52.65/14.41 YES 53.31/14.61 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 53.31/14.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 53.31/14.61 53.31/14.61 53.31/14.61 Termination w.r.t. Q of the given QTRS could be proven: 53.31/14.61 53.31/14.61 (0) QTRS 53.31/14.61 (1) FlatCCProof [EQUIVALENT, 0 ms] 53.31/14.61 (2) QTRS 53.31/14.61 (3) RootLabelingProof [EQUIVALENT, 0 ms] 53.31/14.61 (4) QTRS 53.31/14.61 (5) QTRSRRRProof [EQUIVALENT, 98 ms] 53.31/14.61 (6) QTRS 53.31/14.61 (7) DependencyPairsProof [EQUIVALENT, 223 ms] 53.31/14.61 (8) QDP 53.31/14.61 (9) QDPOrderProof [EQUIVALENT, 669 ms] 53.31/14.61 (10) QDP 53.31/14.61 (11) DependencyGraphProof [EQUIVALENT, 1 ms] 53.31/14.61 (12) AND 53.31/14.61 (13) QDP 53.31/14.61 (14) QDPOrderProof [EQUIVALENT, 73 ms] 53.31/14.61 (15) QDP 53.31/14.61 (16) DependencyGraphProof [EQUIVALENT, 0 ms] 53.31/14.61 (17) TRUE 53.31/14.61 (18) QDP 53.31/14.61 (19) UsableRulesProof [EQUIVALENT, 0 ms] 53.31/14.61 (20) QDP 53.31/14.61 (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] 53.31/14.61 (22) YES 53.31/14.61 (23) QDP 53.31/14.61 (24) QDPOrderProof [EQUIVALENT, 62 ms] 53.31/14.61 (25) QDP 53.31/14.61 (26) PisEmptyProof [EQUIVALENT, 0 ms] 53.31/14.61 (27) YES 53.31/14.61 (28) QDP 53.31/14.61 (29) QDPOrderProof [EQUIVALENT, 67 ms] 53.31/14.61 (30) QDP 53.31/14.61 (31) PisEmptyProof [EQUIVALENT, 0 ms] 53.31/14.61 (32) YES 53.31/14.61 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (0) 53.31/14.61 Obligation: 53.31/14.61 Q restricted rewrite system: 53.31/14.61 The TRS R consists of the following rules: 53.31/14.61 53.31/14.61 s(b(x1)) -> b(s(s(s(x1)))) 53.31/14.61 s(b(s(x1))) -> b(t(x1)) 53.31/14.61 t(b(x1)) -> b(s(x1)) 53.31/14.61 t(b(s(x1))) -> u(t(b(x1))) 53.31/14.61 b(u(x1)) -> b(s(x1)) 53.31/14.61 t(s(x1)) -> t(t(x1)) 53.31/14.61 t(u(x1)) -> u(t(x1)) 53.31/14.61 s(u(x1)) -> s(s(x1)) 53.31/14.61 53.31/14.61 Q is empty. 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (1) FlatCCProof (EQUIVALENT) 53.31/14.61 We used flat context closure [ROOTLAB] 53.31/14.61 As Q is empty the flat context closure was sound AND complete. 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (2) 53.31/14.61 Obligation: 53.31/14.61 Q restricted rewrite system: 53.31/14.61 The TRS R consists of the following rules: 53.31/14.61 53.31/14.61 b(u(x1)) -> b(s(x1)) 53.31/14.61 t(s(x1)) -> t(t(x1)) 53.31/14.61 s(u(x1)) -> s(s(x1)) 53.31/14.61 s(s(b(x1))) -> s(b(s(s(s(x1))))) 53.31/14.61 b(s(b(x1))) -> b(b(s(s(s(x1))))) 53.31/14.61 t(s(b(x1))) -> t(b(s(s(s(x1))))) 53.31/14.61 u(s(b(x1))) -> u(b(s(s(s(x1))))) 53.31/14.61 s(s(b(s(x1)))) -> s(b(t(x1))) 53.31/14.61 b(s(b(s(x1)))) -> b(b(t(x1))) 53.31/14.61 t(s(b(s(x1)))) -> t(b(t(x1))) 53.31/14.61 u(s(b(s(x1)))) -> u(b(t(x1))) 53.31/14.61 s(t(b(x1))) -> s(b(s(x1))) 53.31/14.61 b(t(b(x1))) -> b(b(s(x1))) 53.31/14.61 t(t(b(x1))) -> t(b(s(x1))) 53.31/14.61 u(t(b(x1))) -> u(b(s(x1))) 53.31/14.61 s(t(b(s(x1)))) -> s(u(t(b(x1)))) 53.31/14.61 b(t(b(s(x1)))) -> b(u(t(b(x1)))) 53.31/14.61 t(t(b(s(x1)))) -> t(u(t(b(x1)))) 53.31/14.61 u(t(b(s(x1)))) -> u(u(t(b(x1)))) 53.31/14.61 s(t(u(x1))) -> s(u(t(x1))) 53.31/14.61 b(t(u(x1))) -> b(u(t(x1))) 53.31/14.61 t(t(u(x1))) -> t(u(t(x1))) 53.31/14.61 u(t(u(x1))) -> u(u(t(x1))) 53.31/14.61 53.31/14.61 Q is empty. 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (3) RootLabelingProof (EQUIVALENT) 53.31/14.61 We used plain root labeling [ROOTLAB] with the following heuristic: 53.31/14.61 LabelAll: All function symbols get labeled 53.31/14.61 53.31/14.61 As Q is empty the root labeling was sound AND complete. 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (4) 53.31/14.61 Obligation: 53.31/14.61 Q restricted rewrite system: 53.31/14.61 The TRS R consists of the following rules: 53.31/14.61 53.31/14.61 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.31/14.61 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.31/14.61 b_{u_1}(u_{s_1}(x1)) -> b_{s_1}(s_{s_1}(x1)) 53.31/14.61 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.31/14.61 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.31/14.61 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.31/14.61 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.31/14.61 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.31/14.61 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.31/14.61 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.31/14.61 s_{u_1}(u_{s_1}(x1)) -> s_{s_1}(s_{s_1}(x1)) 53.31/14.61 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.31/14.61 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{s_1}(x1))) -> s_{u_1}(u_{t_1}(t_{s_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{s_1}(x1))) -> b_{u_1}(u_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{s_1}(x1))) -> t_{u_1}(u_{t_1}(t_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{s_1}(x1))) -> u_{u_1}(u_{t_1}(t_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 53.31/14.61 Q is empty. 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (5) QTRSRRRProof (EQUIVALENT) 53.31/14.61 Used ordering: 53.31/14.61 Polynomial interpretation [POLO]: 53.31/14.61 53.31/14.61 POL(b_{b_1}(x_1)) = x_1 53.31/14.61 POL(b_{s_1}(x_1)) = x_1 53.31/14.61 POL(b_{t_1}(x_1)) = x_1 53.31/14.61 POL(b_{u_1}(x_1)) = x_1 53.31/14.61 POL(s_{b_1}(x_1)) = x_1 53.31/14.61 POL(s_{s_1}(x_1)) = x_1 53.31/14.61 POL(s_{t_1}(x_1)) = x_1 53.31/14.61 POL(s_{u_1}(x_1)) = x_1 53.31/14.61 POL(t_{b_1}(x_1)) = x_1 53.31/14.61 POL(t_{s_1}(x_1)) = x_1 53.31/14.61 POL(t_{t_1}(x_1)) = x_1 53.31/14.61 POL(t_{u_1}(x_1)) = x_1 53.31/14.61 POL(u_{b_1}(x_1)) = x_1 53.31/14.61 POL(u_{s_1}(x_1)) = 1 + x_1 53.31/14.61 POL(u_{t_1}(x_1)) = x_1 53.31/14.61 POL(u_{u_1}(x_1)) = x_1 53.31/14.61 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 53.31/14.61 53.31/14.61 b_{u_1}(u_{s_1}(x1)) -> b_{s_1}(s_{s_1}(x1)) 53.31/14.61 s_{u_1}(u_{s_1}(x1)) -> s_{s_1}(s_{s_1}(x1)) 53.31/14.61 u_{s_1}(s_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 u_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{s_1}(x1))) -> s_{u_1}(u_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{s_1}(x1))) -> b_{u_1}(u_{t_1}(t_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{s_1}(x1))) -> t_{u_1}(u_{t_1}(t_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{s_1}(x1))) -> u_{u_1}(u_{t_1}(t_{s_1}(x1))) 