172.38/44.14 YES 172.38/44.15 172.38/44.15 Problem: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 172.38/44.15 Proof: 172.38/44.15 DP Processor: 172.38/44.15 DPs: 172.38/44.15 a#(a(a(x1))) -> b#(a(x1)) 172.38/44.15 a#(a(a(x1))) -> b#(b(a(x1))) 172.38/44.15 a#(b(a(x1))) -> b#(b(a(x1))) 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 TRS: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 TDG Processor: 172.38/44.15 DPs: 172.38/44.15 a#(a(a(x1))) -> b#(a(x1)) 172.38/44.15 a#(a(a(x1))) -> b#(b(a(x1))) 172.38/44.15 a#(b(a(x1))) -> b#(b(a(x1))) 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 TRS: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 graph: 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) -> a#(b(a(x1))) -> b#(b(a(x1))) 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(b(a(x1))) 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(a(x1)) 172.38/44.15 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 a#(a(a(x1))) -> b#(b(a(x1))) -> b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 a#(a(a(x1))) -> b#(a(x1)) -> b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 Arctic Interpretation Processor: 172.38/44.15 dimension: 1 172.38/44.15 usable rules: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 interpretation: 172.38/44.15 [b#](x0) = x0 + 0, 172.38/44.15 172.38/44.15 [a#](x0) = x0 + 0, 172.38/44.15 172.38/44.15 [b](x0) = 8x0 + 9, 172.38/44.15 172.38/44.15 [a](x0) = 8x0 + 8 172.38/44.15 orientation: 172.38/44.15 a#(a(a(x1))) = 16x1 + 16 >= 8x1 + 8 = b#(a(x1)) 172.38/44.15 172.38/44.15 a#(a(a(x1))) = 16x1 + 16 >= 16x1 + 16 = b#(b(a(x1))) 172.38/44.15 172.38/44.15 a#(b(a(x1))) = 16x1 + 16 >= 16x1 + 16 = b#(b(a(x1))) 172.38/44.15 172.38/44.15 b#(a(b(x1))) = 16x1 + 17 >= 16x1 + 17 = a#(a(b(x1))) 172.38/44.15 172.38/44.15 a(a(a(x1))) = 24x1 + 24 >= 24x1 + 24 = b(b(a(x1))) 172.38/44.15 172.38/44.15 a(b(a(x1))) = 24x1 + 24 >= 24x1 + 24 = b(b(a(x1))) 172.38/44.15 172.38/44.15 b(a(b(x1))) = 24x1 + 25 >= 24x1 + 25 = a(a(b(x1))) 172.38/44.15 problem: 172.38/44.15 DPs: 172.38/44.15 a#(a(a(x1))) -> b#(b(a(x1))) 172.38/44.15 a#(b(a(x1))) -> b#(b(a(x1))) 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 TRS: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 Restore Modifier: 172.38/44.15 DPs: 172.38/44.15 a#(a(a(x1))) -> b#(b(a(x1))) 172.38/44.15 a#(b(a(x1))) -> b#(b(a(x1))) 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 TRS: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 EDG Processor: 172.38/44.15 DPs: 172.38/44.15 a#(a(a(x1))) -> b#(b(a(x1))) 172.38/44.15 a#(b(a(x1))) -> b#(b(a(x1))) 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 TRS: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 graph: 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(b(a(x1))) 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) -> a#(b(a(x1))) -> b#(b(a(x1))) 172.38/44.15 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 a#(a(a(x1))) -> b#(b(a(x1))) -> b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 Arctic Interpretation Processor: 172.38/44.15 dimension: 2 172.38/44.15 usable rules: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 interpretation: 172.38/44.15 [b#](x0) = [1 0]x0 + [0], 172.38/44.15 172.38/44.15 [a#](x0) = [2 0]x0 + [0], 172.38/44.15 172.38/44.15 [0 2 ] 172.38/44.15 [b](x0) = [-& 0 ]x0, 172.38/44.15 172.38/44.15 [0 2] [-&] 172.38/44.15 [a](x0) = [2 0]x0 + [0 ] 172.38/44.15 orientation: 172.38/44.15 a#(a(a(x1))) = [6 4]x1 + [4] >= [5 3]x1 + [3] = b#(b(a(x1))) 172.38/44.15 172.38/44.15 a#(b(a(x1))) = [6 4]x1 + [4] >= [5 3]x1 + [3] = b#(b(a(x1))) 172.38/44.15 172.38/44.15 b#(a(b(x1))) = [2 4]x1 + [0] >= [2 4]x1 + [0] = a#(a(b(x1))) 172.38/44.15 172.38/44.15 [4 6] [2] [4 2] [2] 172.38/44.15 a(a(a(x1))) = [6 4]x1 + [4] >= [2 0]x1 + [0] = b(b(a(x1))) 172.38/44.15 172.38/44.15 [4 2] [2] [4 2] [2] 172.38/44.15 a(b(a(x1))) = [6 4]x1 + [4] >= [2 0]x1 + [0] = b(b(a(x1))) 172.38/44.15 172.38/44.15 [4 6] [2] [4 6] [2] 172.38/44.15 b(a(b(x1))) = [2 4]x1 + [0] >= [2 4]x1 + [0] = a(a(b(x1))) 172.38/44.15 problem: 172.38/44.15 DPs: 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 TRS: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 Restore Modifier: 172.38/44.15 DPs: 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 TRS: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 EDG Processor: 172.38/44.15 DPs: 172.38/44.15 b#(a(b(x1))) -> a#(a(b(x1))) 172.38/44.15 TRS: 172.38/44.15 a(a(a(x1))) -> b(b(a(x1))) 172.38/44.15 a(b(a(x1))) -> b(b(a(x1))) 172.38/44.15 b(a(b(x1))) -> a(a(b(x1))) 172.38/44.15 graph: 172.38/44.15 172.38/44.15 SCC Processor: 172.38/44.15 #sccs: 0 172.38/44.15 #rules: 0 172.38/44.15 #arcs: 0/1 172.38/44.15 172.38/44.15 EOF