183.41/46.56 YES 183.41/46.57 183.41/46.57 Problem: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 183.41/46.57 Proof: 183.41/46.57 DP Processor: 183.41/46.57 DPs: 183.41/46.57 a#(a(b(x1))) -> a#(x1) 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(x1) 183.41/46.57 b#(b(x1)) -> a#(a(x1)) 183.41/46.57 b#(b(x1)) -> a#(a(a(x1))) 183.41/46.57 TRS: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 TDG Processor: 183.41/46.57 DPs: 183.41/46.57 a#(a(b(x1))) -> a#(x1) 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(x1) 183.41/46.57 b#(b(x1)) -> a#(a(x1)) 183.41/46.57 b#(b(x1)) -> a#(a(a(x1))) 183.41/46.57 TRS: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 graph: 183.41/46.57 b#(b(x1)) -> a#(a(a(x1))) -> a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(x1) 183.41/46.57 b#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1) 183.41/46.57 b#(b(x1)) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) 183.41/46.57 a#(a(b(x1))) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(a(x1))) 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(x1)) 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(x1) 183.41/46.57 Arctic Interpretation Processor: 183.41/46.57 dimension: 2 183.41/46.57 usable rules: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 interpretation: 183.41/46.57 [b#](x0) = [-& 2 ]x0 + [0], 183.41/46.57 183.41/46.57 [a#](x0) = [0 2]x0 + [0], 183.41/46.57 183.41/46.57 [0 -&] [0] 183.41/46.57 [a](x0) = [1 0 ]x0 + [1], 183.41/46.57 183.41/46.57 [0 0] [-&] 183.41/46.57 [b](x0) = [1 0]x0 + [1 ] 183.41/46.57 orientation: 183.41/46.57 a#(a(b(x1))) = [3 3]x1 + [3] >= [0 2]x1 + [0] = a#(x1) 183.41/46.57 183.41/46.57 a#(b(a(x1))) = [3 2]x1 + [3] >= [3 2]x1 + [3] = b#(b(a(x1))) 183.41/46.57 183.41/46.57 b#(b(x1)) = [3 2]x1 + [3] >= [0 2]x1 + [0] = a#(x1) 183.41/46.57 183.41/46.57 b#(b(x1)) = [3 2]x1 + [3] >= [3 2]x1 + [3] = a#(a(x1)) 183.41/46.57 183.41/46.57 b#(b(x1)) = [3 2]x1 + [3] >= [3 2]x1 + [3] = a#(a(a(x1))) 183.41/46.57 183.41/46.57 [0 0] [0] [0 -&] [0] 183.41/46.57 a(a(b(x1))) = [1 1]x1 + [1] >= [1 0 ]x1 + [1] = a(x1) 183.41/46.57 183.41/46.57 [1 0] [1] [1 0] [1] 183.41/46.57 a(b(a(x1))) = [2 1]x1 + [2] >= [2 1]x1 + [2] = b(b(a(x1))) 183.41/46.57 183.41/46.57 [1 0] [1] [0 -&] [0] 183.41/46.57 b(b(x1)) = [1 1]x1 + [1] >= [1 0 ]x1 + [1] = a(a(a(x1))) 183.41/46.57 problem: 183.41/46.57 DPs: 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(x1) 183.41/46.57 b#(b(x1)) -> a#(a(x1)) 183.41/46.57 b#(b(x1)) -> a#(a(a(x1))) 183.41/46.57 TRS: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 Restore Modifier: 183.41/46.57 DPs: 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(x1) 183.41/46.57 b#(b(x1)) -> a#(a(x1)) 183.41/46.57 b#(b(x1)) -> a#(a(a(x1))) 183.41/46.57 TRS: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 EDG Processor: 183.41/46.57 DPs: 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(x1) 183.41/46.57 b#(b(x1)) -> a#(a(x1)) 183.41/46.57 b#(b(x1)) -> a#(a(a(x1))) 183.41/46.57 TRS: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 graph: 183.41/46.57 b#(b(x1)) -> a#(a(a(x1))) -> a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 b#(b(x1)) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(x1) 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(x1)) 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(a(x1))) 183.41/46.57 Arctic Interpretation Processor: 183.41/46.57 dimension: 2 183.41/46.57 usable rules: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 interpretation: 183.41/46.57 [b#](x0) = [1 0]x0 + [0], 183.41/46.57 183.41/46.57 [a#](x0) = [-& 0 ]x0 + [0], 183.41/46.57 183.41/46.57 [0 0 ] 183.41/46.57 [a](x0) = [-& 0 ]x0, 183.41/46.57 183.41/46.57 [0 0] [-&] 183.41/46.57 [b](x0) = [2 0]x0 + [2 ] 183.41/46.57 orientation: 183.41/46.57 a#(b(a(x1))) = [2 2]x1 + [2] >= [2 2]x1 + [2] = b#(b(a(x1))) 183.41/46.57 183.41/46.57 b#(b(x1)) = [2 1]x1 + [2] >= [-& 0 ]x1 + [0] = a#(x1) 183.41/46.57 183.41/46.57 b#(b(x1)) = [2 1]x1 + [2] >= [-& 0 ]x1 + [0] = a#(a(x1)) 183.41/46.57 183.41/46.57 b#(b(x1)) = [2 1]x1 + [2] >= [-& 0 ]x1 + [0] = a#(a(a(x1))) 183.41/46.57 183.41/46.57 [2 0] [2] [0 0 ] 183.41/46.57 a(a(b(x1))) = [2 0]x1 + [2] >= [-& 0 ]x1 = a(x1) 183.41/46.57 183.41/46.57 [2 2] [2] [2 2] [2] 183.41/46.57 a(b(a(x1))) = [2 2]x1 + [2] >= [2 2]x1 + [2] = b(b(a(x1))) 183.41/46.57 183.41/46.57 [2 0] [2] [0 0 ] 183.41/46.57 b(b(x1)) = [2 2]x1 + [2] >= [-& 0 ]x1 = a(a(a(x1))) 183.41/46.57 problem: 183.41/46.57 DPs: 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 TRS: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 Restore Modifier: 183.41/46.57 DPs: 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 TRS: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 EDG Processor: 183.41/46.57 DPs: 183.41/46.57 a#(b(a(x1))) -> b#(b(a(x1))) 183.41/46.57 TRS: 183.41/46.57 a(a(b(x1))) -> a(x1) 183.41/46.57 a(b(a(x1))) -> b(b(a(x1))) 183.41/46.57 b(b(x1)) -> a(a(a(x1))) 183.41/46.57 graph: 183.41/46.57 183.41/46.57 SCC Processor: 183.41/46.57 #sccs: 0 183.41/46.57 #rules: 0 183.41/46.57 #arcs: 0/1 183.41/46.57 183.41/46.57 EOF