190.93/48.88 YES 190.93/48.89 190.93/48.89 Problem: 190.93/48.89 b(a(b(b(x1)))) -> b(b(a(a(x1)))) 190.93/48.89 a(a(b(b(x1)))) -> a(b(a(a(x1)))) 190.93/48.89 b(b(b(b(x1)))) -> b(a(a(a(x1)))) 190.93/48.89 a(b(a(a(x1)))) -> a(b(b(a(x1)))) 190.93/48.89 190.93/48.89 Proof: 190.93/48.89 String Reversal Processor: 190.93/48.89 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 190.93/48.89 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 190.93/48.89 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 190.93/48.89 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 190.93/48.89 DP Processor: 190.93/48.89 DPs: 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) 190.93/48.89 b#(b(a(b(x1)))) -> a#(b(b(x1))) 190.93/48.89 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) 190.93/48.89 b#(b(a(a(x1)))) -> a#(b(a(x1))) 190.93/48.89 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 190.93/48.89 b#(b(b(b(x1)))) -> a#(b(x1)) 190.93/48.89 b#(b(b(b(x1)))) -> a#(a(b(x1))) 190.93/48.89 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 190.93/48.89 TRS: 190.93/48.89 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 190.93/48.89 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 190.93/48.89 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 190.93/48.89 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 190.93/48.89 TDG Processor: 190.93/48.89 DPs: 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) 190.93/48.89 b#(b(a(b(x1)))) -> a#(b(b(x1))) 190.93/48.89 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) 190.93/48.89 b#(b(a(a(x1)))) -> a#(b(a(x1))) 190.93/48.89 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 190.93/48.89 b#(b(b(b(x1)))) -> a#(b(x1)) 190.93/48.89 b#(b(b(b(x1)))) -> a#(a(b(x1))) 190.93/48.89 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 190.93/48.89 TRS: 190.93/48.89 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 190.93/48.89 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 190.93/48.89 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 190.93/48.89 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 190.93/48.89 graph: 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 190.93/48.89 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 190.93/48.89 b#(b(b(b(x1)))) -> a#(a(b(x1))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(b(b(x1)))) -> a#(b(x1)) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 190.93/48.89 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 190.93/48.89 b#(b(a(a(x1)))) -> a#(b(a(x1))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 190.93/48.89 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 190.93/48.89 b#(b(a(b(x1)))) -> a#(b(b(x1))) 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) 190.93/48.89 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 190.93/48.89 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) 190.93/48.89 b#(b(a(a(x1)))) -> a#(b(a(x1))) -> 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 190.93/48.89 b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(a(b(x1))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(b(x1)) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1)) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> a#(b(b(x1))) 190.93/48.89 b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) 190.93/48.89 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 190.93/48.89 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 190.93/48.89 a#(a(b(a(x1)))) -> b#(b(a(x1))) 190.93/48.89 b#(b(a(b(x1)))) -> a#(b(b(x1))) -> 190.93/48.89 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 190.93/48.89 b#(b(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(b(x1))) 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(b(x1)) 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1))) 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1)) 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 190.93/48.89 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(b(b(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(b(x1))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 EDG Processor: 191.28/48.90 DPs: 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.90 b#(b(a(b(x1)))) -> a#(b(b(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.90 b#(b(a(a(x1)))) -> b#(a(x1)) 191.28/48.90 b#(b(a(a(x1)))) -> a#(b(a(x1))) 191.28/48.90 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(b(x1)) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(b(x1))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 TRS: 191.28/48.90 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.90 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.90 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.90 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.90 graph: 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.90 b#(b(a(b(x1)))) -> a#(b(b(x1))) 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.90 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.90 b#(b(a(a(x1)))) -> b#(a(x1)) 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.90 b#(b(a(a(x1)))) -> a#(b(a(x1))) 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.90 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.90 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(a(a(x1)))) -> a#(b(a(x1))) -> 