1)))))))))))))) 221.85/57.25 3(3(3(5(3(1(1(2(2(3(4(2(0(2(1(1(x1)))))))))))))))) -> 5(5(1(4(1(4(1(2(5(2(0(5(2(3(1(x1))))))))))))))) 221.85/57.25 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.85/57.25 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.85/57.25 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.85/57.25 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.85/57.25 0(2(0(4(4(4(3(4(0(3(5(1(5(5(3(1(4(3(x1)))))))))))))))))) -> 5(2(2(1(1(2(4(2(3(5(0(0(3(1(1(4(0(x1))))))))))))))))) 221.85/57.25 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.85/57.25 3(0(4(4(4(1(1(2(5(2(1(1(4(3(4(4(4(2(x1)))))))))))))))))) -> 3(3(4(5(3(3(5(4(3(3(5(2(3(3(5(3(x1)))))))))))))))) 221.85/57.25 0(0(4(1(2(3(5(0(4(0(5(2(4(3(2(3(1(5(1(x1))))))))))))))))))) -> 4(5(3(2(0(2(3(4(5(5(1(1(5(1(5(5(1(4(x1)))))))))))))))))) 221.85/57.25 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.85/57.25 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.85/57.25 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.85/57.25 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.85/57.25 221.85/57.25 Q is empty. 221.85/57.25 221.85/57.25 ---------------------------------------- 221.85/57.25 221.85/57.25 (1) QTRSRRRProof (EQUIVALENT) 221.85/57.25 Used ordering: 221.85/57.25 Polynomial interpretation [POLO]: 221.85/57.25 221.85/57.25 POL(0(x_1)) = 1 + x_1 221.85/57.25 POL(1(x_1)) = 1 + x_1 221.85/57.25 POL(2(x_1)) = 1 + x_1 221.85/57.25 POL(3(x_1)) = 1 + x_1 221.85/57.25 POL(4(x_1)) = 1 + x_1 221.85/57.25 POL(5(x_1)) = 1 + x_1 221.85/57.25 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 221.85/57.25 221.85/57.25 2(1(4(3(1(x1))))) -> 4(1(5(3(x1)))) 221.85/57.25 0(1(1(3(2(3(1(3(2(x1))))))))) -> 0(0(5(3(3(1(1(0(x1)))))))) 221.85/57.25 0(1(1(1(2(2(4(1(1(1(x1)))))))))) -> 2(1(2(4(0(2(2(5(0(x1))))))))) 221.85/57.25 2(2(2(1(4(1(1(3(0(2(x1)))))))))) -> 0(2(0(4(2(3(5(4(0(x1))))))))) 221.85/57.25 2(2(4(2(1(2(3(2(1(4(x1)))))))))) -> 3(3(3(0(4(5(0(2(4(x1))))))))) 221.85/57.25 3(2(1(1(4(2(4(5(2(5(3(3(x1)))))))))))) -> 5(1(3(1(2(4(1(2(2(1(0(x1))))))))))) 221.85/57.25 5(1(3(3(0(3(5(2(1(4(1(5(x1)))))))))))) -> 3(5(5(5(5(0(1(5(4(2(5(x1))))))))))) 221.85/57.25 1(2(5(2(4(4(0(3(4(0(3(3(2(x1))))))))))))) -> 1(2(4(2(5(3(5(2(1(3(2(0(x1)))))))))))) 221.85/57.25 5(5(0(2(4(4(2(4(2(2(0(3(4(x1))))))))))))) -> 5(3(5(2(0(0(4(4(5(5(5(2(x1)))))))))))) 221.85/57.25 2(2(4(0(2(2(4(3(5(0(2(3(3(5(3(x1))))))))))))))) -> 2(1(5(1(3(5(5(5(5(0(0(2(5(x1))))))))))))) 221.85/57.25 5(0(2(2(0(2(4(3(2(2(4(5(0(2(3(x1))))))))))))))) -> 5(4(1(1(5(4(5(0(2(3(0(3(3(3(x1)))))))))))))) 221.85/57.25 3(3(3(4(0(3(1(4(4(4(4(1(3(3(1(4(x1)))))))))))))))) -> 5(5(2(4(0(0(3(0(4(5(0(2(2(2(x1)))))))))))))) 221.85/57.25 3(3(3(5(3(1(1(2(2(3(4(2(0(2(1(1(x1)))))))))))))))) -> 5(5(1(4(1(4(1(2(5(2(0(5(2(3(1(x1))))))))))))))) 221.85/57.25 0(2(0(4(4(4(3(4(0(3(5(1(5(5(3(1(4(3(x1)))))))))))))))))) -> 5(2(2(1(1(2(4(2(3(5(0(0(3(1(1(4(0(x1))))))))))))))))) 221.85/57.25 3(0(4(4(4(1(1(2(5(2(1(1(4(3(4(4(4(2(x1)))))))))))))))))) -> 3(3(4(5(3(3(5(4(3(3(5(2(3(3(5(3(x1)))))))))))))))) 221.85/57.25 0(0(4(1(2(3(5(0(4(0(5(2(4(3(2(3(1(5(1(x1))))))))))))))))))) -> 4(5(3(2(0(2(3(4(5(5(1(1(5(1(5(5(1(4(x1)))))))))))))))))) 221.85/57.25 221.85/57.25 221.85/57.25 221.85/57.25 221.85/57.25 ---------------------------------------- 221.85/57.25 221.85/57.25 (2) 221.85/57.25 Obligation: 221.85/57.25 Q restricted rewrite system: 221.85/57.25 The TRS R consists of the following rules: 221.85/57.25 221.85/57.25 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.85/57.25 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.85/57.25 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.85/57.25 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.85/57.25 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.85/57.25 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.85/57.25 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.85/57.25 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.85/57.25 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.85/57.25 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.85/57.25 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.85/57.25 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.85/57.25 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.85/57.25 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.85/57.25 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.85/57.25 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.85/57.25 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.85/57.25 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.85/57.25 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.85/57.25 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.85/57.25 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.85/57.25 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.85/57.25 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.85/57.25 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.85/57.25 221.85/57.25 Q is empty. 221.85/57.25 221.85/57.25 ---------------------------------------- 221.85/57.25 221.85/57.25 (3) DependencyPairsProof (EQUIVALENT) 221.85/57.25 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 221.85/57.25 ---------------------------------------- 221.85/57.25 221.85/57.25 (4) 221.85/57.25 Obligation: 221.85/57.25 Q DP problem: 221.85/57.25 The TRS P consists of the following rules: 221.85/57.25 221.85/57.25 0^1(1(2(2(3(x1))))) -> 0^1(4(1(4(3(x1))))) 221.85/57.25 0^1(1(2(2(3(x1))))) -> 4^1(1(4(3(x1)))) 221.85/57.25 0^1(1(2(2(3(x1))))) -> 1^1(4(3(x1))) 221.85/57.25 0^1(1(2(2(3(x1))))) -> 4^1(3(x1)) 221.85/57.25 1^1(2(3(5(3(0(x1)))))) -> 1^1(1(4(3(5(1(x1)))))) 221.85/57.25 1^1(2(3(5(3(0(x1)))))) -> 1^1(4(3(5(1(x1))))) 221.85/57.25 1^1(2(3(5(3(0(x1)))))) -> 4^1(3(5(1(x1)))) 221.85/57.25 1^1(2(3(5(3(0(x1)))))) -> 3^1(5(1(x1))) 221.85/57.25 1^1(2(3(5(3(0(x1)))))) -> 5^1(1(x1)) 221.85/57.25 1^1(2(3(5(3(0(x1)))))) -> 1^1(x1) 221.85/57.25 2^1(1(3(5(0(0(x1)))))) -> 4^1(4(2(4(5(0(x1)))))) 221.85/57.25 2^1(1(3(5(0(0(x1)))))) -> 4^1(2(4(5(0(x1))))) 221.85/57.25 2^1(1(3(5(0(0(x1)))))) -> 2^1(4(5(0(x1)))) 221.85/57.25 2^1(1(3(5(0(0(x1)))))) -> 4^1(5(0(x1))) 221.85/57.25 2^1(1(3(5(0(0(x1)))))) -> 5^1(0(x1)) 221.85/57.25 4^1(3(5(1(5(1(x1)))))) -> 4^1(0(2(4(5(4(x1)))))) 221.85/57.25 4^1(3(5(1(5(1(x1)))))) -> 0^1(2(4(5(4(x1))))) 221.85/57.25 4^1(3(5(1(5(1(x1)))))) -> 2^1(4(5(4(x1)))) 221.85/57.25 4^1(3(5(1(5(1(x1)))))) -> 4^1(5(4(x1))) 221.85/57.25 4^1(3(5(1(5(1(x1)))))) -> 5^1(4(x1)) 221.85/57.25 4^1(3(5(1(5(1(x1)))))) -> 4^1(x1) 221.85/57.25 0^1(0(1(2(2(0(4(2(x1)))))))) -> 2^1(4(0(0(4(4(3(0(x1)))))))) 221.85/57.25 0^1(0(1(2(2(0(4(2(x1)))))))) -> 4^1(0(0(4(4(3(0(x1))))))) 221.85/57.25 0^1(0(1(2(2(0(4(2(x1)))))))) -> 0^1(0(4(4(3(0(x1)))))) 221.85/57.25 0^1(0(1(2(2(0(4(2(x1)))))))) -> 0^1(4(4(3(0(x1))))) 221.85/57.25 0^1(0(1(2(2(0(4(2(x1)))))))) -> 4^1(4(3(0(x1)))) 221.85/57.25 0^1(0(1(2(2(0(4(2(x1)))))))) -> 4^1(3(0(x1))) 221.85/57.25 0^1(0(1(2(2(0(4(2(x1)))))))) -> 3^1(0(x1)) 221.85/57.25 0^1(0(1(2(2(0(4(2(x1)))))))) -> 0^1(x1) 221.85/57.25 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 4^1(5(3(2(5(1(3(2(5(x1))))))))) 221.85/57.25 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 5^1(3(2(5(1(3(2(5(x1)))))))) 221.85/57.25 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 3^1(2(5(1(3(2(5(x1))))))) 221.85/57.25 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 2^1(5(1(3(2(5(x1)))))) 221.85/57.25 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 5^1(1(3(2(5(x1))))) 221.85/57.25 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 1^1(3(2(5(x1)))) 221.85/57.25 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 3^1(2(5(x1))) 221.85/57.25 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 2^1(5(x1)) 221.85/57.25 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 4^1(2(3(1(3(0(1(3(1(x1))))))))) 221.85/57.25 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 2^1(3(1(3(0(1(3(1(x1)))))))) 221.85/57.25 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 3^1(1(3(0(1(3(1(x1))))))) 221.85/57.25 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 1^1(3(0(1(3(1(x1)))))) 221.85/57.25 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 3^1(0(1(3(1(x1))))) 221.85/57.25 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 0^1(1(3(1(x1)))) 221.85/57.25 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 1^1(3(1(x1))) 221.85/57.25 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 3^1(1(x1)) 221.85/57.25 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4^1(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4^1(1(2(2(5(2(2(2(0(5(x1)))))))))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 1^1(2(2(5(2(2(2(0(5(x1))))))))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(2(5(2(2(2(0(5(x1)))))))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(5(2(2(2(0(5(x1))))))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 5^1(2(2(2(0(5(x1)))))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(2(2(0(5(x1))))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(2(0(5(x1)))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(0(5(x1))) 221.85/57.26 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 0^1(5(x1)) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 1^1(2(4(4(2(3(4(2(4(4(x1)))))))))) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(4(4(2(3(4(2(4(4(x1))))))))) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 4^1(4(2(3(4(2(4(4(x1)))))))) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 4^1(2(3(4(2(4(4(x1))))))) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(3(4(2(4(4(x1)))))) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 3^1(4(2(4(4(x1))))) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 4^1(2(4(4(x1)))) 221.85/57.26 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(4(4(x1))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(4(3(3(2(0(2(4(5(3(x1)))))))))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(3(3(2(0(2(4(5(3(x1))))))))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 3^1(3(2(0(2(4(5(3(x1)))))))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 3^1(2(0(2(4(5(3(x1))))))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 2^1(0(2(4(5(3(x1)))))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 0^1(2(4(5(3(x1))))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 2^1(4(5(3(x1)))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(5(3(x1))) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 5^1(3(x1)) 221.85/57.26 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 3^1(x1) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5^1(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5^1(3(2(5(4(4(2(1(1(1(3(x1))))))))))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 3^1(2(5(4(4(2(1(1(1(3(x1)))))))))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 2^1(5(4(4(2(1(1(1(3(x1))))))))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5^1(4(4(2(1(1(1(3(x1)))))))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 4^1(4(2(1(1(1(3(x1))))))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 4^1(2(1(1(1(3(x1)))))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 2^1(1(1(1(3(x1))))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 1^1(1(1(3(x1)))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 1^1(1(3(x1))) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 1^1(3(x1)) 221.85/57.26 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 3^1(x1) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 3^1(4(0(0(4(0(2(1(3(4(3(4(x1)))))))))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 4^1(0(0(4(0(2(1(3(4(3(4(x1))))))))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(0(4(0(2(1(3(4(3(4(x1)))))))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(4(0(2(1(3(4(3(4(x1))))))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 4^1(0(2(1(3(4(3(4(x1)))))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(2(1(3(4(3(4(x1))))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 2^1(1(3(4(3(4(x1)))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 