53.31/14.61 53.31/14.61 53.31/14.61 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (6) 53.31/14.61 Obligation: 53.31/14.61 Q restricted rewrite system: 53.31/14.61 The TRS R consists of the following rules: 53.31/14.61 53.31/14.61 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.31/14.61 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.31/14.61 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.31/14.61 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.31/14.61 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.31/14.61 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.31/14.61 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.31/14.61 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.31/14.61 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.31/14.61 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.31/14.61 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 53.31/14.61 Q is empty. 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (7) DependencyPairsProof (EQUIVALENT) 53.31/14.61 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (8) 53.31/14.61 Obligation: 53.31/14.61 Q DP problem: 53.31/14.61 The TRS P consists of the following rules: 53.31/14.61 53.31/14.61 B_{U_1}(u_{b_1}(x1)) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 B_{U_1}(u_{u_1}(x1)) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 B_{U_1}(u_{u_1}(x1)) -> S_{U_1}(x1) 53.31/14.61 B_{U_1}(u_{t_1}(x1)) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 B_{U_1}(u_{t_1}(x1)) -> S_{T_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(x1)) -> T_{T_1}(t_{b_1}(x1)) 53.31/14.61 T_{S_1}(s_{u_1}(x1)) -> T_{T_1}(t_{u_1}(x1)) 53.31/14.61 T_{S_1}(s_{s_1}(x1)) -> T_{T_1}(t_{s_1}(x1)) 53.31/14.61 T_{S_1}(s_{s_1}(x1)) -> T_{S_1}(x1) 53.31/14.61 T_{S_1}(s_{t_1}(x1)) -> T_{T_1}(t_{t_1}(x1)) 53.31/14.61 T_{S_1}(s_{t_1}(x1)) -> T_{T_1}(x1) 53.31/14.61 S_{U_1}(u_{b_1}(x1)) -> S_{S_1}(s_{b_1}(x1)) 53.31/14.61 S_{U_1}(u_{u_1}(x1)) -> S_{S_1}(s_{u_1}(x1)) 53.31/14.61 S_{U_1}(u_{u_1}(x1)) -> S_{U_1}(x1) 53.31/14.61 S_{U_1}(u_{t_1}(x1)) -> S_{S_1}(s_{t_1}(x1)) 53.31/14.61 S_{U_1}(u_{t_1}(x1)) -> S_{T_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1)))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{s_1}(s_{b_1}(x1))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{b_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1)))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{s_1}(s_{u_1}(x1))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{u_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1)))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(s_{s_1}(x1))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1)))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{s_1}(s_{t_1}(x1))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{t_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1)))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{s_1}(s_{b_1}(x1))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{b_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1)))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{s_1}(s_{u_1}(x1))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{u_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1)))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(s_{s_1}(x1))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1)))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{s_1}(s_{t_1}(x1))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{t_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1)))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{s_1}(s_{b_1}(x1))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{b_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1)))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{s_1}(s_{u_1}(x1))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{u_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1)))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(s_{s_1}(x1))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1)))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{s_1}(s_{t_1}(x1))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{t_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> B_{T_1}(t_{b_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{T_1}(t_{u_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{T_1}(t_{s_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> T_{S_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(t_{t_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> T_{T_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> B_{T_1}(t_{b_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{T_1}(t_{u_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{T_1}(t_{s_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> T_{S_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(t_{t_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> T_{T_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> B_{T_1}(t_{b_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{T_1}(t_{u_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{T_1}(t_{s_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> T_{S_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(t_{t_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> T_{T_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 B_{T_1}(t_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 B_{T_1}(t_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(x1)) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 B_{T_1}(t_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 T_{T_1}(t_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 T_{T_1}(t_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(x1)) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 T_{T_1}(t_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 U_{T_1}(t_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 U_{T_1}(t_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(x1)) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 