188.62/46.05 YES 188.62/46.06 188.62/46.06 Problem: 188.62/46.06 b(b(a(b(x1)))) -> a(b(b(b(x1)))) 188.62/46.06 a(a(a(b(x1)))) -> a(b(b(a(x1)))) 188.62/46.06 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 188.62/46.06 188.62/46.06 Proof: 188.62/46.06 String Reversal Processor: 188.62/46.06 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.06 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.06 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.06 DP Processor: 188.62/46.06 DPs: 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.06 TRS: 188.62/46.06 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.06 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.06 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.06 EDG Processor: 188.62/46.06 DPs: 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.06 TRS: 188.62/46.06 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.06 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.06 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.06 graph: 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) -> 188.62/46.06 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) -> 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) -> 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) -> 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) -> 188.62/46.06 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.06 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) -> 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) -> 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(a(a(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) -> 188.62/46.06 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(a(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> 188.62/46.06 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 188.62/46.06 b#(a(b(b(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 188.62/46.06 b#(a(a(a(x1)))) -> b#(a(x1)) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 188.62/46.06 b#(a(a(a(x1)))) -> b#(b(a(x1))) 188.62/46.06 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.06 Arctic Interpretation Processor: 188.62/46.06 dimension: 1 188.62/46.06 usable rules: 188.62/46.06 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.06 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.06 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.06 interpretation: 188.62/46.06 [b#](x0) = x0, 188.62/46.06 188.62/46.06 [a](x0) = 4x0, 188.62/46.06 188.62/46.06 [b](x0) = 4x0 188.62/46.06 orientation: 188.62/46.06 b#(a(b(b(x1)))) = 12x1 >= 4x1 = b#(a(x1)) 188.62/46.06 188.62/46.06 b#(a(b(b(x1)))) = 12x1 >= 8x1 = b#(b(a(x1))) 188.62/46.06 188.62/46.06 b#(a(b(b(x1)))) = 12x1 >= 12x1 = b#(b(b(a(x1)))) 188.62/46.06 188.62/46.06 b#(a(a(a(x1)))) = 12x1 >= 4x1 = b#(a(x1)) 188.62/46.06 188.62/46.06 b#(a(a(a(x1)))) = 12x1 >= 8x1 = b#(b(a(x1))) 188.62/46.06 188.62/46.06 b#(a(a(b(x1)))) = 12x1 >= 12x1 = b#(a(a(a(x1)))) 188.62/46.06 188.62/46.06 b(a(b(b(x1)))) = 16x1 >= 16x1 = b(b(b(a(x1)))) 188.62/46.06 188.62/46.06 b(a(a(a(x1)))) = 16x1 >= 16x1 = a(b(b(a(x1)))) 188.62/46.07 188.62/46.07 b(a(a(b(x1)))) = 16x1 >= 16x1 = b(a(a(a(x1)))) 188.62/46.07 problem: 188.62/46.07 DPs: 188.62/46.07 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.07 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.07 TRS: 188.62/46.07 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.07 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.07 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.07 Restore Modifier: 188.62/46.07 DPs: 188.62/46.07 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.07 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.07 TRS: 188.62/46.07 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.07 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.07 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.07 EDG Processor: 188.62/46.07 DPs: 188.62/46.07 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.07 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.07 TRS: 188.62/46.07 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.07 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.07 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.07 graph: 188.62/46.07 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 188.62/46.07 b#(a(a(b(x1)))) -> b#(a(a(a(x1)))) 188.62/46.07 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.07 SCC Processor: 188.62/46.07 #sccs: 1 188.62/46.07 #rules: 1 188.62/46.07 #arcs: 2/4 188.62/46.07 DPs: 188.62/46.07 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 188.62/46.07 TRS: 188.62/46.07 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.07 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.07 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.07 Matrix Interpretation Processor: dim=4 188.62/46.07 188.62/46.07 interpretation: 188.62/46.07 [b#](x0) = [0 0 0 1]x0, 188.62/46.07 188.62/46.07 [0 0 0 0] [0] 188.62/46.07 [0 0 0 0] [0] 188.62/46.07 [a](x0) = [0 0 0 1]x0 + [0] 188.62/46.07 [0 0 0 0] [1], 188.62/46.07 188.62/46.07 [0 0 0 0] 188.62/46.07 [0 0 0 0] 188.62/46.07 [b](x0) = [0 0 0 0]x0 188.62/46.07 [0 0 1 0] 188.62/46.07 orientation: 188.62/46.07 b#(a(b(b(x1)))) = [1] >= [0] = b#(b(b(a(x1)))) 188.62/46.07 188.62/46.07 [0] [0] 188.62/46.07 [0] [0] 188.62/46.07 b(a(b(b(x1)))) = [0] >= [0] = b(b(b(a(x1)))) 188.62/46.07 [0] [0] 188.62/46.07 188.62/46.07 [0] [0] 188.62/46.07 [0] [0] 188.62/46.07 b(a(a(a(x1)))) = [0] >= [0] = a(b(b(a(x1)))) 188.62/46.07 [1] [1] 188.62/46.07 188.62/46.07 [0] [0] 188.62/46.07 [0] [0] 188.62/46.07 b(a(a(b(x1)))) = [0] >= [0] = b(a(a(a(x1)))) 188.62/46.07 [1] [1] 188.62/46.07 problem: 188.62/46.07 DPs: 188.62/46.07 188.62/46.07 TRS: 188.62/46.07 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 188.62/46.07 b(a(a(a(x1)))) -> a(b(b(a(x1)))) 188.62/46.07 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 188.62/46.07 Qed 188.62/46.08 EOF