1^1(3(4(3(4(x1))))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 3^1(4(3(4(x1)))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 4^1(3(4(x1))) 221.85/57.26 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 3^1(4(x1)) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(1(0(0(2(0(3(4(2(1(3(0(3(x1))))))))))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 0^1(0(2(0(3(4(2(1(3(0(3(x1))))))))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 0^1(2(0(3(4(2(1(3(0(3(x1)))))))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 2^1(0(3(4(2(1(3(0(3(x1))))))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 0^1(3(4(2(1(3(0(3(x1)))))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 3^1(4(2(1(3(0(3(x1))))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 4^1(2(1(3(0(3(x1)))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 2^1(1(3(0(3(x1))))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(3(0(3(x1)))) 221.85/57.26 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 3^1(0(3(x1))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4^1(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 1^1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1))))))))))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 5^1(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4^1(1(0(2(0(3(4(4(1(1(3(4(2(x1))))))))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 1^1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 0^1(2(0(3(4(4(1(1(3(4(2(x1))))))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 2^1(0(3(4(4(1(1(3(4(2(x1)))))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 0^1(3(4(4(1(1(3(4(2(x1))))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 3^1(4(4(1(1(3(4(2(x1)))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4^1(4(1(1(3(4(2(x1))))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4^1(1(1(3(4(2(x1)))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 1^1(1(3(4(2(x1))))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 1^1(3(4(2(x1)))) 221.85/57.26 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 3^1(4(2(x1))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 5^1(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1))))))))))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 0^1(4(2(4(4(2(3(4(0(0(4(3(2(x1))))))))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(4(4(2(3(4(0(0(4(3(2(x1))))))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(4(2(3(4(0(0(4(3(2(x1)))))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(2(3(4(0(0(4(3(2(x1))))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(3(4(0(0(4(3(2(x1)))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 3^1(4(0(0(4(3(2(x1))))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(0(0(4(3(2(x1)))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 0^1(0(4(3(2(x1))))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 0^1(4(3(2(x1)))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(3(2(x1))) 221.85/57.26 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 3^1(2(x1)) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1))))))))))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 2^1(3(3(4(5(0(5(2(2(1(2(0(3(x1))))))))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 3^1(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 3^1(4(5(0(5(2(2(1(2(0(3(x1))))))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(5(0(5(2(2(1(2(0(3(x1)))))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 5^1(0(5(2(2(1(2(0(3(x1))))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 0^1(5(2(2(1(2(0(3(x1)))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 5^1(2(2(1(2(0(3(x1))))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 2^1(2(1(2(0(3(x1)))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 2^1(1(2(0(3(x1))))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 1^1(2(0(3(x1)))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 2^1(0(3(x1))) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 0^1(3(x1)) 221.85/57.26 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 3^1(x1) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 0^1(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1)))))))))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 3^1(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 0^1(1(4(5(1(5(3(5(2(3(2(0(1(3(x1)))))))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 4^1(5(1(5(3(5(2(3(2(0(1(3(x1)))))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 5^1(1(5(3(5(2(3(2(0(1(3(x1))))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(5(3(5(2(3(2(0(1(3(x1)))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 5^1(3(5(2(3(2(0(1(3(x1))))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 3^1(5(2(3(2(0(1(3(x1)))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 5^1(2(3(2(0(1(3(x1))))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 2^1(3(2(0(1(3(x1)))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 3^1(2(0(1(3(x1))))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 2^1(0(1(3(x1)))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 0^1(1(3(x1))) 221.85/57.26 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(3(x1)) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 5^1(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1)))))))))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 4^1(3(5(0(5(1(2(0(4(1(5(3(2(0(x1)))))))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 5^1(0(5(1(2(0(4(1(5(3(2(0(x1)))))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 0^1(5(1(2(0(4(1(5(3(2(0(x1))))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 5^1(1(2(0(4(1(5(3(2(0(x1)))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 1^1(2(0(4(1(5(3(2(0(x1))))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 2^1(0(4(1(5(3(2(0(x1)))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 0^1(4(1(5(3(2(0(x1))))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 4^1(1(5(3(2(0(x1)))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 1^1(5(3(2(0(x1))))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 5^1(3(2(0(x1)))) 221.85/57.26 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(2(0(x1))) 221.85/57.26 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5^1(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.85/57.26 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1)))))))))))))))) 221.85/57.26 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 0^1(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))) 221.85/57.26 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 1^1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1)))))))))))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 4^1(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(4(1(2(0(0(4(2(3(1(2(2(x1)))))))))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 4^1(1(2(0(0(4(2(3(1(2(2(x1))))))))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 1^1(2(0(0(4(2(3(1(2(2(x1)))))))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(0(0(4(2(3(1(2(2(x1))))))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 0^1(0(4(2(3(1(2(2(x1)))))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 0^1(4(2(3(1(2(2(x1))))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 4^1(2(3(1(2(2(x1)))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(3(1(2(2(x1))))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 3^1(1(2(2(x1)))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 1^1(2(2(x1))) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(2(x1)) 221.85/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(x1) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1))))))))))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1))))))))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(0(1(3(0(3(3(4(4(4(0(2(4(x1))))))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 1^1(3(0(3(3(4(4(4(0(2(4(x1))))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 3^1(0(3(3(4(4(4(0(2(4(x1)))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(3(3(4(4(4(0(2(4(x1))))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 3^1(3(4(4(4(0(2(4(x1)))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 3^1(4(4(4(0(2(4(x1))))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(4(4(0(2(4(x1)))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(4(0(2(4(x1))))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(0(2(4(x1)))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(2(4(x1))) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 2^1(4(x1)) 221.85/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(x1) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2^1(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 4^1(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1)))))))))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 1^1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1)))))))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 5^1(0(2(0(3(3(5(3(0(1(4(5(0(2(x1)))))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 0^1(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2^1(0(3(3(5(3(0(1(4(5(0(2(x1)))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 0^1(3(3(5(3(0(1(4(5(0(2(x1))))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(3(5(3(0(1(4(5(0(2(x1)))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(5(3(0(1(4(5(0(2(x1))))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 5^1(3(0(1(4(5(0(2(x1)))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(0(1(4(5(0(2(x1))))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 0^1(1(4(5(0(2(x1)))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 1^1(4(5(0(2(x1))))) 221.85/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 4^1(5(0(2(x1)))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 5^1(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 3^1(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 5^1(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 2^1(4(4(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(5(0(2(2(1(1(1(1(3(4(x1))))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 5^1(0(2(2(1(1(1(1(3(4(x1)))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 0^1(2(2(1(1(1(1(3(4(x1))))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 2^1(2(1(1(1(1(3(4(x1)))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 2^1(1(1(1(1(3(4(x1))))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(1(1(1(3(4(x1)))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(1(1(3(4(x1))))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(1(3(4(x1)))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(3(4(x1))) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 3^1(4(x1)) 221.85/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(x1) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 0^1(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(3(4(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 0^1(1(4(0(1(5(1(5(4(2(3(x1))))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 1^1(4(0(1(5(1(5(4(2(3(x1)))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(0(1(5(1(5(4(2(3(x1))))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 0^1(1(5(1(5(4(2(3(x1)))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 1^1(5(1(5(4(2(3(x1))))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 5^1(1(5(4(2(3(x1)))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 1^1(5(4(2(3(x1))))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 5^1(4(2(3(x1)))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(2(3(x1))) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 2^1(3(x1)) 221.85/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(x1) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 3^1(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 4^1(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 0^1(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(3(1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 3^1(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 1^1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 