176.98/45.21 YES 176.98/45.21 176.98/45.21 Problem: 176.98/45.21 b(b(x1)) -> a(a(a(x1))) 176.98/45.21 b(a(b(x1))) -> a(x1) 176.98/45.21 b(a(a(x1))) -> b(a(b(x1))) 176.98/45.21 176.98/45.21 Proof: 176.98/45.21 String Reversal Processor: 176.98/45.21 b(b(x1)) -> a(a(a(x1))) 176.98/45.21 b(a(b(x1))) -> a(x1) 176.98/45.21 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.21 DP Processor: 176.98/45.21 DPs: 176.98/45.21 b#(b(x1)) -> a#(x1) 176.98/45.21 b#(b(x1)) -> a#(a(x1)) 176.98/45.21 b#(b(x1)) -> a#(a(a(x1))) 176.98/45.21 b#(a(b(x1))) -> a#(x1) 176.98/45.21 a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.21 TRS: 176.98/45.21 b(b(x1)) -> a(a(a(x1))) 176.98/45.21 b(a(b(x1))) -> a(x1) 176.98/45.21 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.21 TDG Processor: 176.98/45.21 DPs: 176.98/45.21 b#(b(x1)) -> a#(x1) 176.98/45.21 b#(b(x1)) -> a#(a(x1)) 176.98/45.21 b#(b(x1)) -> a#(a(a(x1))) 176.98/45.21 b#(a(b(x1))) -> a#(x1) 176.98/45.21 a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.21 TRS: 176.98/45.21 b(b(x1)) -> a(a(a(x1))) 176.98/45.21 b(a(b(x1))) -> a(x1) 176.98/45.21 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.21 graph: 176.98/45.21 a#(a(b(x1))) -> b#(a(b(x1))) -> b#(a(b(x1))) -> a#(x1) 176.98/45.21 a#(a(b(x1))) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(a(a(x1))) 176.98/45.21 a#(a(b(x1))) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(a(x1)) 176.98/45.21 a#(a(b(x1))) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(x1) 176.98/45.21 b#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 b#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 Arctic Interpretation Processor: 176.98/45.22 dimension: 2 176.98/45.22 usable rules: 176.98/45.22 b(b(x1)) -> a(a(a(x1))) 176.98/45.22 b(a(b(x1))) -> a(x1) 176.98/45.22 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.22 interpretation: 176.98/45.22 [a#](x0) = [0 -&]x0 + [0], 176.98/45.22 176.98/45.22 [b#](x0) = [0 -&]x0 + [0], 176.98/45.22 176.98/45.22 [-& 0 ] [1] 176.98/45.22 [a](x0) = [2 -&]x0 + [0], 176.98/45.22 176.98/45.22 [3 0 ] [3] 176.98/45.22 [b](x0) = [1 -&]x0 + [2] 176.98/45.22 orientation: 176.98/45.22 b#(b(x1)) = [3 0]x1 + [3] >= [0 -&]x1 + [0] = a#(x1) 176.98/45.22 176.98/45.22 b#(b(x1)) = [3 0]x1 + [3] >= [-& 0 ]x1 + [1] = a#(a(x1)) 176.98/45.22 176.98/45.22 b#(b(x1)) = [3 0]x1 + [3] >= [2 -&]x1 + [1] = a#(a(a(x1))) 176.98/45.22 176.98/45.22 b#(a(b(x1))) = [1 -&]x1 + [2] >= [0 -&]x1 + [0] = a#(x1) 176.98/45.22 176.98/45.22 a#(a(b(x1))) = [1 -&]x1 + [2] >= [1 -&]x1 + [2] = b#(a(b(x1))) 176.98/45.22 176.98/45.22 [6 3] [6] [-& 2 ] [3] 176.98/45.22 b(b(x1)) = [4 1]x1 + [4] >= [4 -&]x1 + [3] = a(a(a(x1))) 176.98/45.22 176.98/45.22 [5 2 ] [5] [-& 0 ] [1] 176.98/45.22 b(a(b(x1))) = [2 -&]x1 + [3] >= [2 -&]x1 + [0] = a(x1) 176.98/45.22 176.98/45.22 [5 2 ] [5] [5 2 ] [5] 176.98/45.22 a(a(b(x1))) = [3 -&]x1 + [4] >= [2 -&]x1 + [3] = b(a(b(x1))) 