1141.73/289.57 YES 1143.69/290.01 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1143.69/290.01 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1143.69/290.01 1143.69/290.01 1143.69/290.01 Termination of the given RelTRS could be proven: 1143.69/290.01 1143.69/290.01 (0) RelTRS 1143.69/290.01 (1) FlatCCProof [EQUIVALENT, 0 ms] 1143.69/290.01 (2) RelTRS 1143.69/290.01 (3) RootLabelingProof [EQUIVALENT, 5 ms] 1143.69/290.01 (4) RelTRS 1143.69/290.01 (5) FlatCCProof [EQUIVALENT, 0 ms] 1143.69/290.01 (6) RelTRS 1143.69/290.01 (7) RootLabelingProof [EQUIVALENT, 7 ms] 1143.69/290.01 (8) RelTRS 1143.69/290.01 (9) RelTRSRRRProof [EQUIVALENT, 107 ms] 1143.69/290.01 (10) RelTRS 1143.69/290.01 (11) RelTRSRRRProof [EQUIVALENT, 60 ms] 1143.69/290.01 (12) RelTRS 1143.69/290.01 (13) RelTRSRRRProof [EQUIVALENT, 19.7 s] 1143.69/290.01 (14) RelTRS 1143.69/290.01 (15) RelTRSRRRProof [EQUIVALENT, 11 ms] 1143.69/290.01 (16) RelTRS 1143.69/290.01 (17) RelTRSRRRProof [EQUIVALENT, 0 ms] 1143.69/290.01 (18) RelTRS 1143.69/290.01 (19) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 711 ms] 1143.69/290.01 (20) RelTRS 1143.69/290.01 (21) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 697 ms] 1143.69/290.01 (22) RelTRS 1143.69/290.01 (23) RelTRSRRRProof [EQUIVALENT, 1952 ms] 1143.69/290.01 (24) RelTRS 1143.69/290.01 (25) RelTRSRRRProof [EQUIVALENT, 18 ms] 1143.69/290.01 (26) RelTRS 1143.69/290.01 (27) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 611 ms] 1143.69/290.01 (28) RelTRS 1143.69/290.01 (29) RelTRSRRRProof [EQUIVALENT, 8 ms] 1143.69/290.01 (30) RelTRS 1143.69/290.01 (31) RelTRSRRRProof [EQUIVALENT, 4804 ms] 1143.69/290.01 (32) RelTRS 1143.69/290.01 (33) RelTRSRRRProof [EQUIVALENT, 1063 ms] 1143.69/290.01 (34) RelTRS 1143.69/290.01 (35) RelTRSRRRProof [EQUIVALENT, 1542 ms] 1143.69/290.01 (36) RelTRS 1143.69/290.01 (37) RelTRSRRRProof [EQUIVALENT, 970 ms] 1143.69/290.01 (38) RelTRS 1143.69/290.01 (39) RIsEmptyProof [EQUIVALENT, 0 ms] 1143.69/290.01 (40) YES 1143.69/290.01 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (0) 1143.69/290.01 Obligation: 1143.69/290.01 Relative term rewrite system: 1143.69/290.01 The relative TRS consists of the following R rules: 1143.69/290.01 1143.69/290.01 a(b(a(b(a(x1))))) -> x1 1143.69/290.01 1143.69/290.01 The relative TRS consists of the following S rules: 1143.69/290.01 1143.69/290.01 a(b(x1)) -> b(b(a(a(x1)))) 1143.69/290.01 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (1) FlatCCProof (EQUIVALENT) 1143.69/290.01 We used flat context closure [ROOTLAB] 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (2) 1143.69/290.01 Obligation: 1143.69/290.01 Relative term rewrite system: 1143.69/290.01 The relative TRS consists of the following R rules: 1143.69/290.01 1143.69/290.01 a(a(b(a(b(a(x1)))))) -> a(x1) 1143.69/290.01 b(a(b(a(b(a(x1)))))) -> b(x1) 1143.69/290.01 1143.69/290.01 The relative TRS consists of the following S rules: 1143.69/290.01 1143.69/290.01 a(a(b(x1))) -> a(b(b(a(a(x1))))) 1143.69/290.01 b(a(b(x1))) -> b(b(b(a(a(x1))))) 1143.69/290.01 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (3) RootLabelingProof (EQUIVALENT) 1143.69/290.01 We used plain root labeling [ROOTLAB] with the following heuristic: 1143.69/290.01 LabelAll: All function symbols get labeled 1143.69/290.01 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (4) 1143.69/290.01 Obligation: 1143.69/290.01 Relative term rewrite system: 1143.69/290.01 The relative TRS consists of the following R rules: 1143.69/290.01 1143.69/290.01 a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1)))))) -> a_{a_1}(x1) 1143.69/290.01 a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1)))))) -> a_{b_1}(x1) 1143.69/290.01 b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1)))))) -> b_{a_1}(x1) 1143.69/290.01 b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1)))))) -> b_{b_1}(x1) 1143.69/290.01 1143.69/290.01 The relative TRS consists of the following S rules: 1143.69/290.01 1143.69/290.01 a_{a_1}(a_{b_1}(b_{a_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))) 1143.69/290.01 a_{a_1}(a_{b_1}(b_{b_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1))))) 1143.69/290.01 b_{a_1}(a_{b_1}(b_{a_1}(x1))) -> b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))) 1143.69/290.01 b_{a_1}(a_{b_1}(b_{b_1}(x1))) -> b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1))))) 1143.69/290.01 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (5) FlatCCProof (EQUIVALENT) 1143.69/290.01 We used flat context closure [ROOTLAB] 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (6) 1143.69/290.01 Obligation: 1143.69/290.01 Relative term rewrite system: 1143.69/290.01 The relative TRS consists of the following R rules: 1143.69/290.01 1143.69/290.01 a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1)))))) -> a_{a_1}(x1) 1143.69/290.01 b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1)))))) -> b_{a_1}(x1) 1143.69/290.01 a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))))) -> a_{a_1}(a_{b_1}(x1)) 1143.69/290.01 a_{b_1}(a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))))) -> a_{b_1}(a_{b_1}(x1)) 1143.69/290.01 b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))))) -> b_{a_1}(a_{b_1}(x1)) 1143.69/290.01 b_{b_1}(a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))))) -> b_{b_1}(a_{b_1}(x1)) 1143.69/290.01 a_{a_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))))) -> a_{a_1}(b_{b_1}(x1)) 1143.69/290.01 a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))))) -> a_{b_1}(b_{b_1}(x1)) 1143.69/290.01 b_{a_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))))) -> b_{a_1}(b_{b_1}(x1)) 