4^1(3(2(1(2(1(2(5(5(2(4(x1))))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 3^1(2(1(2(1(2(5(5(2(4(x1)))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(1(2(1(2(5(5(2(4(x1))))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 1^1(2(1(2(5(5(2(4(x1)))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(1(2(5(5(2(4(x1))))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 1^1(2(5(5(2(4(x1)))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(5(5(2(4(x1))))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(5(2(4(x1)))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(2(4(x1))) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(4(x1)) 221.85/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 4^1(x1) 221.85/57.28 221.85/57.28 The TRS R consists of the following rules: 221.85/57.28 221.85/57.28 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.85/57.28 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.85/57.28 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.85/57.28 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.85/57.28 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.85/57.28 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.85/57.28 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.85/57.28 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.85/57.28 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.85/57.28 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.85/57.28 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.85/57.28 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.85/57.28 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.85/57.28 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.85/57.28 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.85/57.28 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.85/57.28 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.85/57.28 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.85/57.28 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.85/57.28 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.85/57.28 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.85/57.28 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.85/57.28 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.85/57.28 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.85/57.28 221.85/57.28 Q is empty. 221.85/57.28 We have to consider all minimal (P,Q,R)-chains. 221.85/57.28 ---------------------------------------- 221.85/57.28 221.85/57.28 (5) QDPOrderProof (EQUIVALENT) 221.85/57.28 We use the reduction pair processor [LPAR04,JAR06]. 221.85/57.28 221.85/57.28 221.85/57.28 The following pairs can be oriented strictly and are deleted. 221.85/57.28 221.85/57.28 0^1(1(2(2(3(x1))))) -> 4^1(1(4(3(x1)))) 221.85/57.28 0^1(1(2(2(3(x1))))) -> 1^1(4(3(x1))) 221.85/57.28 0^1(1(2(2(3(x1))))) -> 4^1(3(x1)) 221.85/57.28 1^1(2(3(5(3(0(x1)))))) -> 1^1(4(3(5(1(x1))))) 221.85/57.28 1^1(2(3(5(3(0(x1)))))) -> 4^1(3(5(1(x1)))) 221.85/57.28 1^1(2(3(5(3(0(x1)))))) -> 3^1(5(1(x1))) 221.85/57.28 1^1(2(3(5(3(0(x1)))))) -> 5^1(1(x1)) 221.85/57.28 1^1(2(3(5(3(0(x1)))))) -> 1^1(x1) 221.85/57.28 2^1(1(3(5(0(0(x1)))))) -> 4^1(4(2(4(5(0(x1)))))) 221.85/57.28 2^1(1(3(5(0(0(x1)))))) -> 4^1(2(4(5(0(x1))))) 221.85/57.28 2^1(1(3(5(0(0(x1)))))) -> 2^1(4(5(0(x1)))) 221.85/57.28 2^1(1(3(5(0(0(x1)))))) -> 4^1(5(0(x1))) 221.85/57.28 2^1(1(3(5(0(0(x1)))))) -> 5^1(0(x1)) 221.85/57.28 4^1(3(5(1(5(1(x1)))))) -> 2^1(4(5(4(x1)))) 221.85/57.28 4^1(3(5(1(5(1(x1)))))) -> 4^1(5(4(x1))) 221.85/57.28 4^1(3(5(1(5(1(x1)))))) -> 5^1(4(x1)) 221.85/57.28 4^1(3(5(1(5(1(x1)))))) -> 4^1(x1) 221.85/57.28 0^1(0(1(2(2(0(4(2(x1)))))))) -> 4^1(0(0(4(4(3(0(x1))))))) 221.85/57.28 0^1(0(1(2(2(0(4(2(x1)))))))) -> 0^1(0(4(4(3(0(x1)))))) 221.85/57.28 0^1(0(1(2(2(0(4(2(x1)))))))) -> 0^1(4(4(3(0(x1))))) 221.85/57.28 0^1(0(1(2(2(0(4(2(x1)))))))) -> 4^1(4(3(0(x1)))) 221.85/57.28 0^1(0(1(2(2(0(4(2(x1)))))))) -> 4^1(3(0(x1))) 221.85/57.28 0^1(0(1(2(2(0(4(2(x1)))))))) -> 3^1(0(x1)) 221.85/57.28 0^1(0(1(2(2(0(4(2(x1)))))))) -> 0^1(x1) 221.85/57.28 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 5^1(3(2(5(1(3(2(5(x1)))))))) 221.85/57.28 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 3^1(2(5(1(3(2(5(x1))))))) 221.85/57.28 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 2^1(5(1(3(2(5(x1)))))) 221.85/57.28 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 5^1(1(3(2(5(x1))))) 221.85/57.28 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 1^1(3(2(5(x1)))) 221.85/57.28 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 3^1(2(5(x1))) 221.85/57.28 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 2^1(5(x1)) 221.85/57.28 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 3^1(1(3(0(1(3(1(x1))))))) 221.85/57.28 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 1^1(3(0(1(3(1(x1)))))) 221.85/57.28 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 3^1(0(1(3(1(x1))))) 221.85/57.28 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 0^1(1(3(1(x1)))) 221.85/57.28 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 1^1(3(1(x1))) 221.85/57.28 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 3^1(1(x1)) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4^1(1(2(2(5(2(2(2(0(5(x1)))))))))) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 1^1(2(2(5(2(2(2(0(5(x1))))))))) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(2(5(2(2(2(0(5(x1)))))))) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(5(2(2(2(0(5(x1))))))) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 5^1(2(2(2(0(5(x1)))))) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(2(2(0(5(x1))))) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(2(0(5(x1)))) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 2^1(0(5(x1))) 221.85/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 0^1(5(x1)) 221.85/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 1^1(2(4(4(2(3(4(2(4(4(x1)))))))))) 221.85/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(4(4(2(3(4(2(4(4(x1))))))))) 221.85/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 4^1(4(2(3(4(2(4(4(x1)))))))) 221.85/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 4^1(2(3(4(2(4(4(x1))))))) 221.85/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(3(4(2(4(4(x1)))))) 221.85/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 3^1(4(2(4(4(x1))))) 221.85/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 4^1(2(4(4(x1)))) 221.85/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(4(4(x1))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(4(3(3(2(0(2(4(5(3(x1)))))))))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(3(3(2(0(2(4(5(3(x1))))))))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 3^1(3(2(0(2(4(5(3(x1)))))))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 3^1(2(0(2(4(5(3(x1))))))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 2^1(0(2(4(5(3(x1)))))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 0^1(2(4(5(3(x1))))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 2^1(4(5(3(x1)))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(5(3(x1))) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 5^1(3(x1)) 221.85/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 3^1(x1) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5^1(3(2(5(4(4(2(1(1(1(3(x1))))))))))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 3^1(2(5(4(4(2(1(1(1(3(x1)))))))))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 2^1(5(4(4(2(1(1(1(3(x1))))))))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5^1(4(4(2(1(1(1(3(x1)))))))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 4^1(4(2(1(1(1(3(x1))))))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 4^1(2(1(1(1(3(x1)))))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 2^1(1(1(1(3(x1))))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 1^1(1(1(3(x1)))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 1^1(1(3(x1))) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 1^1(3(x1)) 221.85/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 3^1(x1) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 3^1(4(0(0(4(0(2(1(3(4(3(4(x1)))))))))))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 4^1(0(0(4(0(2(1(3(4(3(4(x1))))))))))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(0(4(0(2(1(3(4(3(4(x1)))))))))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(4(0(2(1(3(4(3(4(x1))))))))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 4^1(0(2(1(3(4(3(4(x1)))))))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(2(1(3(4(3(4(x1))))))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 2^1(1(3(4(3(4(x1)))))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 1^1(3(4(3(4(x1))))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 3^1(4(3(4(x1)))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 4^1(3(4(x1))) 221.85/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 3^1(4(x1)) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(1(0(0(2(0(3(4(2(1(3(0(3(x1))))))))))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 0^1(0(2(0(3(4(2(1(3(0(3(x1))))))))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 0^1(2(0(3(4(2(1(3(0(3(x1)))))))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 2^1(0(3(4(2(1(3(0(3(x1))))))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 0^1(3(4(2(1(3(0(3(x1)))))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 3^1(4(2(1(3(0(3(x1))))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 4^1(2(1(3(0(3(x1)))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 2^1(1(3(0(3(x1))))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(3(0(3(x1)))) 221.85/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 3^1(0(3(x1))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4^1(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 1^1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1))))))))))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 5^1(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4^1(1(0(2(0(3(4(4(1(1(3(4(2(x1))))))))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 1^1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 0^1(2(0(3(4(4(1(1(3(4(2(x1))))))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 2^1(0(3(4(4(1(1(3(4(2(x1)))))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 0^1(3(4(4(1(1(3(4(2(x1))))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 3^1(4(4(1(1(3(4(2(x1)))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4^1(4(1(1(3(4(2(x1))))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4^1(1(1(3(4(2(x1)))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 1^1(1(3(4(2(x1))))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 1^1(3(4(2(x1)))) 221.85/57.28 0^1(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 3^1(4(2(x1))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 5^1(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1))))))))))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 0^1(4(2(4(4(2(3(4(0(0(4(3(2(x1))))))))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(4(4(2(3(4(0(0(4(3(2(x1))))))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(4(2(3(4(0(0(4(3(2(x1)))))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(2(3(4(0(0(4(3(2(x1))))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(3(4(0(0(4(3(2(x1)))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 3^1(4(0(0(4(3(2(x1))))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(0(0(4(3(2(x1)))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 0^1(0(4(3(2(x1))))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 0^1(4(3(2(x1)))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 4^1(3(2(x1))) 221.85/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 3^1(2(x1)) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1))))))))))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 2^1(3(3(4(5(0(5(2(2(1(2(0(3(x1))))))))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 3^1(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 