U_{T_1}(t_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{b_1}(x1))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{S_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> B_{U_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{b_1}(x1))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{U_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{S_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{U_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{b_1}(x1))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{S_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{b_1}(x1))) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{S_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(x1) 53.31/14.61 S_{T_1}(t_{u_1}(u_{b_1}(x1))) -> S_{U_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 S_{T_1}(t_{u_1}(u_{b_1}(x1))) -> U_{T_1}(t_{b_1}(x1)) 53.31/14.61 S_{T_1}(t_{u_1}(u_{u_1}(x1))) -> S_{U_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 S_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.31/14.61 S_{T_1}(t_{u_1}(u_{t_1}(x1))) -> S_{U_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 S_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.31/14.61 S_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.31/14.61 B_{T_1}(t_{u_1}(u_{b_1}(x1))) -> B_{U_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 B_{T_1}(t_{u_1}(u_{b_1}(x1))) -> U_{T_1}(t_{b_1}(x1)) 53.31/14.61 B_{T_1}(t_{u_1}(u_{u_1}(x1))) -> B_{U_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 B_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.31/14.61 B_{T_1}(t_{u_1}(u_{t_1}(x1))) -> B_{U_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 B_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.31/14.61 B_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.31/14.61 T_{T_1}(t_{u_1}(u_{b_1}(x1))) -> U_{T_1}(t_{b_1}(x1)) 53.31/14.61 T_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.31/14.61 T_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.31/14.61 T_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.31/14.61 U_{T_1}(t_{u_1}(u_{b_1}(x1))) -> U_{T_1}(t_{b_1}(x1)) 53.31/14.61 U_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.31/14.61 U_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.31/14.61 U_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.31/14.61 53.31/14.61 The TRS R consists of the following rules: 53.31/14.61 53.31/14.61 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.31/14.61 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.31/14.61 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.31/14.61 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.31/14.61 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.31/14.61 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.31/14.61 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.31/14.61 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.31/14.61 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.31/14.61 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.31/14.61 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 53.31/14.61 Q is empty. 53.31/14.61 We have to consider all minimal (P,Q,R)-chains. 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (9) QDPOrderProof (EQUIVALENT) 53.31/14.61 We use the reduction pair processor [LPAR04,JAR06]. 53.31/14.61 53.31/14.61 53.31/14.61 The following pairs can be oriented strictly and are deleted. 53.31/14.61 53.31/14.61 B_{U_1}(u_{b_1}(x1)) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 B_{U_1}(u_{u_1}(x1)) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 B_{U_1}(u_{t_1}(x1)) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(x1)) -> T_{T_1}(t_{b_1}(x1)) 53.31/14.61 T_{S_1}(s_{u_1}(x1)) -> T_{T_1}(t_{u_1}(x1)) 53.31/14.61 T_{S_1}(s_{s_1}(x1)) -> T_{T_1}(t_{s_1}(x1)) 53.31/14.61 T_{S_1}(s_{t_1}(x1)) -> T_{T_1}(t_{t_1}(x1)) 53.31/14.61 T_{S_1}(s_{t_1}(x1)) -> T_{T_1}(x1) 53.31/14.61 S_{U_1}(u_{b_1}(x1)) -> S_{S_1}(s_{b_1}(x1)) 53.31/14.61 S_{U_1}(u_{u_1}(x1)) -> S_{S_1}(s_{u_1}(x1)) 53.31/14.61 S_{U_1}(u_{t_1}(x1)) -> S_{S_1}(s_{t_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1)))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{s_1}(s_{b_1}(x1))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{b_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1)))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{s_1}(s_{u_1}(x1))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{u_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1)))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(s_{s_1}(x1))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1)))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{s_1}(s_{t_1}(x1))) 53.31/14.61 S_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{t_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1)))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{s_1}(s_{b_1}(x1))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{b_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1)))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{s_1}(s_{u_1}(x1))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{u_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1)))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(s_{s_1}(x1))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1)))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{s_1}(s_{t_1}(x1))) 53.31/14.61 B_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{t_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1)))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{s_1}(s_{b_1}(x1))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{b_1}(x1))) -> S_{S_1}(s_{b_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1)))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{s_1}(s_{u_1}(x1))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{S_1}(s_{u_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1)))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(s_{s_1}(x1))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(s_{s_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1)))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{s_1}(s_{t_1}(x1))) 