1143.69/290.01 b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))))) -> b_{b_1}(b_{b_1}(x1)) 1143.69/290.01 1143.69/290.01 The relative TRS consists of the following S rules: 1143.69/290.01 1143.69/290.01 a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 1143.69/290.01 a_{b_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{b_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 1143.69/290.01 b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 1143.69/290.01 b_{b_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{b_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 1143.69/290.01 a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 1143.69/290.01 a_{b_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 1143.69/290.01 b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 1143.69/290.01 b_{b_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{b_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 1143.69/290.01 a_{a_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 1143.69/290.01 a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 1143.69/290.01 b_{a_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 1143.69/290.01 b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 1143.69/290.01 a_{a_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{a_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 1143.69/290.01 a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 1143.69/290.01 b_{a_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{a_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 1143.69/290.01 b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 1143.69/290.01 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (7) RootLabelingProof (EQUIVALENT) 1143.69/290.01 We used plain root labeling [ROOTLAB] with the following heuristic: 1143.69/290.01 LabelAll: All function symbols get labeled 1143.69/290.01 1143.69/290.01 1143.69/290.01 ---------------------------------------- 1143.69/290.01 1143.69/290.01 (8) 1143.69/290.01 Obligation: 1143.69/290.01 Relative term rewrite system: 1143.69/290.01 The relative TRS consists of the following R rules: 1143.69/290.01 1143.69/290.01 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) -> a_{a_1}_{a_{a_1}_1}(x1) 1143.69/290.01 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) -> a_{a_1}_{a_{b_1}_1}(x1) 1143.69/290.01 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) -> a_{a_1}_{b_{a_1}_1}(x1) 1143.69/290.01 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) -> a_{a_1}_{b_{b_1}_1}(x1) 1143.69/290.01 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) -> b_{a_1}_{a_{a_1}_1}(x1) 1143.69/290.01 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) -> b_{a_1}_{a_{b_1}_1}(x1) 1143.69/290.01 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) -> b_{a_1}_{b_{a_1}_1}(x1) 1143.69/290.01 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) -> b_{a_1}_{b_{b_1}_1}(x1) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.69/290.01 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.69/290.01 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.69/290.01 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.69/290.01 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.69/290.01 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.69/290.01 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.69/290.01 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.69/290.01 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.69/290.01 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.69/290.01 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.69/290.01 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.69/290.01 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.69/290.01 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.69/290.01 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.69/290.01 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.69/290.01 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.69/290.01 1143.69/290.01 The relative TRS consists of the following S rules: 1143.69/290.01 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.69/290.01 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (9) RelTRSRRRProof (EQUIVALENT) 1143.87/290.05 We used the following monotonic ordering for rule removal: 1143.87/290.05 Polynomial interpretation [POLO]: 1143.87/290.05 1143.87/290.05 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{b_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(a_{a_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{b_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(b_{a_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{a_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(b_{b_1}_{a_{b_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.05 Rules from R: 1143.87/290.05 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 Rules from S: 1143.87/290.05 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (10) 1143.87/290.05 Obligation: 1143.87/290.05 Relative term rewrite system: 1143.87/290.05 The relative TRS consists of the following R rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) -> a_{a_1}_{a_{a_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) -> a_{a_1}_{a_{b_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) -> a_{a_1}_{b_{a_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) -> a_{a_1}_{b_{b_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) -> b_{a_1}_{a_{a_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) -> b_{a_1}_{a_{b_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) -> b_{a_1}_{b_{a_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) -> b_{a_1}_{b_{b_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The