179.74/45.99 YES 179.74/46.00 179.74/46.00 Problem: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 179.74/46.00 Proof: 179.74/46.00 DP Processor: 179.74/46.00 DPs: 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(b(x1))) -> a#(x1) 179.74/46.00 b#(b(b(x1))) -> b#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 TRS: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 TDG Processor: 179.74/46.00 DPs: 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(b(x1))) -> a#(x1) 179.74/46.00 b#(b(b(x1))) -> b#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 TRS: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 graph: 179.74/46.00 b#(b(b(x1))) -> b#(a(x1)) -> b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 b#(b(b(x1))) -> b#(a(x1)) -> b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(b(x1))) -> b#(a(x1)) -> b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(b(x1))) -> b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) 179.74/46.00 b#(b(b(x1))) -> b#(a(x1)) -> b#(b(b(x1))) -> a#(x1) 179.74/46.00 b#(b(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) -> a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(x1)) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(x1)) 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(x1) 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(b(x1))) -> b#(a(x1)) 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(b(x1))) -> a#(x1) 179.74/46.00 Arctic Interpretation Processor: 179.74/46.00 dimension: 2 179.74/46.00 usable rules: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 interpretation: 179.74/46.00 [b#](x0) = [-& 0 ]x0 + [0], 179.74/46.00 179.74/46.00 [a#](x0) = [-& 0 ]x0 + [0], 179.74/46.00 179.74/46.00 [0 0] [0] 179.74/46.00 [b](x0) = [2 0]x0 + [3], 179.74/46.00 179.74/46.00 [0 0] [0] 179.74/46.00 [a](x0) = [0 0]x0 + [0] 179.74/46.00 orientation: 179.74/46.00 a#(b(a(x1))) = [2 2]x1 + [3] >= [2 2]x1 + [3] = b#(b(a(x1))) 179.74/46.00 179.74/46.00 b#(b(b(x1))) = [2 2]x1 + [3] >= [-& 0 ]x1 + [0] = a#(x1) 179.74/46.00 179.74/46.00 b#(b(b(x1))) = [2 2]x1 + [3] >= [0 0]x1 + [0] = b#(a(x1)) 179.74/46.00 179.74/46.00 b#(b(x1)) = [2 0]x1 + [3] >= [-& 0 ]x1 + [0] = a#(x1) 179.74/46.00 179.74/46.00 b#(b(x1)) = [2 0]x1 + [3] >= [0 0]x1 + [0] = a#(a(x1)) 179.74/46.00 179.74/46.00 b#(b(x1)) = [2 0]x1 + [3] >= [0 0]x1 + [0] = a#(a(a(x1))) 179.74/46.00 179.74/46.00 [2 2] [3] [2 2] [3] 179.74/46.00 a(b(a(x1))) = [2 2]x1 + [3] >= [2 2]x1 + [3] = b(b(a(x1))) 179.74/46.00 179.74/46.00 [2 2] [3] [0 0] [0] 179.74/46.00 b(b(b(x1))) = [4 2]x1 + [5] >= [2 2]x1 + [3] = b(a(x1)) 179.74/46.00 179.74/46.00 [2 0] [3] [0 0] [0] 179.74/46.00 b(b(x1)) = [2 2]x1 + [3] >= [0 0]x1 + [0] = a(a(a(x1))) 179.74/46.00 problem: 179.74/46.00 DPs: 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 TRS: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 Restore Modifier: 179.74/46.00 DPs: 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 TRS: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 EDG Processor: 179.74/46.00 DPs: 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 TRS: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 graph: 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) -> a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 b#(b(x1)) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1))) 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(x1) 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(x1)) 179.74/46.00 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 Arctic Interpretation Processor: 179.74/46.00 dimension: 2 179.74/46.00 usable rules: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 interpretation: 179.74/46.00 [b#](x0) = [0 -&]x0 + [0], 179.74/46.00 179.74/46.00 [a#](x0) = [0 0]x0 + [0], 179.74/46.00 179.74/46.00 [0 0 ] [3 ] 179.74/46.00 [b](x0) = [1 -&]x0 + [-&], 179.74/46.00 179.74/46.00 [0 0] [3] 179.74/46.00 [a](x0) = [0 0]x0 + [0] 179.74/46.00 orientation: 179.74/46.00 a#(b(a(x1))) = [1 1]x1 + [4] >= [0 0]x1 + [3] = b#(b(a(x1))) 179.74/46.00 179.74/46.00 b#(b(x1)) = [0 0]x1 + [3] >= [0 0]x1 + [0] = a#(x1) 179.74/46.00 179.74/46.00 b#(b(x1)) = [0 0]x1 + [3] >= [0 0]x1 + [3] = a#(a(x1)) 179.74/46.00 179.74/46.00 b#(b(x1)) = [0 0]x1 + [3] >= [0 0]x1 + [3] = a#(a(a(x1))) 179.74/46.00 179.74/46.00 [1 1] [4] [1 1] [4] 179.74/46.00 a(b(a(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = b(b(a(x1))) 179.74/46.00 179.74/46.00 [1 1] [4] [0 0] [3] 179.74/46.00 b(b(b(x1))) = [2 1]x1 + [4] >= [1 1]x1 + [4] = b(a(x1)) 179.74/46.00 179.74/46.00 [1 0] [3] [0 0] [3] 179.74/46.00 b(b(x1)) = [1 1]x1 + [4] >= [0 0]x1 + [3] = a(a(a(x1))) 179.74/46.00 problem: 179.74/46.00 DPs: 179.74/46.00 b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 TRS: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 Restore Modifier: 179.74/46.00 DPs: 179.74/46.00 b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 TRS: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 EDG Processor: 179.74/46.00 DPs: 179.74/46.00 b#(b(x1)) -> a#(x1) 179.74/46.00 b#(b(x1)) -> a#(a(x1)) 179.74/46.00 b#(b(x1)) -> a#(a(a(x1))) 179.74/46.00 TRS: 179.74/46.00 a(b(a(x1))) -> b(b(a(x1))) 179.74/46.00 b(b(b(x1))) -> b(a(x1)) 179.74/46.00 b(b(x1)) -> a(a(a(x1))) 179.74/46.00 graph: 179.74/46.00 179.74/46.00 SCC Processor: 179.74/46.00 #sccs: 0 179.74/46.00 #rules: 0 179.74/46.00 #arcs: 0/9 179.74/46.00 180.04/46.00 EOF