183.72/46.98 YES 183.72/46.99 183.72/46.99 Problem: 183.72/46.99 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.72/46.99 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.72/46.99 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.72/46.99 183.72/46.99 Proof: 183.72/46.99 DP Processor: 183.72/46.99 DPs: 183.72/46.99 b#(b(a(a(x1)))) -> b#(x1) 183.72/46.99 b#(b(a(a(x1)))) -> a#(b(x1)) 183.72/46.99 b#(b(a(a(x1)))) -> a#(a(b(x1))) 183.72/46.99 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.72/46.99 a#(a(a(b(x1)))) -> a#(x1) 183.72/46.99 a#(a(a(b(x1)))) -> b#(a(x1)) 183.72/46.99 a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.72/46.99 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.72/46.99 a#(b(a(b(x1)))) -> b#(b(x1)) 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.72/46.99 TRS: 183.72/46.99 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.72/46.99 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.72/46.99 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.72/46.99 TDG Processor: 183.72/46.99 DPs: 183.72/46.99 b#(b(a(a(x1)))) -> b#(x1) 183.72/46.99 b#(b(a(a(x1)))) -> a#(b(x1)) 183.72/46.99 b#(b(a(a(x1)))) -> a#(a(b(x1))) 183.72/46.99 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.72/46.99 a#(a(a(b(x1)))) -> a#(x1) 183.72/46.99 a#(a(a(b(x1)))) -> b#(a(x1)) 183.72/46.99 a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.72/46.99 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.72/46.99 a#(b(a(b(x1)))) -> b#(b(x1)) 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.72/46.99 TRS: 183.72/46.99 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.72/46.99 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.72/46.99 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.72/46.99 graph: 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) -> 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) -> 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) -> a#(b(a(b(x1)))) -> b#(b(x1)) 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) -> 183.72/46.99 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) -> 183.72/46.99 a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(b(x1)))) -> b#(a(x1)) 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) -> a#(a(a(b(x1)))) -> a#(x1) 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 183.72/46.99 a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 183.72/46.99 a#(b(a(b(x1)))) -> b#(b(x1)) 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 183.72/46.99 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.72/46.99 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 183.72/46.99 a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.72/47.00 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(x1)) 183.72/47.00 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(x1) 183.72/47.00 a#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.72/47.00 a#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(x1))) 183.72/47.00 a#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(x1)) 183.72/47.00 a#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) 183.72/47.00 a#(a(a(b(x1)))) -> a#(b(a(x1))) -> 183.72/47.00 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.72/47.00 a#(a(a(b(x1)))) -> a#(b(a(x1))) -> 183.72/47.00 a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.72/47.00 a#(a(a(b(x1)))) -> a#(b(a(x1))) -> a#(b(a(b(x1)))) -> b#(b(x1)) 183.72/47.00 a#(a(a(b(x1)))) -> a#(b(a(x1))) -> 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.72/47.00 a#(a(a(b(x1)))) -> a#(b(a(x1))) -> 183.72/47.00 a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.72/47.00 a#(a(a(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> b#(a(x1)) 183.72/47.00 a#(a(a(b(x1)))) -> a#(b(a(x1))) -> a#(a(a(b(x1)))) -> a#(x1) 183.72/47.00 a#(a(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.72/47.00 a#(a(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.72/47.00 a#(a(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(b(x1)) 183.72/47.00 a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.72/47.00 a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.72/47.00 a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(x1)) 183.72/47.00 a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(x1) 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> 183.72/47.00 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> 183.72/47.00 b#(b(a(a(x1)))) -> a#(a(b(x1))) 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> 183.72/47.00 b#(b(a(a(x1)))) -> a#(b(x1)) 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> b#(b(a(a(x1)))) -> b#(x1) 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(x1))) 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(b(x1)) 183.72/47.00 a#(a(a(b(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(x1) 183.72/47.00 b#(b(a(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.72/47.00 b#(b(a(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(x1)) 183.99/47.01 b#(b(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> b#(a(x1)) 183.99/47.01 b#(b(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> a#(x1) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(b(x1))) -> 183.99/47.01 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(b(x1))) -> 183.99/47.01 a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(b(x1)) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(b(x1))) -> 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(b(x1))) -> 183.99/47.01 a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(a(a(b(x1)))) -> b#(a(x1)) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(a(a(b(x1)))) -> a#(x1) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> 