relative TRS consists of the following S rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (11) RelTRSRRRProof (EQUIVALENT) 1143.87/290.05 We used the following monotonic ordering for rule removal: 1143.87/290.05 Polynomial interpretation [POLO]: 1143.87/290.05 1143.87/290.05 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{a_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(b_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.05 Rules from R: 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 Rules from S: 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (12) 1143.87/290.05 Obligation: 1143.87/290.05 Relative term rewrite system: 1143.87/290.05 The relative TRS consists of the following R rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) -> a_{a_1}_{a_{a_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) -> a_{a_1}_{a_{b_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) -> a_{a_1}_{b_{a_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) -> a_{a_1}_{b_{b_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) -> b_{a_1}_{a_{a_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) -> b_{a_1}_{a_{b_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) -> b_{a_1}_{b_{a_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) -> b_{a_1}_{b_{b_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The relative TRS consists of the following S rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (13) RelTRSRRRProof (EQUIVALENT) 1143.87/290.05 We used the following monotonic ordering for rule removal: 1143.87/290.05 Matrix interpretation [MATRO] to (N^3, +, *, >=, >) : 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 1, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 1, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 1, 0], [0, 1, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [1], [0]] + [[1, 0, 0], [0, 1, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 1, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(a_{a_1}_{b_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [1, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(a_{a_1}_{b_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(b_{a_1}_{b_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(b_{a_1}_{b_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(b_{b_1}_{a_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(b_{b_1}_{a_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 <<< 1143.87/290.05 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.05 >>> 1143.87/290.05 1143.87/290.05 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.05 Rules from R: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) -> a_{a_1}_{a_{a_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) -> a_{a_1}_{a_{b_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) -> a_{a_1}_{b_{a_1}_1}(x1) 1143.87/290.05 a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) -> a_{a_1}_{b_{b_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) -> b_{a_1}_{a_{a_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) -> b_{a_1}_{a_{b_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) -> b_{a_1}_{b_{a_1}_1}(x1) 1143.87/290.05 b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) -> b_{a_1}_{b_{b_1}_1}(x1) 1143.87/290.05 Rules from S: 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (14) 1143.87/290.05 Obligation: 1143.87/290.05 Relative term rewrite system: 1143.87/290.05 The relative TRS consists of the following R rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The relative TRS consists of the following S rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (15) RelTRSRRRProof (EQUIVALENT) 1143.87/290.05 We used the following monotonic ordering for rule removal: 1143.87/290.05 Polynomial interpretation [POLO]: 1143.87/290.05 1143.87/290.05 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{b_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(a_{a_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{b_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(b_{a_1}_{b_{b_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(b_{b_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.05 Rules from R: 1143.87/290.05 none 1143.87/290.05 Rules from S: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (16) 1143.87/290.05 Obligation: 1143.87/290.05 Relative term rewrite system: 1143.87/290.05 The relative TRS consists of the following R rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The relative TRS consists of the following S rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (17) RelTRSRRRProof (EQUIVALENT) 1143.87/290.05 We used the following monotonic ordering for rule removal: 1143.87/290.05 Polynomial interpretation [POLO]: 1143.87/290.05 1143.87/290.05 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{a_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{a_1}_{b_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.05 POL(b_{b_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.05 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.05 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.05 Rules from R: 1143.87/290.05 none 1143.87/290.05 Rules from S: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (18) 1143.87/290.05 Obligation: 1143.87/290.05 Relative term rewrite system: 1143.87/290.05 The relative TRS consists of the following R rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The relative TRS consists of the following S rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (19) RelTRSSemanticLabellingPOLOProof (EQUIVALENT) 1143.87/290.05 We use Semantic Labelling over tuples of bools combined with a polynomial order [SEMLAB] 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 We use semantic labelling over boolean tuples of size 1. 