182.90/45.49 YES 183.23/45.50 183.23/45.50 Problem: 183.23/45.50 a(b(a(b(x1)))) -> b(b(a(a(x1)))) 183.23/45.50 a(a(a(b(x1)))) -> a(a(b(a(x1)))) 183.23/45.50 b(b(a(b(x1)))) -> b(a(b(b(x1)))) 183.23/45.50 183.23/45.50 Proof: 183.23/45.50 String Reversal Processor: 183.23/45.50 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.50 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.50 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.50 DP Processor: 183.23/45.50 DPs: 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) 183.23/45.50 b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 TRS: 183.23/45.50 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.50 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.50 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.50 EDG Processor: 183.23/45.50 DPs: 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) 183.23/45.50 b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 TRS: 183.23/45.50 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.50 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.50 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.50 graph: 183.23/45.50 b#(a(a(a(x1)))) -> b#(a(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(a(x1)))) -> b#(x1) 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(a(x1)))) -> b#(b(x1)) 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(x1) 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(a(x1)))) -> b#(b(x1)) 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) -> b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(x1) 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(x1)))) -> b#(b(x1)) 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) -> 183.23/45.50 b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) -> 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) -> 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> 183.23/45.50 b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 SCC Processor: 183.23/45.50 #sccs: 2 183.23/45.50 #rules: 5 183.23/45.50 #arcs: 21/25 183.23/45.50 DPs: 183.23/45.50 b#(a(b(a(x1)))) -> b#(b(x1)) 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 b#(a(b(b(x1)))) -> b#(a(b(x1))) 183.23/45.50 b#(a(b(a(x1)))) -> b#(x1) 183.23/45.50 TRS: 183.23/45.50 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.50 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.50 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.50 Arctic Interpretation Processor: 183.23/45.50 dimension: 1 183.23/45.50 usable rules: 183.23/45.50 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.50 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.50 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.50 interpretation: 183.23/45.50 [b#](x0) = x0, 183.23/45.50 183.23/45.50 [a](x0) = 2x0, 183.23/45.50 183.23/45.50 [b](x0) = 8x0 183.23/45.50 orientation: 183.23/45.50 b#(a(b(a(x1)))) = 12x1 >= 8x1 = b#(b(x1)) 183.23/45.50 183.23/45.50 b#(a(b(b(x1)))) = 18x1 >= 18x1 = b#(b(a(b(x1)))) 183.23/45.50 183.23/45.50 b#(a(b(b(x1)))) = 18x1 >= 10x1 = b#(a(b(x1))) 183.23/45.50 183.23/45.50 b#(a(b(a(x1)))) = 12x1 >= x1 = b#(x1) 183.23/45.50 183.23/45.50 b(a(b(a(x1)))) = 20x1 >= 20x1 = a(a(b(b(x1)))) 183.23/45.50 183.23/45.50 b(a(a(a(x1)))) = 14x1 >= 14x1 = a(b(a(a(x1)))) 183.23/45.50 183.23/45.50 b(a(b(b(x1)))) = 26x1 >= 26x1 = b(b(a(b(x1)))) 183.23/45.50 problem: 183.23/45.50 DPs: 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 TRS: 183.23/45.50 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.50 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.50 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.50 Restore Modifier: 183.23/45.50 DPs: 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 TRS: 183.23/45.50 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.50 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.50 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.50 EDG Processor: 183.23/45.50 DPs: 183.23/45.50 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.50 TRS: 183.23/45.50 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.50 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.50 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.51 graph: 183.23/45.51 b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(b(x1)))) 183.23/45.51 Matrix Interpretation Processor: dim=4 183.23/45.51 183.23/45.51 interpretation: 183.23/45.51 [b#](x0) = [1 0 0 0]x0, 183.23/45.51 183.23/45.51 [0 1 0 0] 183.23/45.51 [0 0 0 0] 183.23/45.51 [a](x0) = [0 0 0 0]x0 183.23/45.51 [0 1 0 0] , 183.23/45.51 183.23/45.51 [0 0 0 0] [0] 183.23/45.51 [1 1 1 0] [0] 183.23/45.51 [b](x0) = [0 0 0 0]x0 + [1] 183.23/45.51 [1 0 1 0] [0] 183.23/45.51 orientation: 183.23/45.51 b#(a(b(b(x1)))) = [1 1 1 0]x1 + [1] >= [0] = b#(b(a(b(x1)))) 183.23/45.51 183.23/45.51 [0 0 0 0] [0] [0] 183.23/45.51 [0 1 0 0] [0] [0] 183.23/45.51 b(a(b(a(x1)))) = [0 0 0 0]x1 + [1] >= [0] = a(a(b(b(x1)))) 183.23/45.51 [0 1 0 0] [0] [0] 183.23/45.51 183.23/45.51 [0] [0] 183.23/45.51 [0] [0] 183.23/45.51 b(a(a(a(x1)))) = [1] >= [0] = a(b(a(a(x1)))) 183.23/45.51 [0] [0] 183.23/45.51 183.23/45.51 [0 0 0 0] [0] [0 0 0 0] [0] 183.23/45.51 [1 1 1 0] [1] [1 1 1 0] [1] 183.23/45.51 b(a(b(b(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(b(a(b(x1)))) 183.23/45.51 [1 1 1 0] [1] [0 0 0 0] [1] 183.23/45.51 problem: 183.23/45.51 DPs: 183.23/45.51 183.23/45.51 TRS: 183.23/45.51 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.51 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.51 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.51 Qed 183.23/45.51 183.23/45.51 DPs: 183.23/45.51 b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.51 TRS: 183.23/45.51 b(a(b(a(x1)))) -> a(a(b(b(x1)))) 183.23/45.51 b(a(a(a(x1)))) -> a(b(a(a(x1)))) 183.23/45.51 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 183.23/45.51 Usable Rule Processor: 183.23/45.51 DPs: 183.23/45.51 b#(a(a(a(x1)))) -> b#(a(a(x1))) 183.23/45.51 TRS: 183.23/45.51 183.23/45.51 Arctic Interpretation Processor: 183.23/45.51 dimension: 1 183.23/45.51 usable rules: 183.23/45.51 183.23/45.51 interpretation: 183.23/45.51 [b#](x0) = 10x0 + 1, 183.23/45.51 183.23/45.51 [a](x0) = 4x0 + 7 183.23/45.51 orientation: 183.23/45.51 b#(a(a(a(x1)))) = 22x1 + 25 >= 18x1 + 21 = b#(a(a(x1))) 183.23/45.51 problem: 183.23/45.51 DPs: 183.23/45.51 183.23/45.51 TRS: 183.23/45.51 183.23/45.51 Qed 183.23/45.51 EOF