53.31/14.61 T_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{S_1}(s_{t_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> T_{T_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> T_{T_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> B_{T_1}(t_{b_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{T_1}(t_{u_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{T_1}(t_{s_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> T_{S_1}(x1) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(t_{t_1}(x1)) 53.31/14.61 T_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> T_{T_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 B_{T_1}(t_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 B_{T_1}(t_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(x1)) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 B_{T_1}(t_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 T_{T_1}(t_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(x1)) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 U_{T_1}(t_{b_1}(b_{b_1}(x1))) -> B_{S_1}(s_{b_1}(x1)) 53.31/14.61 U_{T_1}(t_{b_1}(b_{u_1}(x1))) -> B_{S_1}(s_{u_1}(x1)) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(x1))) -> B_{S_1}(s_{s_1}(x1)) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(x1))) -> S_{S_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{t_1}(x1))) -> B_{S_1}(s_{t_1}(x1)) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{b_1}(x1))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{S_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{b_1}(x1))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{S_1}(x1) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{S_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{S_1}(x1) 53.31/14.61 S_{T_1}(t_{u_1}(u_{b_1}(x1))) -> U_{T_1}(t_{b_1}(x1)) 53.31/14.61 S_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.31/14.61 S_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.31/14.61 S_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.31/14.61 B_{T_1}(t_{u_1}(u_{b_1}(x1))) -> U_{T_1}(t_{b_1}(x1)) 53.31/14.61 B_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.31/14.61 B_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.31/14.61 B_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.31/14.61 The remaining pairs can at least be oriented weakly. 53.31/14.61 Used ordering: Polynomial interpretation [POLO]: 53.31/14.61 53.31/14.61 POL(B_{S_1}(x_1)) = x_1 53.31/14.61 POL(B_{T_1}(x_1)) = 1 + x_1 53.31/14.61 POL(B_{U_1}(x_1)) = 1 + x_1 53.31/14.61 POL(S_{S_1}(x_1)) = x_1 53.31/14.61 POL(S_{T_1}(x_1)) = 1 + x_1 53.31/14.61 POL(S_{U_1}(x_1)) = 1 + x_1 53.31/14.61 POL(T_{S_1}(x_1)) = 1 + x_1 53.31/14.61 POL(T_{T_1}(x_1)) = x_1 53.31/14.61 POL(U_{T_1}(x_1)) = x_1 53.31/14.61 POL(b_{b_1}(x_1)) = 1 + x_1 53.31/14.61 POL(b_{s_1}(x_1)) = x_1 53.31/14.61 POL(b_{t_1}(x_1)) = x_1 53.31/14.61 POL(b_{u_1}(x_1)) = x_1 53.31/14.61 POL(s_{b_1}(x_1)) = 1 + x_1 53.31/14.61 POL(s_{s_1}(x_1)) = x_1 53.31/14.61 POL(s_{t_1}(x_1)) = x_1 53.31/14.61 POL(s_{u_1}(x_1)) = x_1 53.31/14.61 POL(t_{b_1}(x_1)) = 1 + x_1 53.31/14.61 POL(t_{s_1}(x_1)) = x_1 53.31/14.61 POL(t_{t_1}(x_1)) = x_1 53.31/14.61 POL(t_{u_1}(x_1)) = x_1 53.31/14.61 POL(u_{b_1}(x_1)) = 1 + x_1 53.31/14.61 POL(u_{t_1}(x_1)) = x_1 53.31/14.61 POL(u_{u_1}(x_1)) = x_1 53.31/14.61 53.31/14.61 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 53.31/14.61 53.31/14.61 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.31/14.61 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.31/14.61 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.31/14.61 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.31/14.61 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.31/14.61 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.31/14.61 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.31/14.61 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.31/14.61 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.31/14.61 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.31/14.61 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (10) 53.31/14.61 Obligation: 53.31/14.61 Q DP problem: 53.31/14.61 The TRS P consists of the following rules: 53.31/14.61 53.31/14.61 B_{U_1}(u_{u_1}(x1)) -> S_{U_1}(x1) 53.31/14.61 B_{U_1}(u_{t_1}(x1)) -> S_{T_1}(x1) 53.31/14.61 T_{S_1}(s_{s_1}(x1)) -> T_{S_1}(x1) 53.31/14.61 S_{U_1}(u_{u_1}(x1)) -> S_{U_1}(x1) 53.31/14.61 S_{U_1}(u_{t_1}(x1)) -> S_{T_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> B_{T_1}(t_{b_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{T_1}(t_{u_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{T_1}(t_{s_1}(x1)) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> T_{S_1}(x1) 53.31/14.61 S_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(t_{t_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> B_{T_1}(t_{b_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{T_1}(t_{u_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{T_1}(t_{s_1}(x1)) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> T_{S_1}(x1) 53.31/14.61 B_{S_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(t_{t_1}(x1)) 53.31/14.61 T_{T_1}(t_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{u_1}(x1))) -> S_{U_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{t_1}(x1))) -> S_{T_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> B_{U_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> B_{U_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 B_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{U_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{b_1}(x1))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(x1) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.31/14.61 T_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{b_1}(x1))) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> B_{U_1}(x1) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.31/14.61 U_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> B_{T_1}(x1) 53.31/14.61 S_{T_1}(t_{u_1}(u_{b_1}(x1))) -> S_{U_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 