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 We used the following model: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}_1: component 1: OR[x_1^1] 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{a_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{a_1}_{a_{a_1}_1}_1: component 1: OR[x_1^1] 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{a_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{a_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{a_{a_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{a_1}_1}_1: component 1: AND[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 Our labelling function was: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{b_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{a_1}_1}_1:component 1: XOR[] 1143.87/290.05 1143.87/290.05 b_{a_1}_{a_{a_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{b_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{a_1}_1}_1:component 1: OR[x_1^1] 1143.87/290.05 1143.87/290.05 b_{a_1}_{a_{b_1}_1}_1:component 1: OR[x_1^1] 1143.87/290.05 1143.87/290.05 b_{b_1}_{a_{a_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{a_1}_1}_1:component 1: XOR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{a_{b_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{b_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{b_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 Our labelled system was: 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[t]b_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[t](^[t]b_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[t]b_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[t](^[t]b_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[t](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[t](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[t](^[t]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[t](^[t]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[t](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[t](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 Our polynomial interpretation was: 1143.87/290.05 1143.87/290.05 P(a_{a_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{a_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{a_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{a_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{b_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{b_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{a_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{a_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{b_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{b_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{b_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{b_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{a_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{a_1}_{a_{b_1}_1}^[true])(x_1) = 1 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{b_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{b_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 1143.87/290.05 The following rules were deleted from R: 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The following rules were deleted from S: 1143.87/290.05 none 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (20) 1143.87/290.05 Obligation: 1143.87/290.05 Relative term rewrite system: 1143.87/290.05 The relative TRS consists of the following R rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The relative TRS consists of the following S rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (21) RelTRSSemanticLabellingPOLOProof (EQUIVALENT) 1143.87/290.05 We use Semantic Labelling over tuples of bools combined with a polynomial order [SEMLAB] 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 We use semantic labelling over boolean tuples of size 1. 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 We used the following model: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}_1: component 1: OR[x_1^1] 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{a_1}_1}_1: component 1: OR[x_1^1] 1143.87/290.05 1143.87/290.05 b_{a_1}_{a_{a_1}_1}_1: component 1: OR[x_1^1] 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{a_1}_1}_1: component 1: OR[x_1^1] 1143.87/290.05 1143.87/290.05 b_{a_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{a_{a_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{a_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{b_1}_1}_1: component 1: AND[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{b_1}_1}_1: component 1: OR[] 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 Our labelling function was: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}_1:component 1: XOR[x_1^1] 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{b_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{a_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{a_1}_{a_{a_1}_1}_1:component 1: XOR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{b_{b_1}_1}_1:component 1: XOR[x_1^1] 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{a_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{a_1}_{a_{b_1}_1}_1:component 1: XOR[x_1^1] 1143.87/290.05 1143.87/290.05 b_{b_1}_{a_{a_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{a_1}_1}_1:component 1: XOR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{a_{b_1}_1}_1:component 1: XOR[] 1143.87/290.05 1143.87/290.05 