183.99/47.01 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> 183.99/47.01 a#(b(a(b(x1)))) -> a#(b(b(x1))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> 183.99/47.01 a#(b(a(b(x1)))) -> b#(b(x1)) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> 183.99/47.01 a#(a(a(b(x1)))) -> a#(b(a(x1))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(x1)) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(a(a(b(x1)))) -> a#(x1) 183.99/47.01 b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.99/47.01 b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(x1))) 183.99/47.01 b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(b(x1)) 183.99/47.01 b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) 183.99/47.01 Arctic Interpretation Processor: 183.99/47.01 dimension: 1 183.99/47.01 usable rules: 183.99/47.01 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.99/47.01 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.99/47.01 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.99/47.01 interpretation: 183.99/47.01 [a#](x0) = 14x0, 183.99/47.01 183.99/47.01 [b#](x0) = 14x0, 183.99/47.01 183.99/47.01 [b](x0) = 1x0, 183.99/47.01 183.99/47.01 [a](x0) = 1x0 183.99/47.01 orientation: 183.99/47.01 b#(b(a(a(x1)))) = 17x1 >= 14x1 = b#(x1) 183.99/47.01 183.99/47.01 b#(b(a(a(x1)))) = 17x1 >= 15x1 = a#(b(x1)) 183.99/47.01 183.99/47.01 b#(b(a(a(x1)))) = 17x1 >= 16x1 = a#(a(b(x1))) 183.99/47.01 183.99/47.01 b#(b(a(a(x1)))) = 17x1 >= 17x1 = a#(a(a(b(x1)))) 183.99/47.01 183.99/47.01 a#(a(a(b(x1)))) = 17x1 >= 14x1 = a#(x1) 183.99/47.01 183.99/47.01 a#(a(a(b(x1)))) = 17x1 >= 15x1 = b#(a(x1)) 183.99/47.01 183.99/47.01 a#(a(a(b(x1)))) = 17x1 >= 16x1 = a#(b(a(x1))) 183.99/47.01 183.99/47.01 a#(a(a(b(x1)))) = 17x1 >= 17x1 = b#(a(b(a(x1)))) 183.99/47.01 183.99/47.01 a#(b(a(b(x1)))) = 17x1 >= 15x1 = b#(b(x1)) 183.99/47.01 183.99/47.01 a#(b(a(b(x1)))) = 17x1 >= 16x1 = a#(b(b(x1))) 183.99/47.01 183.99/47.01 a#(b(a(b(x1)))) = 17x1 >= 17x1 = a#(a(b(b(x1)))) 183.99/47.01 183.99/47.01 b(b(a(a(x1)))) = 4x1 >= 4x1 = a(a(a(b(x1)))) 183.99/47.01 183.99/47.01 a(a(a(b(x1)))) = 4x1 >= 4x1 = b(a(b(a(x1)))) 183.99/47.01 183.99/47.01 a(b(a(b(x1)))) = 4x1 >= 4x1 = a(a(b(b(x1)))) 183.99/47.01 problem: 183.99/47.01 DPs: 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.99/47.01 TRS: 183.99/47.01 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.99/47.01 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.99/47.01 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.99/47.01 Restore Modifier: 183.99/47.01 DPs: 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.99/47.01 TRS: 183.99/47.01 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.99/47.01 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.99/47.01 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.99/47.01 EDG Processor: 183.99/47.01 DPs: 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.99/47.01 TRS: 183.99/47.01 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.99/47.01 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.99/47.01 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.99/47.01 graph: 183.99/47.01 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) -> 183.99/47.01 a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) -> 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 b#(b(a(a(x1)))) -> a#(a(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(a(b(b(x1)))) 183.99/47.01 Matrix Interpretation Processor: dim=3 183.99/47.01 183.99/47.01 interpretation: 183.99/47.01 [a#](x0) = [1 0 0]x0, 183.99/47.01 183.99/47.01 [b#](x0) = [1 0 0]x0, 183.99/47.01 183.99/47.01 [0 0 1] 183.99/47.01 [b](x0) = [1 0 0]x0 183.99/47.01 [0 1 1] , 183.99/47.01 183.99/47.01 [0 0 1] [0] 183.99/47.01 [a](x0) = [1 0 0]x0 + [0] 183.99/47.01 [0 1 1] [1] 183.99/47.01 orientation: 183.99/47.01 b#(b(a(a(x1)))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [1] = a#(a(a(b(x1)))) 183.99/47.01 183.99/47.01 a#(a(a(b(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = b#(a(b(a(x1)))) 183.99/47.01 183.99/47.01 a#(b(a(b(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 = a#(a(b(b(x1)))) 183.99/47.01 183.99/47.01 [1 1 2] [2] [1 1 2] [2] 183.99/47.01 b(b(a(a(x1)))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [1] = a(a(a(b(x1)))) 183.99/47.01 [1 2 3] [3] [1 2 3] [3] 183.99/47.01 183.99/47.01 [1 1 2] [2] [1 1 2] [2] 183.99/47.01 a(a(a(b(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = b(a(b(a(x1)))) 183.99/47.01 [1 2 3] [3] [1 2 3] [3] 183.99/47.01 183.99/47.01 [1 1 2] [1] [1 1 2] [1] 183.99/47.01 a(b(a(b(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [0] = a(a(b(b(x1)))) 183.99/47.01 [1 2 3] [2] [1 2 3] [2] 183.99/47.01 problem: 183.99/47.01 DPs: 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 TRS: 183.99/47.01 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.99/47.01 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.99/47.01 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.99/47.01 Restore Modifier: 183.99/47.01 DPs: 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 TRS: 183.99/47.01 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.99/47.01 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.99/47.01 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.99/47.01 EDG Processor: 183.99/47.01 DPs: 183.99/47.01 a#(a(a(b(x1)))) -> b#(a(b(a(x1)))) 183.99/47.01 TRS: 183.99/47.01 b(b(a(a(x1)))) -> a(a(a(b(x1)))) 183.99/47.01 a(a(a(b(x1)))) -> b(a(b(a(x1)))) 183.99/47.01 a(b(a(b(x1)))) -> a(a(b(b(x1)))) 183.99/47.01 graph: 183.99/47.01 183.99/47.01 SCC Processor: 183.99/47.01 #sccs: 0 183.99/47.01 #rules: 0 183.99/47.01 #arcs: 0/1 183.99/47.01 183.99/47.02 EOF