187.38/47.87 YES 187.38/47.88 187.38/47.88 Problem: 187.38/47.88 b(b(a(a(x1)))) -> b(b(a(b(x1)))) 187.38/47.88 a(a(b(b(x1)))) -> b(b(a(a(x1)))) 187.38/47.88 b(a(a(b(x1)))) -> b(a(a(a(x1)))) 187.38/47.88 187.38/47.88 Proof: 187.38/47.88 String Reversal Processor: 187.38/47.88 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.88 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.88 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.88 DP Processor: 187.38/47.88 DPs: 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> b#(x1) 187.38/47.88 b#(b(a(a(x1)))) -> b#(b(x1)) 187.38/47.88 b#(b(a(a(x1)))) -> a#(b(b(x1))) 187.38/47.88 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.88 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.88 TRS: 187.38/47.88 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.88 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.88 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.88 TDG Processor: 187.38/47.88 DPs: 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> b#(x1) 187.38/47.88 b#(b(a(a(x1)))) -> b#(b(x1)) 187.38/47.88 b#(b(a(a(x1)))) -> a#(b(b(x1))) 187.38/47.88 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.88 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.88 TRS: 187.38/47.88 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.88 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.88 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.88 graph: 187.38/47.88 b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(b(x1))) 187.38/47.88 b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) 187.38/47.88 b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) 187.38/47.88 b#(b(a(a(x1)))) -> b#(x1) -> b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(b(b(x1))) 187.38/47.88 b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) 187.38/47.88 b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) 187.38/47.88 b#(b(a(a(x1)))) -> a#(b(b(x1))) -> 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) -> 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.88 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) -> 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> 187.38/47.88 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> 187.38/47.88 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> 187.38/47.88 b#(b(a(a(x1)))) -> a#(b(b(x1))) 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> 187.38/47.88 b#(b(a(a(x1)))) -> b#(b(x1)) 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(x1) 187.38/47.88 Arctic Interpretation Processor: 187.38/47.88 dimension: 1 187.38/47.88 usable rules: 187.38/47.88 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.88 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.88 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.88 interpretation: 187.38/47.88 [b#](x0) = x0, 187.38/47.88 187.38/47.88 [a#](x0) = x0, 187.38/47.88 187.38/47.88 [b](x0) = 1x0, 187.38/47.88 187.38/47.88 [a](x0) = 1x0 187.38/47.88 orientation: 187.38/47.88 a#(a(b(b(x1)))) = 3x1 >= 3x1 = b#(a(b(b(x1)))) 187.38/47.88 187.38/47.88 b#(b(a(a(x1)))) = 3x1 >= x1 = b#(x1) 187.38/47.88 187.38/47.88 b#(b(a(a(x1)))) = 3x1 >= 1x1 = b#(b(x1)) 187.38/47.88 187.38/47.88 b#(b(a(a(x1)))) = 3x1 >= 2x1 = a#(b(b(x1))) 187.38/47.88 187.38/47.88 b#(b(a(a(x1)))) = 3x1 >= 3x1 = a#(a(b(b(x1)))) 187.38/47.88 187.38/47.88 b#(a(a(b(x1)))) = 3x1 >= 3x1 = a#(a(a(b(x1)))) 187.38/47.88 187.38/47.88 a(a(b(b(x1)))) = 4x1 >= 4x1 = b(a(b(b(x1)))) 187.38/47.88 187.38/47.88 b(b(a(a(x1)))) = 4x1 >= 4x1 = a(a(b(b(x1)))) 187.38/47.88 187.38/47.88 b(a(a(b(x1)))) = 4x1 >= 4x1 = a(a(a(b(x1)))) 187.38/47.88 problem: 187.38/47.88 DPs: 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.88 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.88 TRS: 187.38/47.88 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.88 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.88 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.88 Restore Modifier: 187.38/47.88 DPs: 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.88 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.88 TRS: 187.38/47.88 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.88 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.88 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.88 EDG Processor: 187.38/47.88 DPs: 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.88 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.88 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.88 TRS: 187.38/47.88 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.88 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.88 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.88 graph: 187.38/47.88 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) -> 187.38/47.88 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.90 