3^1(4(5(0(5(2(2(1(2(0(3(x1))))))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(5(0(5(2(2(1(2(0(3(x1)))))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 5^1(0(5(2(2(1(2(0(3(x1))))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 0^1(5(2(2(1(2(0(3(x1)))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 5^1(2(2(1(2(0(3(x1))))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 2^1(2(1(2(0(3(x1)))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 2^1(1(2(0(3(x1))))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 1^1(2(0(3(x1)))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 2^1(0(3(x1))) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 0^1(3(x1)) 221.85/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 3^1(x1) 221.85/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 3^1(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))) 221.85/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 0^1(1(4(5(1(5(3(5(2(3(2(0(1(3(x1)))))))))))))) 221.85/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 4^1(5(1(5(3(5(2(3(2(0(1(3(x1)))))))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 5^1(1(5(3(5(2(3(2(0(1(3(x1))))))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(5(3(5(2(3(2(0(1(3(x1)))))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 5^1(3(5(2(3(2(0(1(3(x1))))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 3^1(5(2(3(2(0(1(3(x1)))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 5^1(2(3(2(0(1(3(x1))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 2^1(3(2(0(1(3(x1)))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 3^1(2(0(1(3(x1))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 2^1(0(1(3(x1)))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 0^1(1(3(x1))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(3(x1)) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 5^1(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1)))))))))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 4^1(3(5(0(5(1(2(0(4(1(5(3(2(0(x1)))))))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 5^1(0(5(1(2(0(4(1(5(3(2(0(x1)))))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 0^1(5(1(2(0(4(1(5(3(2(0(x1))))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 5^1(1(2(0(4(1(5(3(2(0(x1)))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 1^1(2(0(4(1(5(3(2(0(x1))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 2^1(0(4(1(5(3(2(0(x1)))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 0^1(4(1(5(3(2(0(x1))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 4^1(1(5(3(2(0(x1)))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 1^1(5(3(2(0(x1))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 5^1(3(2(0(x1)))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(2(0(x1))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 0^1(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 1^1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1)))))))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 4^1(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(4(1(2(0(0(4(2(3(1(2(2(x1)))))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 4^1(1(2(0(0(4(2(3(1(2(2(x1))))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 1^1(2(0(0(4(2(3(1(2(2(x1)))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(0(0(4(2(3(1(2(2(x1))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 0^1(0(4(2(3(1(2(2(x1)))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 0^1(4(2(3(1(2(2(x1))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 4^1(2(3(1(2(2(x1)))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(3(1(2(2(x1))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 3^1(1(2(2(x1)))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 1^1(2(2(x1))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(2(x1)) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(x1) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1))))))))))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1))))))))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(0(1(3(0(3(3(4(4(4(0(2(4(x1))))))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 1^1(3(0(3(3(4(4(4(0(2(4(x1))))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 3^1(0(3(3(4(4(4(0(2(4(x1)))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(3(3(4(4(4(0(2(4(x1))))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 3^1(3(4(4(4(0(2(4(x1)))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 3^1(4(4(4(0(2(4(x1))))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(4(4(0(2(4(x1)))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(4(0(2(4(x1))))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(0(2(4(x1)))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 0^1(2(4(x1))) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 2^1(4(x1)) 221.99/57.28 0^1(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4^1(x1) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 4^1(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1)))))))))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 1^1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1)))))))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 5^1(0(2(0(3(3(5(3(0(1(4(5(0(2(x1)))))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 0^1(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2^1(0(3(3(5(3(0(1(4(5(0(2(x1)))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 0^1(3(3(5(3(0(1(4(5(0(2(x1))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(3(5(3(0(1(4(5(0(2(x1)))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(5(3(0(1(4(5(0(2(x1))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 5^1(3(0(1(4(5(0(2(x1)))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 3^1(0(1(4(5(0(2(x1))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 0^1(1(4(5(0(2(x1)))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 1^1(4(5(0(2(x1))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 4^1(5(0(2(x1)))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 5^1(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 3^1(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 5^1(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 2^1(4(4(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(4(5(0(2(2(1(1(1(1(3(4(x1)))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(5(0(2(2(1(1(1(1(3(4(x1))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 5^1(0(2(2(1(1(1(1(3(4(x1)))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 0^1(2(2(1(1(1(1(3(4(x1))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 2^1(2(1(1(1(1(3(4(x1)))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 2^1(1(1(1(1(3(4(x1))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(1(1(1(3(4(x1)))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(1(1(3(4(x1))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(1(3(4(x1)))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(3(4(x1))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 3^1(4(x1)) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 4^1(x1) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 0^1(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(3(4(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(0(1(4(0(1(5(1(5(4(2(3(x1)))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 0^1(1(4(0(1(5(1(5(4(2(3(x1))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 1^1(4(0(1(5(1(5(4(2(3(x1)))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(0(1(5(1(5(4(2(3(x1))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 0^1(1(5(1(5(4(2(3(x1)))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 1^1(5(1(5(4(2(3(x1))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 5^1(1(5(4(2(3(x1)))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 1^1(5(4(2(3(x1))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 5^1(4(2(3(x1)))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 4^1(2(3(x1))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 2^1(3(x1)) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(x1) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 3^1(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 4^1(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 0^1(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(3(1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 3^1(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 1^1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 4^1(3(2(1(2(1(2(5(5(2(4(x1))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 3^1(2(1(2(1(2(5(5(2(4(x1)))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(1(2(1(2(5(5(2(4(x1))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 1^1(2(1(2(5(5(2(4(x1)))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(1(2(5(5(2(4(x1))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 1^1(2(5(5(2(4(x1)))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(5(5(2(4(x1))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(5(2(4(x1)))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(2(4(x1))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(4(x1)) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 4^1(x1) 221.99/57.28 The remaining pairs can at least be oriented weakly. 221.99/57.28 Used ordering: Polynomial interpretation [POLO]: 221.99/57.28 221.99/57.28 POL(0(x_1)) = 1 + x_1 221.99/57.28 POL(0^1(x_1)) = 1 + x_1 221.99/57.28 POL(1(x_1)) = 1 + x_1 221.99/57.28 POL(1^1(x_1)) = x_1 221.99/57.28 POL(2(x_1)) = 1 + x_1 221.99/57.28 POL(2^1(x_1)) = 1 + x_1 221.99/57.28 POL(3(x_1)) = 1 + x_1 221.99/57.28 POL(3^1(x_1)) = x_1 221.99/57.28 POL(4(x_1)) = 1 + x_1 221.99/57.28 POL(4^1(x_1)) = x_1 221.99/57.28 POL(5(x_1)) = 1 + x_1 221.99/57.28 POL(5^1(x_1)) = x_1 221.99/57.28 221.99/57.28 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.28 221.99/57.28 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.28 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.28 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.28 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.28 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.28 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.28 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.28 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.28 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.28 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.28 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.28 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.28 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.28 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.28 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.28 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.28 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.28 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.28 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.28 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.28 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.28 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.28 221.99/57.28 221.99/57.28 ---------------------------------------- 221.99/57.28 221.99/57.28 (6) 221.99/57.28 Obligation: 221.99/57.28 Q DP problem: 221.99/57.28 The TRS P consists of the following rules: 221.99/57.28 221.99/57.28 0^1(1(2(2(3(x1))))) -> 0^1(4(1(4(3(x1))))) 221.99/57.28 1^1(2(3(5(3(0(x1)))))) -> 1^1(1(4(3(5(1(x1)))))) 221.99/57.28 4^1(3(5(1(5(1(x1)))))) -> 4^1(0(2(4(5(4(x1)))))) 221.99/57.28 4^1(3(5(1(5(1(x1)))))) -> 0^1(2(4(5(4(x1))))) 221.99/57.28 0^1(0(1(2(2(0(4(2(x1)))))))) -> 2^1(4(0(0(4(4(3(0(x1)))))))) 221.99/57.28 1^1(2(5(5(5(2(5(3(5(x1))))))))) -> 4^1(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.28 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 4^1(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.28 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 2^1(3(1(3(0(1(3(1(x1)))))))) 221.99/57.28 1^1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4^1(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.28 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.28 