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(a(a(x1)))) -> a#(b(a(x1))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(a(b(x1)))) -> a#(b(b(x1))) -> 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> a#(b(b(x1))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(b(b(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> 191.28/48.90 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1)) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> 191.28/48.90 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(b(x1)) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> a#(a(b(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) -> 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(b(x1))) -> 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(b(x1))) -> 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(b(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 SCC Processor: 191.28/48.90 #sccs: 1 191.28/48.90 #rules: 10 191.28/48.90 #arcs: 31/121 191.28/48.90 DPs: 191.28/48.90 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.90 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.90 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.90 b#(b(a(a(x1)))) -> a#(b(a(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.90 b#(b(a(b(x1)))) -> a#(b(b(x1))) 191.28/48.90 b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(a(b(x1))) 191.28/48.90 b#(b(b(b(x1)))) -> a#(b(x1)) 191.28/48.91 TRS: 191.28/48.91 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.91 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.91 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.91 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.91 Arctic Interpretation Processor: 191.28/48.91 dimension: 1 191.28/48.91 usable rules: 191.28/48.91 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.91 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.91 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.91 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.91 interpretation: 191.28/48.91 [a#](x0) = x0 + 2, 191.28/48.91 191.28/48.91 [b#](x0) = x0 + 3, 191.28/48.91 191.28/48.91 [a](x0) = 1x0 + 1, 191.28/48.91 191.28/48.91 [b](x0) = 1x0 + 0 191.28/48.91 orientation: 191.28/48.91 a#(a(b(a(x1)))) = 3x1 + 3 >= 3x1 + 3 = a#(b(b(a(x1)))) 191.28/48.91 191.28/48.91 a#(a(b(a(x1)))) = 3x1 + 3 >= 2x1 + 3 = b#(b(a(x1))) 191.28/48.91 191.28/48.91 b#(b(a(a(x1)))) = 3x1 + 3 >= 3x1 + 3 = a#(a(b(a(x1)))) 191.28/48.91 191.28/48.91 b#(b(a(a(x1)))) = 3x1 + 3 >= 2x1 + 2 = a#(b(a(x1))) 191.28/48.91 191.28/48.91 b#(b(a(b(x1)))) = 3x1 + 3 >= 3x1 + 2 = a#(a(b(b(x1)))) 191.28/48.91 191.28/48.91 b#(b(a(b(x1)))) = 3x1 + 3 >= 2x1 + 2 = a#(b(b(x1))) 191.28/48.91 191.28/48.91 b#(b(a(b(x1)))) = 3x1 + 3 >= 1x1 + 3 = b#(b(x1)) 191.28/48.91 191.28/48.91 b#(b(b(b(x1)))) = 3x1 + 3 >= 3x1 + 2 = a#(a(a(b(x1)))) 191.28/48.91 191.28/48.91 b#(b(b(b(x1)))) = 3x1 + 3 >= 2x1 + 2 = a#(a(b(x1))) 191.28/48.91 191.28/48.91 b#(b(b(b(x1)))) = 3x1 + 3 >= 1x1 + 2 = a#(b(x1)) 191.28/48.91 191.28/48.91 b(b(a(b(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(a(b(b(x1)))) 191.28/48.91 191.28/48.91 b(b(a(a(x1)))) = 4x1 + 4 >= 4x1 + 4 = a(a(b(a(x1)))) 191.28/48.91 191.28/48.91 b(b(b(b(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(a(a(b(x1)))) 191.28/48.91 191.28/48.91 a(a(b(a(x1)))) = 4x1 + 4 >= 4x1 + 4 = a(b(b(a(x1)))) 191.28/48.91 problem: 191.28/48.91 DPs: 191.28/48.91 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.91 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.91 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.91 TRS: 191.28/48.91 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.91 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.91 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.91 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.91 Restore Modifier: 191.28/48.91 DPs: 191.28/48.91 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.91 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.91 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.91 TRS: 191.28/48.91 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.91 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.91 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.91 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.91 EDG Processor: 191.28/48.91 DPs: 191.28/48.91 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.91 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.91 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.91 TRS: 191.28/48.91 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.91 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.91 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.91 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.91 graph: 191.28/48.91 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> 191.28/48.91 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.91 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.91 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.91 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) -> 191.28/48.91 b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.91 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> 191.28/48.91 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.91 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.91 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 