176.98/45.22 problem: 176.98/45.22 DPs: 176.98/45.22 b#(b(x1)) -> a#(a(x1)) 176.98/45.22 a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 TRS: 176.98/45.22 b(b(x1)) -> a(a(a(x1))) 176.98/45.22 b(a(b(x1))) -> a(x1) 176.98/45.22 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.22 Restore Modifier: 176.98/45.22 DPs: 176.98/45.22 b#(b(x1)) -> a#(a(x1)) 176.98/45.22 a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 TRS: 176.98/45.22 b(b(x1)) -> a(a(a(x1))) 176.98/45.22 b(a(b(x1))) -> a(x1) 176.98/45.22 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.22 EDG Processor: 176.98/45.22 DPs: 176.98/45.22 b#(b(x1)) -> a#(a(x1)) 176.98/45.22 a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 TRS: 176.98/45.22 b(b(x1)) -> a(a(a(x1))) 176.98/45.22 b(a(b(x1))) -> a(x1) 176.98/45.22 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.22 graph: 176.98/45.22 a#(a(b(x1))) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(a(x1)) 176.98/45.22 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 Arctic Interpretation Processor: 176.98/45.22 dimension: 2 176.98/45.22 usable rules: 176.98/45.22 b(b(x1)) -> a(a(a(x1))) 176.98/45.22 b(a(b(x1))) -> a(x1) 176.98/45.22 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.22 interpretation: 176.98/45.22 [a#](x0) = [1 2]x0 + [0], 176.98/45.22 176.98/45.22 [b#](x0) = [2 2]x0 + [0], 176.98/45.22 176.98/45.22 [0 3] [0 ] 176.98/45.22 [a](x0) = [0 0]x0 + [-&], 176.98/45.22 176.98/45.22 [3 3] [0 ] 176.98/45.22 [b](x0) = [0 0]x0 + [-&] 176.98/45.22 orientation: 176.98/45.22 b#(b(x1)) = [5 5]x1 + [2] >= [2 4]x1 + [1] = a#(a(x1)) 176.98/45.22 176.98/45.22 a#(a(b(x1))) = [5 5]x1 + [2] >= [5 5]x1 + [2] = b#(a(b(x1))) 176.98/45.22 176.98/45.22 [6 6] [3] [3 6] [3] 176.98/45.22 b(b(x1)) = [3 3]x1 + [0] >= [3 3]x1 + [0] = a(a(a(x1))) 176.98/45.22 176.98/45.22 [6 6] [3] [0 3] [0 ] 176.98/45.22 b(a(b(x1))) = [3 3]x1 + [0] >= [0 0]x1 + [-&] = a(x1) 176.98/45.22 176.98/45.22 [6 6] [3] [6 6] [3] 176.98/45.22 a(a(b(x1))) = [3 3]x1 + [0] >= [3 3]x1 + [0] = b(a(b(x1))) 176.98/45.22 problem: 176.98/45.22 DPs: 176.98/45.22 a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 TRS: 176.98/45.22 b(b(x1)) -> a(a(a(x1))) 176.98/45.22 b(a(b(x1))) -> a(x1) 176.98/45.22 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.22 Restore Modifier: 176.98/45.22 DPs: 176.98/45.22 a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 TRS: 176.98/45.22 b(b(x1)) -> a(a(a(x1))) 176.98/45.22 b(a(b(x1))) -> a(x1) 176.98/45.22 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.22 EDG Processor: 176.98/45.22 DPs: 176.98/45.22 a#(a(b(x1))) -> b#(a(b(x1))) 176.98/45.22 TRS: 176.98/45.22 b(b(x1)) -> a(a(a(x1))) 176.98/45.22 b(a(b(x1))) -> a(x1) 176.98/45.22 a(a(b(x1))) -> b(a(b(x1))) 176.98/45.22 graph: 176.98/45.22 176.98/45.22 SCC Processor: 176.98/45.22 #sccs: 0 176.98/45.22 #rules: 0 176.98/45.22 #arcs: 0/1 176.98/45.22 176.98/45.22 EOF