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.28 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5^1(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.28 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.28 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.28 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.28 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.28 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 0^1(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1)))))))))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5^1(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.28 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 2^1(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1)))))))))))))))) 221.99/57.28 0^1(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2^1(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.28 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.28 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 2^1(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1)))))))))))))))))))) 221.99/57.28 221.99/57.28 The TRS R consists of the following rules: 221.99/57.28 221.99/57.28 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.28 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.28 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.28 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.28 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.28 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.28 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.28 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.28 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.28 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.28 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.28 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.28 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.28 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.28 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.28 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.28 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.28 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.28 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.28 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.28 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.28 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.28 221.99/57.28 Q is empty. 221.99/57.28 We have to consider all minimal (P,Q,R)-chains. 221.99/57.28 ---------------------------------------- 221.99/57.28 221.99/57.28 (7) DependencyGraphProof (EQUIVALENT) 221.99/57.28 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 6 SCCs with 9 less nodes. 221.99/57.28 ---------------------------------------- 221.99/57.28 221.99/57.28 (8) 221.99/57.28 Complex Obligation (AND) 221.99/57.28 221.99/57.28 ---------------------------------------- 221.99/57.28 221.99/57.28 (9) 221.99/57.28 Obligation: 221.99/57.28 Q DP problem: 221.99/57.28 The TRS P consists of the following rules: 221.99/57.28 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 221.99/57.28 The TRS R consists of the following rules: 221.99/57.28 221.99/57.28 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.28 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.28 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.28 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.28 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.28 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.28 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.28 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.28 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.28 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.28 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.28 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.28 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.28 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.28 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.28 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.28 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.28 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.28 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.28 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.28 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.28 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.28 221.99/57.28 Q is empty. 221.99/57.28 We have to consider all minimal (P,Q,R)-chains. 221.99/57.28 ---------------------------------------- 221.99/57.28 221.99/57.28 (10) QDPOrderProof (EQUIVALENT) 221.99/57.28 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.28 221.99/57.28 221.99/57.28 The following pairs can be oriented strictly and are deleted. 221.99/57.28 221.99/57.28 3^1(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3^1(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 The remaining pairs can at least be oriented weakly. 221.99/57.28 Used ordering: Polynomial interpretation [POLO]: 221.99/57.28 221.99/57.28 POL(0(x_1)) = 0 221.99/57.28 POL(1(x_1)) = 1 221.99/57.28 POL(2(x_1)) = 0 221.99/57.28 POL(3(x_1)) = 0 221.99/57.28 POL(3^1(x_1)) = x_1 221.99/57.28 POL(4(x_1)) = 0 221.99/57.28 POL(5(x_1)) = x_1 221.99/57.28 221.99/57.28 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.28 221.99/57.28 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.28 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.28 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.28 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.28 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.28 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.28 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.28 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.28 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.28 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.28 221.99/57.28 221.99/57.28 ---------------------------------------- 221.99/57.28 221.99/57.28 (11) 221.99/57.28 Obligation: 221.99/57.28 Q DP problem: 221.99/57.28 The TRS P consists of the following rules: 221.99/57.28 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 221.99/57.28 The TRS R consists of the following rules: 221.99/57.28 221.99/57.28 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.28 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.28 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.28 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.28 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.28 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.28 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.28 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.28 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.28 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.28 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.28 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.28 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.28 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.28 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.28 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.28 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.28 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.28 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.28 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.28 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.28 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.28 221.99/57.28 Q is empty. 221.99/57.28 We have to consider all minimal (P,Q,R)-chains. 221.99/57.28 ---------------------------------------- 221.99/57.28 221.99/57.28 (12) QDPOrderProof (EQUIVALENT) 221.99/57.28 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.28 221.99/57.28 221.99/57.28 The following pairs can be oriented strictly and are deleted. 221.99/57.28 221.99/57.28 3^1(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3^1(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 The remaining pairs can at least be oriented weakly. 221.99/57.28 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 221.99/57.28 221.99/57.28 POL( 3^1_1(x_1) ) = max{0, x_1 - 1} 221.99/57.28 POL( 4_1(x_1) ) = max{0, 2x_1 - 2} 221.99/57.28 POL( 3_1(x_1) ) = max{0, -2} 221.99/57.28 POL( 2_1(x_1) ) = 2x_1 221.99/57.28 POL( 1_1(x_1) ) = 1 221.99/57.28 POL( 5_1(x_1) ) = 0 221.99/57.28 POL( 0_1(x_1) ) = 1 221.99/57.28 221.99/57.28 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.28 221.99/57.28 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.28 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.28 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.28 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.28 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.28 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.28 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.28 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.28 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.28 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.28 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.28 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.28 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.28 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.28 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.28 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.28 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.28 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.28 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.28 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.28 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.28 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.28 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.28 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.28 221.99/57.28 221.99/57.28 ---------------------------------------- 221.99/57.28 221.99/57.28 (13) 221.99/57.28 Obligation: 221.99/57.28 Q DP problem: 221.99/57.28 P is empty. 221.99/57.28 The TRS R consists of the following rules: 221.99/57.28 221.99/57.28 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.28 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.28 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.28 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.28 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.28 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.28 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.28 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.28 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.28 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.28 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.28 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.28 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.28 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.28 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.28 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.29 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.29 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.29 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.29 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.29 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.29 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.29 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 221.99/57.29 Q is empty. 221.99/57.29 We have to consider all minimal (P,Q,R)-chains. 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (14) PisEmptyProof (EQUIVALENT) 221.99/57.29 The TRS P is empty. Hence, there is no (P,Q,R) chain. 