191.28/48.91 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 191.28/48.91 a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.91 b#(b(a(b(x1)))) -> b#(b(x1)) -> 191.28/48.91 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> b#(b(x1)) -> 191.28/48.91 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> b#(b(x1)) -> 191.28/48.91 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.91 b#(b(a(b(x1)))) -> b#(b(x1)) -> 191.28/48.92 b#(b(a(b(x1)))) -> b#(b(x1)) 191.28/48.92 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(a(x1)))) -> b#(b(a(x1))) 191.28/48.92 Arctic Interpretation Processor: 191.28/48.92 dimension: 1 191.28/48.92 usable rules: 191.28/48.92 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.92 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.92 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.92 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.92 interpretation: 191.28/48.92 [a#](x0) = x0 + 0, 191.28/48.92 191.28/48.92 [b#](x0) = x0 + 0, 191.28/48.92 191.28/48.92 [a](x0) = 1x0 + 0, 191.28/48.92 191.28/48.92 [b](x0) = 1x0 + 0 191.28/48.92 orientation: 191.28/48.92 a#(a(b(a(x1)))) = 3x1 + 2 >= 3x1 + 2 = a#(b(b(a(x1)))) 191.28/48.92 191.28/48.92 a#(a(b(a(x1)))) = 3x1 + 2 >= 2x1 + 1 = b#(b(a(x1))) 191.28/48.92 191.28/48.92 b#(b(a(a(x1)))) = 3x1 + 2 >= 3x1 + 2 = a#(a(b(a(x1)))) 191.28/48.92 191.28/48.92 b#(b(a(b(x1)))) = 3x1 + 2 >= 3x1 + 2 = a#(a(b(b(x1)))) 191.28/48.92 191.28/48.92 b#(b(a(b(x1)))) = 3x1 + 2 >= 1x1 + 0 = b#(b(x1)) 191.28/48.92 191.28/48.92 b#(b(b(b(x1)))) = 3x1 + 2 >= 3x1 + 2 = a#(a(a(b(x1)))) 191.28/48.92 191.28/48.92 b(b(a(b(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(a(b(b(x1)))) 191.28/48.92 191.28/48.92 b(b(a(a(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(a(b(a(x1)))) 191.28/48.92 191.28/48.92 b(b(b(b(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(a(a(b(x1)))) 191.28/48.92 191.28/48.92 a(a(b(a(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(b(b(a(x1)))) 191.28/48.92 problem: 191.28/48.92 DPs: 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.92 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.92 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.92 TRS: 191.28/48.92 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.92 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.92 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.92 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.92 Restore Modifier: 191.28/48.92 DPs: 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.92 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.92 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.92 TRS: 191.28/48.92 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.92 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.92 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.92 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.92 EDG Processor: 191.28/48.92 DPs: 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) 191.28/48.92 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 191.28/48.92 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) 191.28/48.92 TRS: 191.28/48.92 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.92 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.92 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.92 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.92 graph: 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) -> 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 b#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 b#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 SCC Processor: 191.28/48.92 #sccs: 1 191.28/48.92 #rules: 1 191.28/48.92 #arcs: 4/16 191.28/48.92 DPs: 191.28/48.92 a#(a(b(a(x1)))) -> a#(b(b(a(x1)))) 191.28/48.92 TRS: 191.28/48.92 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.92 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.92 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.92 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.92 Matrix Interpretation Processor: dim=4 191.28/48.92 191.28/48.92 interpretation: 191.28/48.92 [a#](x0) = [0 0 1 0]x0, 191.28/48.92 191.28/48.92 [0 0 0 0] [0] 191.28/48.92 [0 0 0 0] [0] 191.28/48.92 [a](x0) = [1 0 0 0]x0 + [0] 191.28/48.92 [0 0 0 0] [1], 191.28/48.92 191.28/48.92 [0 0 0 1] [0] 191.28/48.92 [0 0 0 0] [1] 191.28/48.92 [b](x0) = [0 0 0 0]x0 + [0] 191.28/48.92 [0 1 0 0] [0] 191.28/48.92 orientation: 191.28/48.92 a#(a(b(a(x1)))) = [1] >= [0] = a#(b(b(a(x1)))) 191.28/48.93 191.28/48.93 [0] [0] 191.28/48.93 [1] [0] 191.28/48.93 b(b(a(b(x1)))) = [0] >= [0] = a(a(b(b(x1)))) 191.28/48.93 [1] [1] 191.28/48.93 191.28/48.93 [0] [0] 191.28/48.93 [1] [0] 191.28/48.93 b(b(a(a(x1)))) = [0] >= [0] = a(a(b(a(x1)))) 191.28/48.93 [1] [1] 191.28/48.93 191.28/48.93 [1] [0] 191.28/48.93 [1] [0] 191.28/48.93 b(b(b(b(x1)))) = [0] >= [0] = a(a(a(b(x1)))) 191.28/48.93 [1] [1] 191.28/48.93 191.28/48.93 [0] [0] 191.28/48.93 [0] [0] 191.28/48.93 a(a(b(a(x1)))) = [0] >= [0] = a(b(b(a(x1)))) 191.28/48.93 [1] [1] 191.28/48.93 problem: 191.28/48.93 DPs: 191.28/48.93 191.28/48.93 TRS: 191.28/48.93 b(b(a(b(x1)))) -> a(a(b(b(x1)))) 191.28/48.93 b(b(a(a(x1)))) -> a(a(b(a(x1)))) 191.28/48.93 b(b(b(b(x1)))) -> a(a(a(b(x1)))) 191.28/48.93 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 191.28/48.93 Qed 191.28/48.93 EOF