a_{b_1}_{a_{b_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{b_1}_1}_1:component 1: OR[] 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 Our labelled system was: 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]b_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]b_{b_1}_{b_{a_1}_1}^[f](^[t]b_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[t](^[t]a_{a_1}_{a_{a_1}_1}^[t](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]b_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]b_{b_1}_{b_{a_1}_1}^[f](^[t]b_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[t](^[t]a_{a_1}_{a_{a_1}_1}^[t](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]b_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]b_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]b_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[t]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]b_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[t]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1)))))) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]b_{b_1}_{b_{a_1}_1}^[f](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{b_{a_1}_1}^[f](^[t]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[t]b_{b_1}_{b_{a_1}_1}^[f](^[t]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.05 1143.87/290.05 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[t](^[t]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[t]x1)) 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 Our polynomial interpretation was: 1143.87/290.05 1143.87/290.05 P(a_{a_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{a_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{a_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{a_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{b_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{b_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{a_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{a_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{b_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{b_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{b_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{b_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{a_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{a_1}_{a_{b_1}_1}^[true])(x_1) = 1 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(a_{b_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{b_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 P(b_{b_1}_{b_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.05 1143.87/290.05 1143.87/290.05 The following rules were deleted from R: 1143.87/290.05 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The following rules were deleted from S: 1143.87/290.05 none 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 1143.87/290.05 ---------------------------------------- 1143.87/290.05 1143.87/290.05 (22) 1143.87/290.05 Obligation: 1143.87/290.05 Relative term rewrite system: 1143.87/290.05 The relative TRS consists of the following R rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.05 1143.87/290.05 The relative TRS consists of the following S rules: 1143.87/290.05 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.05 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.05 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (23) RelTRSRRRProof (EQUIVALENT) 1143.87/290.06 We used the following monotonic ordering for rule removal: 1143.87/290.06 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [2]] + [[1, 0], [2, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 1], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = [[0], [1]] + [[1, 0], [1, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = [[0], [0]] + [[2, 0], [2, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{b_1}_{a_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{b_1}_{a_{b_1}_1}(x_1)) = [[0], [0]] + [[2, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.06 Rules from R: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.06 Rules from S: 1143.87/290.06 none 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (24) 1143.87/290.06 Obligation: 1143.87/290.06 Relative term rewrite system: 1143.87/290.06 The relative TRS consists of the following R rules: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 1143.87/290.06 The relative TRS consists of the following S rules: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (25) RelTRSRRRProof (EQUIVALENT) 1143.87/290.06 We used the following monotonic ordering for rule removal: 1143.87/290.06 Polynomial interpretation [POLO]: 1143.87/290.06 1143.87/290.06 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{b_1}_{a_{a_1}_1}(x_1)) = 1 + x_1 1143.87/290.06 POL(b_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.06 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.06 Rules from R: 1143.87/290.06 none 1143.87/290.06 Rules from S: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (26) 1143.87/290.06 Obligation: 1143.87/290.06 Relative term rewrite system: 1143.87/290.06 The relative TRS consists of the following R rules: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 1143.87/290.06 The relative TRS consists of the following S rules: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (27) RelTRSSemanticLabellingPOLOProof (EQUIVALENT) 1143.87/290.06 We use Semantic Labelling over tuples of bools combined with a polynomial order [SEMLAB] 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 We use semantic labelling over boolean tuples of size 1. 