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (15) 221.99/57.29 YES 221.99/57.29 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (16) 221.99/57.29 Obligation: 221.99/57.29 Q DP problem: 221.99/57.29 The TRS P consists of the following rules: 221.99/57.29 221.99/57.29 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.29 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.29 221.99/57.29 The TRS R consists of the following rules: 221.99/57.29 221.99/57.29 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.29 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.29 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.29 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.29 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.29 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.29 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.29 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.29 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.29 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.29 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.29 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.29 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.29 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.29 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.29 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.29 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.29 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.29 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.29 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.29 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.29 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 221.99/57.29 Q is empty. 221.99/57.29 We have to consider all minimal (P,Q,R)-chains. 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (17) QDPOrderProof (EQUIVALENT) 221.99/57.29 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.29 221.99/57.29 221.99/57.29 The following pairs can be oriented strictly and are deleted. 221.99/57.29 221.99/57.29 2^1(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2^1(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.29 The remaining pairs can at least be oriented weakly. 221.99/57.29 Used ordering: Polynomial interpretation [POLO]: 221.99/57.29 221.99/57.29 POL(0(x_1)) = 1 + x_1 221.99/57.29 POL(1(x_1)) = 1 221.99/57.29 POL(2(x_1)) = 0 221.99/57.29 POL(2^1(x_1)) = x_1 221.99/57.29 POL(3(x_1)) = 0 221.99/57.29 POL(4(x_1)) = 0 221.99/57.29 POL(5(x_1)) = 0 221.99/57.29 221.99/57.29 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.29 221.99/57.29 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.29 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.29 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.29 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.29 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.29 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.29 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.29 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.29 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.29 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.29 221.99/57.29 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (18) 221.99/57.29 Obligation: 221.99/57.29 Q DP problem: 221.99/57.29 The TRS P consists of the following rules: 221.99/57.29 221.99/57.29 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.29 221.99/57.29 The TRS R consists of the following rules: 221.99/57.29 221.99/57.29 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.29 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.29 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.29 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.29 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.29 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.29 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.29 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.29 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.29 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.29 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.29 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.29 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.29 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.29 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.29 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.29 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.29 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.29 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.29 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.29 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.29 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 221.99/57.29 Q is empty. 221.99/57.29 We have to consider all minimal (P,Q,R)-chains. 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (19) QDPOrderProof (EQUIVALENT) 221.99/57.29 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.29 221.99/57.29 221.99/57.29 The following pairs can be oriented strictly and are deleted. 221.99/57.29 221.99/57.29 2^1(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2^1(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.29 The remaining pairs can at least be oriented weakly. 221.99/57.29 Used ordering: Polynomial interpretation [POLO]: 221.99/57.29 221.99/57.29 POL(0(x_1)) = 0 221.99/57.29 POL(1(x_1)) = 0 221.99/57.29 POL(2(x_1)) = 1 221.99/57.29 POL(2^1(x_1)) = x_1 221.99/57.29 POL(3(x_1)) = 0 221.99/57.29 POL(4(x_1)) = 0 221.99/57.29 POL(5(x_1)) = 0 221.99/57.29 221.99/57.29 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.29 221.99/57.29 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 221.99/57.29 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (20) 221.99/57.29 Obligation: 221.99/57.29 Q DP problem: 221.99/57.29 P is empty. 221.99/57.29 The TRS R consists of the following rules: 221.99/57.29 221.99/57.29 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.29 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.29 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.29 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.29 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.29 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.29 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.29 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.29 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.29 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.29 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.29 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.29 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.29 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.29 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.29 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.29 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.29 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.29 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.29 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.29 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.29 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 221.99/57.29 Q is empty. 221.99/57.29 We have to consider all minimal (P,Q,R)-chains. 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (21) PisEmptyProof (EQUIVALENT) 221.99/57.29 The TRS P is empty. Hence, there is no (P,Q,R) chain. 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (22) 221.99/57.29 YES 221.99/57.29 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (23) 221.99/57.29 Obligation: 221.99/57.29 Q DP problem: 221.99/57.29 The TRS P consists of the following rules: 221.99/57.29 221.99/57.29 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5^1(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5^1(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 221.99/57.29 The TRS R consists of the following rules: 221.99/57.29 221.99/57.29 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.29 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.29 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.29 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.29 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.29 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.29 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.29 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.29 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.29 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.29 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.29 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.29 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.29 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.29 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.29 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.29 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.29 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.29 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.29 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.29 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.29 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 221.99/57.29 Q is empty. 221.99/57.29 We have to consider all minimal (P,Q,R)-chains. 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (24) QDPOrderProof (EQUIVALENT) 221.99/57.29 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.29 221.99/57.29 221.99/57.29 The following pairs can be oriented strictly and are deleted. 221.99/57.29 221.99/57.29 5^1(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5^1(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 The remaining pairs can at least be oriented weakly. 221.99/57.29 Used ordering: Polynomial interpretation [POLO]: 221.99/57.29 221.99/57.29 POL(0(x_1)) = 0 221.99/57.29 POL(1(x_1)) = 0 221.99/57.29 POL(2(x_1)) = 0 221.99/57.29 POL(3(x_1)) = 1 221.99/57.29 POL(4(x_1)) = 0 221.99/57.29 POL(5(x_1)) = 0 221.99/57.29 POL(5^1(x_1)) = x_1 221.99/57.29 221.99/57.29 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.29 221.99/57.29 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.29 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.29 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.29 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.29 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.29 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.29 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.29 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.29 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.29 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.29 221.99/57.29 221.99/57.29 ---------------------------------------- 221.99/57.29 221.99/57.29 (25) 221.99/57.29 Obligation: 221.99/57.29 Q DP problem: 221.99/57.29 The TRS P consists of the following rules: 221.99/57.29 221.99/57.29 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5^1(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 Q is empty. 221.99/57.32 We have to consider all minimal (P,Q,R)-chains. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (26) QDPOrderProof (EQUIVALENT) 221.99/57.32 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.32 221.99/57.32 221.99/57.32 The following pairs can be oriented strictly and are deleted. 221.99/57.32 221.99/57.32 5^1(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5^1(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 The remaining pairs can at least be oriented weakly. 221.99/57.32 Used ordering: Polynomial interpretation [POLO]: 221.99/57.32 221.99/57.32 POL(0(x_1)) = 1 221.99/57.32 POL(1(x_1)) = 1 221.99/57.32 POL(2(x_1)) = x_1 221.99/57.32 POL(3(x_1)) = 0 221.99/57.32 POL(4(x_1)) = 1 221.99/57.32 POL(5(x_1)) = 0 221.99/57.32 POL(5^1(x_1)) = x_1 221.99/57.32 221.99/57.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.32 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (27) 221.99/57.32 Obligation: 221.99/57.32 Q DP problem: 221.99/57.32 The TRS P consists of the following rules: 221.99/57.32 221.99/57.32 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5^1(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 Q is empty. 221.99/57.32 We have to consider all minimal (P,Q,R)-chains. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (28) QDPOrderProof (EQUIVALENT) 221.99/57.32 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.32 221.99/57.32 221.99/57.32 The following pairs can be oriented strictly and are deleted. 221.99/57.32 221.99/57.32 5^1(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5^1(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 The remaining pairs can at least be oriented weakly. 221.99/57.32 Used ordering: Polynomial interpretation [POLO]: 221.99/57.32 221.99/57.32 POL(0(x_1)) = 1 221.99/57.32 POL(1(x_1)) = 1 221.99/57.32 POL(2(x_1)) = 0 221.99/57.32 POL(3(x_1)) = 1 221.99/57.32 POL(4(x_1)) = x_1 221.99/57.32 POL(5(x_1)) = x_1 221.99/57.32 POL(5^1(x_1)) = x_1 221.99/57.32 221.99/57.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.32 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (29) 221.99/57.32 Obligation: 221.99/57.32 Q DP problem: 221.99/57.32 P is empty. 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 Q is empty. 221.99/57.32 We have to consider all minimal (P,Q,R)-chains. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (30) PisEmptyProof (EQUIVALENT) 221.99/57.32 The TRS P is empty. Hence, there is no (P,Q,R) chain. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (31) 221.99/57.32 YES 221.99/57.32 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (32) 221.99/57.32 Obligation: 221.99/57.32 Q DP problem: 221.99/57.32 The TRS P consists of the following rules: 221.99/57.32 221.99/57.32 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 0^1(1(2(2(3(x1))))) -> 0^1(4(1(4(3(x1))))) 221.99/57.32 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 Q is empty. 221.99/57.32 We have to consider all minimal (P,Q,R)-chains. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (33) QDPOrderProof (EQUIVALENT) 221.99/57.32 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.32 221.99/57.32 221.99/57.32 The following pairs can be oriented strictly and are deleted. 221.99/57.32 221.99/57.32 0^1(1(2(2(3(x1))))) -> 0^1(4(1(4(3(x1))))) 221.99/57.32 The remaining pairs can at least be oriented weakly. 221.99/57.32 Used ordering: Polynomial interpretation [POLO]: 221.99/57.32 221.99/57.32 POL(0(x_1)) = 0 221.99/57.32 POL(0^1(x_1)) = x_1 221.99/57.32 POL(1(x_1)) = x_1 221.99/57.32 POL(2(x_1)) = 1 221.99/57.32 POL(3(x_1)) = 0 221.99/57.32 POL(4(x_1)) = 0 221.99/57.32 POL(5(x_1)) = 0 221.99/57.32 221.99/57.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.32 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 221.99/57.32 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (34) 221.99/57.32 Obligation: 221.99/57.32 Q DP problem: 221.99/57.32 The TRS P consists of the following rules: 221.99/57.32 221.99/57.32 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 Q is empty. 221.99/57.32 We have to consider all minimal (P,Q,R)-chains. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (35) QDPOrderProof (EQUIVALENT) 221.99/57.32 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.32 221.99/57.32 221.99/57.32 The following pairs can be oriented strictly and are deleted. 221.99/57.32 221.99/57.32 0^1(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0^1(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 The remaining pairs can at least be oriented weakly. 221.99/57.32 Used ordering: Polynomial interpretation [POLO]: 221.99/57.32 221.99/57.32 POL(0(x_1)) = 0 221.99/57.32 POL(0^1(x_1)) = x_1 221.99/57.32 POL(1(x_1)) = 1 + x_1 221.99/57.32 POL(2(x_1)) = 0 221.99/57.32 POL(3(x_1)) = 1 221.99/57.32 POL(4(x_1)) = 0 221.99/57.32 POL(5(x_1)) = 0 221.99/57.32 221.99/57.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.32 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 221.99/57.32 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (36) 221.99/57.32 Obligation: 221.99/57.32 Q DP problem: 221.99/57.32 P is empty. 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 Q is empty. 221.99/57.32 We have to consider all minimal (P,Q,R)-chains. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (37) PisEmptyProof (EQUIVALENT) 221.99/57.32 The TRS P is empty. Hence, there is no (P,Q,R) chain. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (38) 221.99/57.32 YES 221.99/57.32 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (39) 221.99/57.32 Obligation: 221.99/57.32 Q DP problem: 221.99/57.32 The TRS P consists of the following rules: 221.99/57.32 221.99/57.32 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 4^1(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 4^1(3(5(1(5(1(x1)))))) -> 4^1(0(2(4(5(4(x1)))))) 221.99/57.32 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 Q is empty. 221.99/57.32 We have to consider all minimal (P,Q,R)-chains. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (40) QDPOrderProof (EQUIVALENT) 221.99/57.32 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.32 221.99/57.32 221.99/57.32 The following pairs can be oriented strictly and are deleted. 221.99/57.32 221.99/57.32 4^1(3(5(1(5(1(x1)))))) -> 4^1(0(2(4(5(4(x1)))))) 221.99/57.32 4^1(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4^1(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 The remaining pairs can at least be oriented weakly. 221.99/57.32 Used ordering: Polynomial interpretation [POLO]: 221.99/57.32 221.99/57.32 POL(0(x_1)) = 0 221.99/57.32 POL(1(x_1)) = 0 221.99/57.32 POL(2(x_1)) = 0 221.99/57.32 POL(3(x_1)) = 1 221.99/57.32 POL(4(x_1)) = 0 221.99/57.32 POL(4^1(x_1)) = x_1 221.99/57.32 POL(5(x_1)) = 0 221.99/57.32 221.99/57.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.32 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 221.99/57.32 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (41) 221.99/57.32 Obligation: 221.99/57.32 Q DP problem: 221.99/57.32 The TRS P consists of the following rules: 221.99/57.32 221.99/57.32 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 4^1(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 221.99/57.32 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 221.99/57.32 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 221.99/57.32 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 221.99/57.32 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 221.99/57.32 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 221.99/57.32 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 221.99/57.32 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 221.99/57.32 221.99/57.32 Q is empty. 221.99/57.32 We have to consider all minimal (P,Q,R)-chains. 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (42) QDPOrderProof (EQUIVALENT) 221.99/57.32 We use the reduction pair processor [LPAR04,JAR06]. 221.99/57.32 221.99/57.32 221.99/57.32 The following pairs can be oriented strictly and are deleted. 221.99/57.32 221.99/57.32 4^1(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4^1(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 The remaining pairs can at least be oriented weakly. 221.99/57.32 Used ordering: Polynomial interpretation [POLO]: 221.99/57.32 221.99/57.32 POL(0(x_1)) = 1 + x_1 221.99/57.32 POL(1(x_1)) = x_1 221.99/57.32 POL(2(x_1)) = 0 221.99/57.32 POL(3(x_1)) = 0 221.99/57.32 POL(4(x_1)) = 0 221.99/57.32 POL(4^1(x_1)) = x_1 221.99/57.32 POL(5(x_1)) = 0 221.99/57.32 221.99/57.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 221.99/57.32 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 221.99/57.32 221.99/57.32 221.99/57.32 ---------------------------------------- 221.99/57.32 221.99/57.32 (43) 221.99/57.32 Obligation: 221.99/57.32 Q DP problem: 221.99/57.32 The TRS P consists of the following rules: 221.99/57.32 221.99/57.32 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 4^1(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 221.99/57.32 The TRS R consists of the following rules: 221.99/57.32 221.99/57.32 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 221.99/57.32 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 221.99/57.32 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 221.99/57.32 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 221.99/57.32 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 221.99/57.32 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 221.99/57.32 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 221.99/57.32 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 221.99/57.32 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 221.99/57.32 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 221.99/57.32 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 221.99/57.32 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 221.99/57.32 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 221.99/57.32 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 221.99/57.32 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 221.99/57.32 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 222.17/57.33 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.33 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 222.17/57.33 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 222.17/57.33 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 222.17/57.33 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 222.17/57.33 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.33 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 222.17/57.33 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 222.17/57.33 222.17/57.33 Q is empty. 222.17/57.33 We have to consider all minimal (P,Q,R)-chains. 222.17/57.33 ---------------------------------------- 222.17/57.33 222.17/57.33 (44) QDPOrderProof (EQUIVALENT) 222.17/57.33 We use the reduction pair processor [LPAR04,JAR06]. 222.17/57.33 222.17/57.33 222.17/57.33 The following pairs can be oriented strictly and are deleted. 222.17/57.33 222.17/57.33 4^1(1(5(1(2(4(1(4(1(x1))))))))) -> 4^1(2(3(1(3(0(1(3(1(x1))))))))) 222.17/57.33 The remaining pairs can at least be oriented weakly. 222.17/57.33 Used ordering: Polynomial interpretation [POLO]: 222.17/57.33 222.17/57.33 POL(0(x_1)) = 1 + x_1 222.17/57.33 POL(1(x_1)) = 1 + x_1 222.17/57.33 POL(2(x_1)) = 0 222.17/57.33 POL(3(x_1)) = x_1 222.17/57.33 POL(4(x_1)) = 0 222.17/57.33 POL(4^1(x_1)) = x_1 222.17/57.33 POL(5(x_1)) = 0 222.17/57.33 222.17/57.33 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 222.17/57.33 222.17/57.33 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 222.17/57.33 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 222.17/57.33 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 222.17/57.33 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 222.17/57.33 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 222.17/57.33 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 222.17/57.33 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 222.17/57.33 222.17/57.33 222.17/57.33 ---------------------------------------- 222.17/57.33 222.17/57.33 (45) 222.17/57.33 Obligation: 222.17/57.33 Q DP problem: 222.17/57.33 P is empty. 222.17/57.33 The TRS R consists of the following rules: 222.17/57.33 222.17/57.33 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 222.17/57.33 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 222.17/57.33 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 222.17/57.33 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 222.17/57.33 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 222.17/57.33 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 222.17/57.33 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 222.17/57.33 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 222.17/57.33 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 222.17/57.33 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 222.17/57.33 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 222.17/57.33 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 222.17/57.33 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.33 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 222.17/57.33 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 222.17/57.33 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 222.17/57.33 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.33 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 222.17/57.33 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 222.17/57.33 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 222.17/57.33 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 222.17/57.33 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.33 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 222.17/57.33 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 222.17/57.33 222.17/57.33 Q is empty. 