S_{T_1}(t_{u_1}(u_{u_1}(x1))) -> S_{U_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 S_{T_1}(t_{u_1}(u_{t_1}(x1))) -> S_{U_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 B_{T_1}(t_{u_1}(u_{b_1}(x1))) -> B_{U_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 B_{T_1}(t_{u_1}(u_{u_1}(x1))) -> B_{U_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 B_{T_1}(t_{u_1}(u_{t_1}(x1))) -> B_{U_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 T_{T_1}(t_{u_1}(u_{b_1}(x1))) -> U_{T_1}(t_{b_1}(x1)) 53.31/14.61 T_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.31/14.61 T_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.31/14.61 T_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.31/14.61 U_{T_1}(t_{u_1}(u_{b_1}(x1))) -> U_{T_1}(t_{b_1}(x1)) 53.31/14.61 U_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.31/14.61 U_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.31/14.61 U_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.31/14.61 53.31/14.61 The TRS R consists of the following rules: 53.31/14.61 53.31/14.61 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.31/14.61 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.31/14.61 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.31/14.61 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.31/14.61 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.31/14.61 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.31/14.61 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.31/14.61 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.31/14.61 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.31/14.61 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.31/14.61 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 53.31/14.61 Q is empty. 53.31/14.61 We have to consider all minimal (P,Q,R)-chains. 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (11) DependencyGraphProof (EQUIVALENT) 53.31/14.61 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs with 38 less nodes. 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (12) 53.31/14.61 Complex Obligation (AND) 53.31/14.61 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (13) 53.31/14.61 Obligation: 53.31/14.61 Q DP problem: 53.31/14.61 The TRS P consists of the following rules: 53.31/14.61 53.31/14.61 S_{U_1}(u_{t_1}(x1)) -> S_{T_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 S_{U_1}(u_{u_1}(x1)) -> S_{U_1}(x1) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 S_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 S_{T_1}(t_{u_1}(u_{b_1}(x1))) -> S_{U_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 S_{T_1}(t_{u_1}(u_{u_1}(x1))) -> S_{U_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 S_{T_1}(t_{u_1}(u_{t_1}(x1))) -> S_{U_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 53.31/14.61 The TRS R consists of the following rules: 53.31/14.61 53.31/14.61 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.31/14.61 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.31/14.61 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.31/14.61 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.31/14.61 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.31/14.61 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.31/14.61 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.31/14.61 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.31/14.61 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.31/14.61 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.31/14.61 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 53.31/14.61 Q is empty. 53.31/14.61 We have to consider all minimal (P,Q,R)-chains. 53.31/14.61 ---------------------------------------- 53.31/14.61 53.31/14.61 (14) QDPOrderProof (EQUIVALENT) 53.31/14.61 We use the reduction pair processor [LPAR04,JAR06]. 53.31/14.61 53.31/14.61 53.31/14.61 The following pairs can be oriented strictly and are deleted. 53.31/14.61 53.31/14.61 S_{U_1}(u_{t_1}(x1)) -> S_{T_1}(x1) 53.31/14.61 S_{U_1}(u_{u_1}(x1)) -> S_{U_1}(x1) 53.31/14.61 The remaining pairs can at least be oriented weakly. 53.31/14.61 Used ordering: Polynomial interpretation [POLO]: 53.31/14.61 53.31/14.61 POL(S_{T_1}(x_1)) = 1 + x_1 53.31/14.61 POL(S_{U_1}(x_1)) = 1 + x_1 53.31/14.61 POL(b_{b_1}(x_1)) = 0 53.31/14.61 POL(b_{s_1}(x_1)) = 1 + x_1 53.31/14.61 POL(b_{t_1}(x_1)) = 1 + x_1 53.31/14.61 POL(b_{u_1}(x_1)) = 1 + x_1 53.31/14.61 POL(s_{b_1}(x_1)) = 0 53.31/14.61 POL(s_{s_1}(x_1)) = 1 + x_1 53.31/14.61 POL(s_{t_1}(x_1)) = 1 + x_1 53.31/14.61 POL(s_{u_1}(x_1)) = 1 + x_1 53.31/14.61 POL(t_{b_1}(x_1)) = 1 + x_1 53.31/14.61 POL(t_{s_1}(x_1)) = 0 53.31/14.61 POL(t_{t_1}(x_1)) = 1 + x_1 53.31/14.61 POL(t_{u_1}(x_1)) = 1 + x_1 53.31/14.61 POL(u_{b_1}(x_1)) = 1 + x_1 53.31/14.61 POL(u_{t_1}(x_1)) = 1 + x_1 53.31/14.61 POL(u_{u_1}(x_1)) = 1 + x_1 53.31/14.61 53.31/14.61 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 53.31/14.61 53.31/14.61 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.31/14.61 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.31/14.61 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.31/14.61 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.61 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.61 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.61 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.61 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.62 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.62 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.62 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.62 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.31/14.62 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.31/14.62 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.31/14.62 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.62 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.62 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.62 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.62 53.31/14.62 53.31/14.62 ---------------------------------------- 53.31/14.62 53.31/14.62 (15) 53.31/14.62 Obligation: 53.31/14.62 Q DP problem: 53.31/14.62 The TRS P consists of the