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 We used the following model: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}_1: component 1: OR[x_1^1] 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 a_{b_1}_{b_{a_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 b_{a_1}_{a_{a_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 a_{b_1}_{b_{b_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 b_{b_1}_{b_{a_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 b_{a_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 b_{b_1}_{a_{b_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 a_{b_1}_{a_{b_1}_1}_1: component 1: AND[] 1143.87/290.06 1143.87/290.06 b_{b_1}_{b_{b_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 a_{b_1}_{a_{a_1}_1}_1: component 1: OR[] 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 Our labelling function was: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}_1:component 1: XOR[] 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{b_1}_1}_1:component 1: XOR[] 1143.87/290.06 1143.87/290.06 a_{b_1}_{b_{a_1}_1}_1:component 1: OR[] 1143.87/290.06 1143.87/290.06 b_{a_1}_{a_{a_1}_1}_1:component 1: OR[] 1143.87/290.06 1143.87/290.06 a_{b_1}_{b_{b_1}_1}_1:component 1: XOR[] 1143.87/290.06 1143.87/290.06 b_{b_1}_{b_{a_1}_1}_1:component 1: OR[] 1143.87/290.06 1143.87/290.06 b_{a_1}_{a_{b_1}_1}_1:component 1: XOR[x_1^1] 1143.87/290.06 1143.87/290.06 b_{b_1}_{a_{b_1}_1}_1:component 1: OR[] 1143.87/290.06 1143.87/290.06 a_{b_1}_{a_{b_1}_1}_1:component 1: XOR[] 1143.87/290.06 1143.87/290.06 b_{b_1}_{b_{b_1}_1}_1:component 1: XOR[] 1143.87/290.06 1143.87/290.06 a_{b_1}_{a_{a_1}_1}_1:component 1: OR[] 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 Our labelled system was: 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[f](^[t]a_{a_1}_{a_{a_1}_1}^[f](^[t]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)))))) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]a_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{a_{a_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]b_{a_1}_{a_{a_1}_1}^[f](^[f]a_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[t](^[t]a_{b_1}_{a_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{a_{b_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 ^[f]b_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{a_1}_1}^[f](^[f]b_{a_1}_{a_{b_1}_1}^[f](^[f]a_{b_1}_{b_{b_1}_1}^[f](^[f]x1))))))) -> ^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]b_{b_1}_{b_{b_1}_1}^[f](^[f]x1)) 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 Our polynomial interpretation was: 1143.87/290.06 1143.87/290.06 P(a_{a_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{a_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{a_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{a_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{b_1}_{b_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{b_1}_{b_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{a_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{a_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{b_1}_{b_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{b_1}_{b_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{b_1}_{b_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{b_1}_{b_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{a_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{a_1}_{a_{b_1}_1}^[true])(x_1) = 1 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{b_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{b_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{b_1}_{a_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{b_1}_{a_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{b_1}_{b_{b_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(b_{b_1}_{b_{b_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{b_1}_{a_{a_1}_1}^[false])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 P(a_{b_1}_{a_{a_1}_1}^[true])(x_1) = 0 + 1*x_1 1143.87/290.06 1143.87/290.06 1143.87/290.06 The following rules were deleted from R: 1143.87/290.06 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 1143.87/290.06 The following rules were deleted from S: 1143.87/290.06 none 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (28) 1143.87/290.06 Obligation: 1143.87/290.06 Relative term rewrite system: 1143.87/290.06 The relative TRS consists of the following R rules: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 1143.87/290.06 The relative TRS consists of the following S rules: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (29) RelTRSRRRProof (EQUIVALENT) 1143.87/290.06 We used the following monotonic ordering for rule removal: 1143.87/290.06 Polynomial interpretation [POLO]: 1143.87/290.06 1143.87/290.06 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{b_1}_{a_{b_1}_1}(x_1)) = 1 + x_1 1143.87/290.06 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = x_1 1143.87/290.06 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = x_1 1143.87/290.06 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.06 Rules from R: 1143.87/290.06 none 1143.87/290.06 Rules from S: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (30) 1143.87/290.06 Obligation: 1143.87/290.06 Relative term rewrite system: 1143.87/290.06 The relative TRS consists of the following R rules: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.06 1143.87/290.06 The relative TRS consists of the following S rules: 1143.87/290.06 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.06 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.06 1143.87/290.06 1143.87/290.06 ---------------------------------------- 1143.87/290.06 1143.87/290.06 (31) RelTRSRRRProof (EQUIVALENT) 1143.87/290.06 We used the following