191.97/49.14 YES 192.31/49.15 192.31/49.15 Problem: 192.31/49.15 a(a(b(x1))) -> b(a(a(a(x1)))) 192.31/49.15 b(a(b(a(x1)))) -> a(b(b(x1))) 192.31/49.15 192.31/49.15 Proof: 192.31/49.15 String Reversal Processor: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 DP Processor: 192.31/49.15 DPs: 192.31/49.15 b#(a(a(x1))) -> b#(x1) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 a#(b(a(b(x1)))) -> a#(x1) 192.31/49.15 a#(b(a(b(x1)))) -> b#(a(x1)) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 TRS: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 TDG Processor: 192.31/49.15 DPs: 192.31/49.15 b#(a(a(x1))) -> b#(x1) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 a#(b(a(b(x1)))) -> a#(x1) 192.31/49.15 a#(b(a(b(x1)))) -> b#(a(x1)) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 TRS: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 graph: 192.31/49.15 a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(a(x1)) 192.31/49.15 a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1) 192.31/49.15 a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(x1) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) -> 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) -> 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(a(b(x1)))) -> b#(a(x1)) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(x1) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(a(x1)) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> a#(x1) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(a(x1)) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(x1) 192.31/49.15 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1) 192.31/49.15 Arctic Interpretation Processor: 192.31/49.15 dimension: 1 192.31/49.15 usable rules: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 interpretation: 192.31/49.15 [a#](x0) = x0, 192.31/49.15 192.31/49.15 [b#](x0) = 8x0, 192.31/49.15 192.31/49.15 [a](x0) = x0, 192.31/49.15 192.31/49.15 [b](x0) = 8x0 192.31/49.15 orientation: 192.31/49.15 b#(a(a(x1))) = 8x1 >= 8x1 = b#(x1) 192.31/49.15 192.31/49.15 b#(a(a(x1))) = 8x1 >= 8x1 = a#(b(x1)) 192.31/49.15 192.31/49.15 b#(a(a(x1))) = 8x1 >= 8x1 = a#(a(b(x1))) 192.31/49.15 192.31/49.15 b#(a(a(x1))) = 8x1 >= 8x1 = a#(a(a(b(x1)))) 192.31/49.15 192.31/49.15 a#(b(a(b(x1)))) = 16x1 >= x1 = a#(x1) 192.31/49.15 192.31/49.15 a#(b(a(b(x1)))) = 16x1 >= 8x1 = b#(a(x1)) 192.31/49.15 192.31/49.15 a#(b(a(b(x1)))) = 16x1 >= 16x1 = b#(b(a(x1))) 192.31/49.15 192.31/49.15 b(a(a(x1))) = 8x1 >= 8x1 = a(a(a(b(x1)))) 192.31/49.15 192.31/49.15 a(b(a(b(x1)))) = 16x1 >= 16x1 = b(b(a(x1))) 192.31/49.15 problem: 192.31/49.15 DPs: 192.31/49.15 b#(a(a(x1))) -> b#(x1) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 TRS: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 Restore Modifier: 192.31/49.15 DPs: 192.31/49.15 b#(a(a(x1))) -> b#(x1) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 TRS: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 EDG Processor: 192.31/49.15 DPs: 192.31/49.15 b#(a(a(x1))) -> b#(x1) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 TRS: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 graph: 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) -> 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) -> 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 b#(a(a(x1))) -> a#(a(a(b(x1)))) -> 192.31/49.15 a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(x1))) 192.31/49.15 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1) 192.31/49.15 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1)) 192.31/49.15 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1))) 192.31/49.15 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1)))) 192.31/49.15 Matrix Interpretation Processor: dim=1 192.31/49.15 192.31/49.15 usable rules: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 interpretation: 192.31/49.15 [a#](x0) = 2x0 + 13/2, 192.31/49.15 192.31/49.15 [b#](x0) = 3x0 + 1, 192.31/49.15 192.31/49.15 [a](x0) = x0 + 4, 192.31/49.15 192.31/49.15 [b](x0) = 3/2x0 + 1 192.31/49.15 orientation: 192.31/49.15 b#(a(a(x1))) = 3x1 + 25 >= 3x1 + 1 = b#(x1) 192.31/49.15 192.31/49.15 b#(a(a(x1))) = 3x1 + 25 >= 3x1 + 17/2 = a#(b(x1)) 192.31/49.15 192.31/49.15 b#(a(a(x1))) = 3x1 + 25 >= 3x1 + 33/2 = a#(a(b(x1))) 192.31/49.15 192.31/49.15 b#(a(a(x1))) = 3x1 + 25 >= 3x1 + 49/2 = a#(a(a(b(x1)))) 192.31/49.15 192.31/49.15 a#(b(a(b(x1)))) = 9/2x1 + 47/2 >= 9/2x1 + 22 = b#(b(a(x1))) 192.31/49.15 192.31/49.15 b(a(a(x1))) = 3/2x1 + 13 >= 3/2x1 + 13 = a(a(a(b(x1)))) 192.31/49.15 192.31/49.15 a(b(a(b(x1)))) = 9/4x1 + 25/2 >= 9/4x1 + 23/2 = b(b(a(x1))) 192.31/49.15 problem: 192.31/49.15 DPs: 192.31/49.15 192.31/49.15 TRS: 192.31/49.15 b(a(a(x1))) -> a(a(a(b(x1)))) 192.31/49.15 a(b(a(b(x1)))) -> b(b(a(x1))) 192.31/49.15 Qed 192.31/49.16 EOF