following rules: 53.31/14.62 53.31/14.62 S_{T_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.62 S_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.62 S_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.62 S_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> S_{U_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.62 S_{T_1}(t_{u_1}(u_{b_1}(x1))) -> S_{U_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.62 S_{T_1}(t_{u_1}(u_{u_1}(x1))) -> S_{U_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.62 S_{T_1}(t_{u_1}(u_{t_1}(x1))) -> S_{U_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.62 53.31/14.62 The TRS R consists of the following rules: 53.31/14.62 53.31/14.62 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.31/14.62 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.31/14.62 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.31/14.62 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.31/14.62 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.31/14.62 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.31/14.62 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.31/14.62 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.31/14.62 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.31/14.62 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.31/14.62 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.62 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.62 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.62 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.62 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.62 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.31/14.62 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.31/14.62 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.31/14.62 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.62 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.62 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.62 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.62 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.62 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.62 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.31/14.62 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.31/14.62 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.31/14.62 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.62 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.62 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.62 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.62 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.62 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.31/14.62 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.31/14.62 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.31/14.62 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.62 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.62 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.62 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.62 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.62 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.62 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.62 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.31/14.62 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.31/14.62 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.31/14.62 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.31/14.62 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.62 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.62 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.62 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.62 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.62 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.31/14.62 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.31/14.62 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.31/14.62 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 53.64/14.64 Q is empty. 53.64/14.64 We have to consider all minimal (P,Q,R)-chains. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (16) DependencyGraphProof (EQUIVALENT) 53.64/14.64 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 7 less nodes. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (17) 53.64/14.64 TRUE 53.64/14.64 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (18) 53.64/14.64 Obligation: 53.64/14.64 Q DP problem: 53.64/14.64 The TRS P consists of the following rules: 53.64/14.64 53.64/14.64 T_{S_1}(s_{s_1}(x1)) -> T_{S_1}(x1) 53.64/14.64 53.64/14.64 The TRS R consists of the following rules: 53.64/14.64 53.64/14.64 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.64/14.64 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.64/14.64 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.64/14.64 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.64/14.64 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.64/14.64 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.64/14.64 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.64/14.64 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.64/14.64 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.64/14.64 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.64/14.64 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 53.64/14.64 Q is empty. 53.64/14.64 We have to consider all minimal (P,Q,R)-chains. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (19) UsableRulesProof (EQUIVALENT) 53.64/14.64 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (20) 53.64/14.64 Obligation: 53.64/14.64 Q DP problem: 53.64/14.64 The TRS P consists of the following rules: 53.64/14.64 53.64/14.64 T_{S_1}(s_{s_1}(x1)) -> T_{S_1}(x1) 53.64/14.64 53.64/14.64 R is empty. 53.64/14.64 Q is empty. 53.64/14.64 We have to consider all minimal (P,Q,R)-chains. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (21) QDPSizeChangeProof (EQUIVALENT) 53.64/14.64 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 53.64/14.64 53.64/14.64 From the DPs we obtained the following set of size-change graphs: 53.64/14.64 *T_{S_1}(s_{s_1}(x1)) -> T_{S_1}(x1) 53.64/14.64 The graph contains the following edges 1 > 1 53.64/14.64 53.64/14.64 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (22) 53.64/14.64 YES 53.64/14.64 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (23) 53.64/14.64 Obligation: 53.64/14.64 Q DP problem: 53.64/14.64 The TRS P consists of the following rules: 53.64/14.64 53.64/14.64 U_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.64/14.64 U_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.64/14.64 U_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.64/14.64 53.64/14.64 The TRS R consists of the following rules: 53.64/14.64 53.64/14.64 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.64/14.64 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.64/14.64 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.64/14.64 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.64/14.64 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.64/14.64 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.64/14.64 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.64/14.64 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.64/14.64 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.64/14.64 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.64/14.64 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 53.64/14.64 Q is empty. 53.64/14.64 We have to consider all minimal (P,Q,R)-chains. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (24) QDPOrderProof (EQUIVALENT) 53.64/14.64 We use the reduction pair processor [LPAR04,JAR06]. 53.64/14.64 53.64/14.64 53.64/14.64 The following pairs can be oriented strictly and are deleted. 53.64/14.64 53.64/14.64 U_{T_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{s_1}(x1))) 53.64/14.64 U_{T_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{u_1}(x1))) 53.64/14.64 U_{T_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> U_{T_1}(t_{b_1}(b_{t_1}(x1))) 53.64/14.64 The remaining pairs can at least be oriented weakly. 53.64/14.64 Used ordering: Polynomial interpretation [POLO]: 53.64/14.64 53.64/14.64 POL(U_{T_1}(x_1)) = x_1 53.64/14.64 POL(b_{b_1}(x_1)) = 0 53.64/14.64 POL(b_{s_1}(x_1)) = x_1 53.64/14.64 POL(b_{t_1}(x_1)) = x_1 53.64/14.64 POL(b_{u_1}(x_1)) = x_1 53.64/14.64 POL(s_{b_1}(x_1)) = 1 53.64/14.64 POL(s_{s_1}(x_1)) = 1 + x_1 53.64/14.64 POL(s_{t_1}(x_1)) = 1 + x_1 53.64/14.64 POL(s_{u_1}(x_1)) = 1 + x_1 53.64/14.64 POL(t_{b_1}(x_1)) = 1 + x_1 53.64/14.64 POL(t_{s_1}(x_1)) = 0 53.64/14.64 POL(t_{t_1}(x_1)) = 1 + x_1 53.64/14.64 POL(t_{u_1}(x_1)) = 1 + x_1 53.64/14.64 POL(u_{b_1}(x_1)) = 1 + x_1 53.64/14.64 POL(u_{t_1}(x_1)) = 1 + x_1 53.64/14.64 POL(u_{u_1}(x_1)) = 1 + x_1 53.64/14.64 53.64/14.64 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 53.64/14.64 53.64/14.64 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.64/14.64 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.64/14.64 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.64/14.64 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.64/14.64 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.64/14.64 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.64/14.64 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 53.64/14.64 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (25) 53.64/14.64 Obligation: 53.64/14.64 Q DP problem: 53.64/14.64 P is empty. 53.64/14.64 The TRS R consists of the following rules: 53.64/14.64 53.64/14.64 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.64/14.64 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.64/14.64 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.64/14.64 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.64/14.64 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.64/14.64 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.64/14.64 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.64/14.64 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.64/14.64 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.64/14.64 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.64/14.64 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 53.64/14.64 Q is empty. 53.64/14.64 We have to consider all minimal (P,Q,R)-chains. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (26) PisEmptyProof (EQUIVALENT) 53.64/14.64 The TRS P is empty. Hence, there is no (P,Q,R) chain. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (27) 53.64/14.64 YES 53.64/14.64 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (28) 53.64/14.64 Obligation: 53.64/14.64 Q DP problem: 53.64/14.64 The TRS P consists of the following rules: 53.64/14.64 53.64/14.64 T_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.64/14.64 U_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.64/14.64 U_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.64/14.64 U_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.64/14.64 T_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.64/14.64 T_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.64/14.64 53.64/14.64 The TRS R consists of the following rules: 53.64/14.64 53.64/14.64 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.64/14.64 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.64/14.64 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.64/14.64 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.64/14.64 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.64/14.64 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.64/14.64 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.64/14.64 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.64/14.64 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.64/14.64 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.64/14.64 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 53.64/14.64 Q is empty. 53.64/14.64 We have to consider all minimal (P,Q,R)-chains. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (29) QDPOrderProof (EQUIVALENT) 53.64/14.64 We use the reduction pair processor [LPAR04,JAR06]. 53.64/14.64 53.64/14.64 53.64/14.64 The following pairs can be oriented strictly and are deleted. 