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) -> 187.38/47.90 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.90 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> 187.38/47.90 b#(b(a(a(x1)))) -> a#(a(b(b(x1)))) 187.38/47.90 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.90 Matrix Interpretation Processor: dim=4 187.38/47.90 187.38/47.90 interpretation: 187.38/47.90 [b#](x0) = [0 1 0 0]x0, 187.38/47.90 187.38/47.90 [a#](x0) = [0], 187.38/47.90 187.38/47.90 [0 0 0 0] [0] 187.38/47.90 [0 0 0 0] [1] 187.38/47.90 [b](x0) = [0 0 0 0]x0 + [0] 187.38/47.90 [0 1 0 0] [0], 187.38/47.90 187.38/47.90 [0 0 0 0] 187.38/47.90 [0 0 1 0] 187.38/47.90 [a](x0) = [0 0 0 1]x0 187.38/47.90 [0 0 0 0] 187.38/47.90 orientation: 187.38/47.90 a#(a(b(b(x1)))) = [0] >= [0] = b#(a(b(b(x1)))) 187.38/47.90 187.38/47.90 b#(b(a(a(x1)))) = [1] >= [0] = a#(a(b(b(x1)))) 187.38/47.90 187.38/47.90 b#(a(a(b(x1)))) = [0 1 0 0]x1 >= [0] = a#(a(a(b(x1)))) 187.38/47.90 187.38/47.90 [0] [0] 187.38/47.90 [1] [1] 187.38/47.90 a(a(b(b(x1)))) = [0] >= [0] = b(a(b(b(x1)))) 187.38/47.90 [0] [0] 187.38/47.90 187.38/47.90 [0] [0] 187.38/47.90 [1] [1] 187.38/47.90 b(b(a(a(x1)))) = [0] >= [0] = a(a(b(b(x1)))) 187.38/47.90 [1] [0] 187.38/47.90 187.38/47.90 [0 0 0 0] [0] [0] 187.38/47.90 [0 0 0 0] [1] [0] 187.38/47.90 b(a(a(b(x1)))) = [0 0 0 0]x1 + [0] >= [0] = a(a(a(b(x1)))) 187.38/47.90 [0 1 0 0] [0] [0] 187.38/47.90 problem: 187.38/47.90 DPs: 187.38/47.90 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.90 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.90 TRS: 187.38/47.90 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.90 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.90 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.90 Restore Modifier: 187.38/47.90 DPs: 187.38/47.90 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.90 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.90 TRS: 187.38/47.90 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.90 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.90 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.90 EDG Processor: 187.38/47.90 DPs: 187.38/47.90 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.90 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.90 TRS: 187.38/47.90 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.90 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.90 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.90 graph: 187.38/47.90 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) -> 187.38/47.90 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) 187.38/47.90 a#(a(b(b(x1)))) -> b#(a(b(b(x1)))) -> b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.90 Matrix Interpretation Processor: dim=4 187.38/47.90 187.38/47.90 interpretation: 187.38/47.90 [b#](x0) = [0], 187.38/47.90 187.38/47.90 [a#](x0) = [0 0 1 0]x0, 187.38/47.90 187.38/47.90 [0 0 0 0] [0] 187.38/47.90 [0 0 0 0] [1] 187.38/47.90 [b](x0) = [0 1 0 0]x0 + [0] 187.38/47.90 [0 1 0 0] [0], 187.38/47.90 187.38/47.90 [0 0 0 1] 187.38/47.90 [1 0 0 0] 187.38/47.90 [a](x0) = [0 1 0 0]x0 187.38/47.90 [0 0 0 0] 187.38/47.90 orientation: 187.38/47.90 a#(a(b(b(x1)))) = [1] >= [0] = b#(a(b(b(x1)))) 187.38/47.90 187.38/47.90 b#(a(a(b(x1)))) = [0] >= [0] = a#(a(a(b(x1)))) 187.38/47.90 187.38/47.90 [0] [0] 187.38/47.90 [1] [1] 187.38/47.90 a(a(b(b(x1)))) = [0] >= [0] = b(a(b(b(x1)))) 187.38/47.90 [0] [0] 187.38/47.90 187.38/47.90 [0] [0] 187.38/47.90 [1] [1] 187.38/47.90 b(b(a(a(x1)))) = [1] >= [0] = a(a(b(b(x1)))) 187.38/47.90 [1] [0] 187.38/47.90 187.38/47.90 [0 0 0 0] [0] [0 0 0 0] 187.38/47.90 [0 0 0 0] [1] [0 0 0 0] 187.38/47.90 b(a(a(b(x1)))) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 = a(a(a(b(x1)))) 187.38/47.90 [0 1 0 0] [0] [0 0 0 0] 187.38/47.90 problem: 187.38/47.90 DPs: 187.38/47.90 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.90 TRS: 187.38/47.90 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.90 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.90 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.90 Restore Modifier: 187.38/47.90 DPs: 187.38/47.90 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.90 TRS: 187.38/47.90 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.90 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.90 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.90 EDG Processor: 187.38/47.90 DPs: 187.38/47.90 b#(a(a(b(x1)))) -> a#(a(a(b(x1)))) 187.38/47.90 TRS: 187.38/47.90 a(a(b(b(x1)))) -> b(a(b(b(x1)))) 187.38/47.90 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 187.38/47.90 b(a(a(b(x1)))) -> a(a(a(b(x1)))) 187.38/47.90 graph: 187.38/47.90 187.38/47.90 SCC Processor: 187.38/47.90 #sccs: 0 187.38/47.90 #rules: 0 187.38/47.90 #arcs: 0/1 187.38/47.90 187.38/47.90 EOF