monotonic ordering for rule removal: 1143.87/290.06 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 2], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = [[0], [1]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [2]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [2]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 <<< 1143.87/290.06 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.06 >>> 1143.87/290.06 1143.87/290.06 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.07 Rules from R: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.07 Rules from S: 1143.87/290.07 none 1143.87/290.07 1143.87/290.07 1143.87/290.07 1143.87/290.07 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (32) 1143.87/290.07 Obligation: 1143.87/290.07 Relative term rewrite system: 1143.87/290.07 The relative TRS consists of the following R rules: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 1143.87/290.07 The relative TRS consists of the following S rules: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 1143.87/290.07 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (33) RelTRSRRRProof (EQUIVALENT) 1143.87/290.07 We used the following monotonic ordering for rule removal: 1143.87/290.07 Matrix interpretation [MATRO] to (N^3, +, *, >=, >) : 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 1, 1], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 1, 0], [0, 0, 1], [0, 0, 1]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [1], [1]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{a_{a_1}_1}(x_1)) = [[0], [0], [1]] + [[1, 0, 0], [1, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.07 Rules from R: 1143.87/290.07 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{a_1}_1}(x1)) 1143.87/290.07 Rules from S: 1143.87/290.07 none 1143.87/290.07 1143.87/290.07 1143.87/290.07 1143.87/290.07 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (34) 1143.87/290.07 Obligation: 1143.87/290.07 Relative term rewrite system: 1143.87/290.07 The relative TRS consists of the following R rules: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 1143.87/290.07 The relative TRS consists of the following S rules: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 1143.87/290.07 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (35) RelTRSRRRProof (EQUIVALENT) 1143.87/290.07 We used the following monotonic ordering for rule removal: 1143.87/290.07 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [2]] + [[1, 0], [2, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [2, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 2], [0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{a_{b_1}_1}(x_1)) = [[1], [0]] + [[2, 0], [0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.07 Rules from R: 1143.87/290.07 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{a_{b_1}_1}(x1)) 1143.87/290.07 Rules from S: 1143.87/290.07 none 1143.87/290.07 1143.87/290.07 1143.87/290.07 1143.87/290.07 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (36) 1143.87/290.07 Obligation: 1143.87/290.07 Relative term rewrite system: 1143.87/290.07 The relative TRS consists of the following R rules: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 1143.87/290.07 The relative TRS consists of the following S rules: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 1143.87/290.07 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (37) RelTRSRRRProof (EQUIVALENT) 1143.87/290.07 We used the following monotonic ordering for rule removal: 1143.87/290.07 Matrix interpretation [MATRO] to (N^3, +, *, >=, >) : 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [1], [0]] + [[1, 0, 0], [0, 1, 0], [1, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [1], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [1], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{a_1}_{a_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 1, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(a_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{a_1}_{a_{a_1}_1}(x_1)) = [[0], [0], [1]] + [[1, 0, 0], [0, 0, 0], [0, 1, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{b_1}_{b_{a_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 <<< 1143.87/290.07 POL(b_{b_1}_{b_{b_1}_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 1143.87/290.07 >>> 1143.87/290.07 1143.87/290.07 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 1143.87/290.07 Rules from R: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1))))))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)) 1143.87/290.07 Rules from S: 1143.87/290.07 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 1143.87/290.07 1143.87/290.07 1143.87/290.07 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (38) 1143.87/290.07 Obligation: 1143.87/290.07 Relative term rewrite system: 1143.87/290.07 R is empty. 1143.87/290.07 The relative TRS consists of the following S rules: 1143.87/290.07 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 a_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 a_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{a_1}_1}(x1)))))) 1143.87/290.07 b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(x1)))) -> b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{b_1}_1}(b_{b_1}_{b_{a_1}_1}(b_{a_1}_{a_{a_1}_1}(a_{a_1}_{a_{b_1}_1}(a_{b_1}_{b_{b_1}_1}(x1)))))) 1143.87/290.07 1143.87/290.07 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (39) RIsEmptyProof (EQUIVALENT) 1143.87/290.07 The TRS R is empty. Hence, termination is trivially proven. 1143.87/290.07 ---------------------------------------- 1143.87/290.07 1143.87/290.07 (40) 1143.87/290.07 YES 1144.03/290.14 EOF