222.17/57.33 We have to consider all minimal (P,Q,R)-chains. 222.17/57.33 ---------------------------------------- 222.17/57.33 222.17/57.33 (46) PisEmptyProof (EQUIVALENT) 222.17/57.33 The TRS P is empty. Hence, there is no (P,Q,R) chain. 222.17/57.33 ---------------------------------------- 222.17/57.33 222.17/57.33 (47) 222.17/57.33 YES 222.17/57.33 222.17/57.33 ---------------------------------------- 222.17/57.33 222.17/57.33 (48) 222.17/57.33 Obligation: 222.17/57.33 Q DP problem: 222.17/57.33 The TRS P consists of the following rules: 222.17/57.33 222.17/57.33 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.33 1^1(2(3(5(3(0(x1)))))) -> 1^1(1(4(3(5(1(x1)))))) 222.17/57.33 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.33 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.33 222.17/57.33 The TRS R consists of the following rules: 222.17/57.33 222.17/57.33 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 222.17/57.33 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 222.17/57.33 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 222.17/57.33 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 222.17/57.33 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 222.17/57.33 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 222.17/57.33 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 222.17/57.33 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 222.17/57.33 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 222.17/57.33 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 222.17/57.33 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 222.17/57.34 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 222.17/57.34 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.34 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 222.17/57.34 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 222.17/57.34 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 222.17/57.34 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.34 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 222.17/57.34 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 222.17/57.34 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 222.17/57.34 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 222.17/57.34 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.34 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 222.17/57.34 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 222.17/57.34 222.17/57.34 Q is empty. 222.17/57.34 We have to consider all minimal (P,Q,R)-chains. 222.17/57.34 ---------------------------------------- 222.17/57.34 222.17/57.34 (49) QDPOrderProof (EQUIVALENT) 222.17/57.34 We use the reduction pair processor [LPAR04,JAR06]. 222.17/57.34 222.17/57.34 222.17/57.34 The following pairs can be oriented strictly and are deleted. 222.17/57.34 222.17/57.34 1^1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1^1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.34 The remaining pairs can at least be oriented weakly. 222.17/57.34 Used ordering: Polynomial interpretation [POLO]: 222.17/57.34 222.17/57.34 POL(0(x_1)) = 1 222.17/57.34 POL(1(x_1)) = 0 222.17/57.34 POL(1^1(x_1)) = x_1 222.17/57.34 POL(2(x_1)) = x_1 222.17/57.34 POL(3(x_1)) = x_1 222.17/57.34 POL(4(x_1)) = 0 222.17/57.34 POL(5(x_1)) = 0 222.17/57.34 222.17/57.34 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 222.17/57.34 222.17/57.34 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 222.17/57.34 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 222.17/57.34 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 222.17/57.34 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 222.17/57.34 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 222.17/57.34 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 222.17/57.34 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.34 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 222.17/57.34 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.34 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.34 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 222.17/57.34 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 222.17/57.34 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 222.17/57.34 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 222.17/57.34 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 222.17/57.34 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 222.17/57.34 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 222.17/57.34 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 222.17/57.34 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 222.17/57.34 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 222.17/57.34 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 222.17/57.34 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 222.17/57.34 222.17/57.34 222.17/57.34 ---------------------------------------- 222.17/57.34 222.17/57.34 (50) 222.17/57.34 Obligation: 222.17/57.34 Q DP problem: 222.17/57.34 The TRS P consists of the following rules: 222.17/57.34 222.17/57.34 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.34 1^1(2(3(5(3(0(x1)))))) -> 1^1(1(4(3(5(1(x1)))))) 222.17/57.34 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.34 222.17/57.34 The TRS R consists of the following rules: 222.17/57.34 222.17/57.34 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 222.17/57.34 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 222.17/57.34 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 222.17/57.34 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 222.17/57.34 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 222.17/57.34 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 222.17/57.34 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 222.17/57.34 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 222.17/57.34 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 222.17/57.34 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 222.17/57.34 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 222.17/57.34 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 222.17/57.34 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.34 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 222.17/57.34 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 222.17/57.34 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 222.17/57.34 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.34 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 222.17/57.34 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 222.17/57.34 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 222.17/57.34 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 222.17/57.34 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.34 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 222.17/57.34 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 222.17/57.34 222.17/57.34 Q is empty. 222.17/57.34 We have to consider all minimal (P,Q,R)-chains. 222.17/57.34 ---------------------------------------- 222.17/57.34 222.17/57.34 (51) QDPOrderProof (EQUIVALENT) 222.17/57.34 We use the reduction pair processor [LPAR04,JAR06]. 222.17/57.34 222.17/57.34 222.17/57.34 The following pairs can be oriented strictly and are deleted. 222.17/57.34 222.17/57.34 1^1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1^1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.34 1^1(2(3(5(3(0(x1)))))) -> 1^1(1(4(3(5(1(x1)))))) 222.17/57.34 1^1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1^1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.34 The remaining pairs can at least be oriented weakly. 222.17/57.34 Used ordering: Polynomial interpretation [POLO]: 222.17/57.34 222.17/57.34 POL(0(x_1)) = 1 222.17/57.34 POL(1(x_1)) = 0 222.17/57.34 POL(1^1(x_1)) = x_1 222.17/57.34 POL(2(x_1)) = 1 222.17/57.34 POL(3(x_1)) = 1 + x_1 222.17/57.34 POL(4(x_1)) = 0 222.17/57.34 POL(5(x_1)) = 1 + x_1 222.17/57.34 222.17/57.34 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 222.17/57.34 222.17/57.34 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 222.17/57.34 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 222.17/57.34 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 222.17/57.34 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 222.17/57.34 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 222.17/57.34 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 222.17/57.34 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.34 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 222.17/57.34 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.34 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.34 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 222.17/57.34 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 222.17/57.34 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 222.17/57.34 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 222.17/57.34 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 222.17/57.34 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 222.17/57.34 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 222.17/57.34 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 222.17/57.34 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 222.17/57.34 222.17/57.34 222.17/57.34 ---------------------------------------- 222.17/57.34 222.17/57.34 (52) 222.17/57.34 Obligation: 222.17/57.34 Q DP problem: 222.17/57.34 P is empty. 222.17/57.34 The TRS R consists of the following rules: 222.17/57.34 222.17/57.34 0(1(2(2(3(x1))))) -> 0(4(1(4(3(x1))))) 222.17/57.34 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 222.17/57.34 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 222.17/57.34 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 222.17/57.34 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 222.17/57.34 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 222.17/57.34 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 222.17/57.34 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 222.17/57.34 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 222.17/57.34 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 222.17/57.34 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 222.17/57.34 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 222.17/57.34 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 222.17/57.34 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 222.17/57.34 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 222.17/57.34 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 222.17/57.34 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 222.17/57.34 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 222.17/57.34 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 222.17/57.34 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 222.17/57.34 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 222.17/57.34 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 222.17/57.34 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 222.17/57.34 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) 222.17/57.34 222.17/57.34 Q is empty. 222.17/57.34 We have to consider all minimal (P,Q,R)-chains. 222.17/57.34 ---------------------------------------- 222.17/57.34 222.17/57.34 (53) PisEmptyProof (EQUIVALENT) 222.17/57.34 The TRS P is empty. Hence, there is no (P,Q,R) chain. 222.17/57.34 ---------------------------------------- 222.17/57.34 222.17/57.34 (54) 222.17/57.34 YES 222.40/57.44 EOF