53.64/14.64 53.64/14.64 T_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.64/14.64 U_{T_1}(t_{u_1}(u_{u_1}(x1))) -> U_{T_1}(t_{u_1}(x1)) 53.64/14.64 U_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.64/14.64 U_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.64/14.64 T_{T_1}(t_{u_1}(u_{t_1}(x1))) -> U_{T_1}(t_{t_1}(x1)) 53.64/14.64 T_{T_1}(t_{u_1}(u_{t_1}(x1))) -> T_{T_1}(x1) 53.64/14.64 The remaining pairs can at least be oriented weakly. 53.64/14.64 Used ordering: Polynomial interpretation [POLO]: 53.64/14.64 53.64/14.64 POL(T_{T_1}(x_1)) = x_1 53.64/14.64 POL(U_{T_1}(x_1)) = x_1 53.64/14.64 POL(b_{b_1}(x_1)) = 0 53.64/14.64 POL(b_{s_1}(x_1)) = 1 + x_1 53.64/14.64 POL(b_{t_1}(x_1)) = 1 + x_1 53.64/14.64 POL(b_{u_1}(x_1)) = 1 + x_1 53.64/14.64 POL(s_{b_1}(x_1)) = 0 53.64/14.64 POL(s_{s_1}(x_1)) = 1 + x_1 53.64/14.64 POL(s_{t_1}(x_1)) = 1 + x_1 53.64/14.64 POL(s_{u_1}(x_1)) = 1 + x_1 53.64/14.64 POL(t_{b_1}(x_1)) = x_1 53.64/14.64 POL(t_{s_1}(x_1)) = 0 53.64/14.64 POL(t_{t_1}(x_1)) = 1 + x_1 53.64/14.64 POL(t_{u_1}(x_1)) = 1 + x_1 53.64/14.64 POL(u_{b_1}(x_1)) = x_1 53.64/14.64 POL(u_{t_1}(x_1)) = 1 + x_1 53.64/14.64 POL(u_{u_1}(x_1)) = 1 + x_1 53.64/14.64 53.64/14.64 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 53.64/14.64 53.64/14.64 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.64/14.64 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.64/14.64 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.64/14.64 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.64/14.64 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.64/14.64 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.64/14.64 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 53.64/14.64 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (30) 53.64/14.64 Obligation: 53.64/14.64 Q DP problem: 53.64/14.64 P is empty. 53.64/14.64 The TRS R consists of the following rules: 53.64/14.64 53.64/14.64 b_{u_1}(u_{b_1}(x1)) -> b_{s_1}(s_{b_1}(x1)) 53.64/14.64 b_{u_1}(u_{u_1}(x1)) -> b_{s_1}(s_{u_1}(x1)) 53.64/14.64 b_{u_1}(u_{t_1}(x1)) -> b_{s_1}(s_{t_1}(x1)) 53.64/14.64 t_{s_1}(s_{b_1}(x1)) -> t_{t_1}(t_{b_1}(x1)) 53.64/14.64 t_{s_1}(s_{u_1}(x1)) -> t_{t_1}(t_{u_1}(x1)) 53.64/14.64 t_{s_1}(s_{s_1}(x1)) -> t_{t_1}(t_{s_1}(x1)) 53.64/14.64 t_{s_1}(s_{t_1}(x1)) -> t_{t_1}(t_{t_1}(x1)) 53.64/14.64 s_{u_1}(u_{b_1}(x1)) -> s_{s_1}(s_{b_1}(x1)) 53.64/14.64 s_{u_1}(u_{u_1}(x1)) -> s_{s_1}(s_{u_1}(x1)) 53.64/14.64 s_{u_1}(u_{t_1}(x1)) -> s_{s_1}(s_{t_1}(x1)) 53.64/14.64 s_{s_1}(s_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{b_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{u_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{s_1}(x1))))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(s_{s_1}(s_{t_1}(x1))))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 s_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 b_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{s_1}(x1))) 53.64/14.64 t_{s_1}(s_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{b_1}(b_{t_1}(t_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{b_1}(x1))) -> s_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{u_1}(x1))) -> s_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(x1))) -> s_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{t_1}(x1))) -> s_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{u_1}(x1))) -> b_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(x1))) -> b_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{t_1}(x1))) -> b_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{b_1}(x1))) -> t_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{u_1}(x1))) -> t_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(x1))) -> t_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{t_1}(x1))) -> t_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{b_1}(x1))) -> u_{b_1}(b_{s_1}(s_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{u_1}(x1))) -> u_{b_1}(b_{s_1}(s_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(x1))) -> u_{b_1}(b_{s_1}(s_{s_1}(x1))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{t_1}(x1))) -> u_{b_1}(b_{s_1}(s_{t_1}(x1))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 s_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> s_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 b_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> b_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 t_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> t_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{b_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{b_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{u_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{u_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{s_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{s_1}(x1)))) 53.64/14.64 u_{t_1}(t_{b_1}(b_{s_1}(s_{t_1}(x1)))) -> u_{u_1}(u_{t_1}(t_{b_1}(b_{t_1}(x1)))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{b_1}(x1))) -> s_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{u_1}(x1))) -> s_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 s_{t_1}(t_{u_1}(u_{t_1}(x1))) -> s_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{b_1}(x1))) -> b_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{u_1}(x1))) -> b_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 b_{t_1}(t_{u_1}(u_{t_1}(x1))) -> b_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{b_1}(x1))) -> t_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{u_1}(x1))) -> t_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 t_{t_1}(t_{u_1}(u_{t_1}(x1))) -> t_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{b_1}(x1))) -> u_{u_1}(u_{t_1}(t_{b_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{u_1}(x1))) -> u_{u_1}(u_{t_1}(t_{u_1}(x1))) 53.64/14.64 u_{t_1}(t_{u_1}(u_{t_1}(x1))) -> u_{u_1}(u_{t_1}(t_{t_1}(x1))) 53.64/14.64 53.64/14.64 Q is empty. 53.64/14.64 We have to consider all minimal (P,Q,R)-chains. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (31) PisEmptyProof (EQUIVALENT) 53.64/14.64 The TRS P is empty. Hence, there is no (P,Q,R) chain. 53.64/14.64 ---------------------------------------- 53.64/14.64 53.64/14.64 (32) 53.64/14.64 YES 53.86/14.73 EOF