182.41/46.62 YES 182.41/46.63 182.41/46.63 Problem: 182.41/46.63 a(a(x1)) -> c(b(a(b(a(x1))))) 182.41/46.63 b(a(b(x1))) -> b(x1) 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(c(x1)) -> a(b(c(b(a(x1))))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 182.41/46.63 Proof: 182.41/46.63 Matrix Interpretation Processor: dim=3 182.41/46.63 182.41/46.63 interpretation: 182.41/46.63 [1 0 1] [0] 182.41/46.63 [c](x0) = [0 0 0]x0 + [0] 182.41/46.63 [0 0 0] [1], 182.41/46.63 182.41/46.63 [1 0 0] 182.41/46.63 [b](x0) = [0 0 0]x0 182.41/46.63 [0 0 0] , 182.41/46.63 182.41/46.63 [1 0 1] [0] 182.41/46.63 [a](x0) = [0 0 0]x0 + [0] 182.41/46.63 [0 0 0] [1] 182.41/46.63 orientation: 182.41/46.63 [1 0 1] [1] [1 0 1] [0] 182.41/46.63 a(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(b(a(b(a(x1))))) 182.41/46.63 [0 0 0] [1] [0 0 0] [1] 182.41/46.63 182.41/46.63 [1 0 0] [1 0 0] 182.41/46.63 b(a(b(x1))) = [0 0 0]x1 >= [0 0 0]x1 = b(x1) 182.41/46.63 [0 0 0] [0 0 0] 182.41/46.63 182.41/46.63 [1 0 1] [2] [1 0 1] [2] 182.41/46.63 a(a(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c(a(x1))) 182.41/46.63 [0 0 0] [1] [0 0 0] [1] 182.41/46.63 182.41/46.63 [1 0 1] [1] [1 0 1] [0] 182.41/46.63 c(c(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b(c(b(a(x1))))) 182.41/46.63 [0 0 0] [1] [0 0 0] [1] 182.41/46.63 182.41/46.63 [1 0 1] [2] [1 0 1] [2] 182.41/46.63 a(c(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c(a(x1))) 182.41/46.63 [0 0 0] [1] [0 0 0] [1] 182.41/46.63 182.41/46.63 [1 0 1] [2] [1 0 1] [2] 182.41/46.63 c(a(c(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(a(c(x1))) 182.41/46.63 [0 0 0] [1] [0 0 0] [1] 182.41/46.63 problem: 182.41/46.63 b(a(b(x1))) -> b(x1) 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 Matrix Interpretation Processor: dim=1 182.41/46.63 182.41/46.63 interpretation: 182.41/46.63 [c](x0) = x0 + 2, 182.41/46.63 182.41/46.63 [b](x0) = 4x0, 182.41/46.63 182.41/46.63 [a](x0) = x0 + 2 182.41/46.63 orientation: 182.41/46.63 b(a(b(x1))) = 16x1 + 8 >= 4x1 = b(x1) 182.41/46.63 182.41/46.63 a(a(a(x1))) = x1 + 6 >= x1 + 6 = c(c(a(x1))) 182.41/46.63 182.41/46.63 a(c(a(x1))) = x1 + 6 >= x1 + 6 = c(c(a(x1))) 182.41/46.63 182.41/46.63 c(a(c(x1))) = x1 + 6 >= x1 + 6 = a(a(c(x1))) 182.41/46.63 problem: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 DP Processor: 182.41/46.63 DPs: 182.41/46.63 a#(a(a(x1))) -> c#(a(x1)) 182.41/46.63 a#(a(a(x1))) -> c#(c(a(x1))) 182.41/46.63 a#(c(a(x1))) -> c#(c(a(x1))) 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 TRS: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 TDG Processor: 182.41/46.63 DPs: 182.41/46.63 a#(a(a(x1))) -> c#(a(x1)) 182.41/46.63 a#(a(a(x1))) -> c#(c(a(x1))) 182.41/46.63 a#(c(a(x1))) -> c#(c(a(x1))) 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 TRS: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 graph: 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) -> a#(c(a(x1))) -> c#(c(a(x1))) 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) -> a#(a(a(x1))) -> c#(c(a(x1))) 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) -> a#(a(a(x1))) -> c#(a(x1)) 182.41/46.63 a#(c(a(x1))) -> c#(c(a(x1))) -> c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 a#(a(a(x1))) -> c#(c(a(x1))) -> c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 a#(a(a(x1))) -> c#(a(x1)) -> c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 Arctic Interpretation Processor: 182.41/46.63 dimension: 1 182.41/46.63 usable rules: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 interpretation: 182.41/46.63 [c#](x0) = x0 + 0, 182.41/46.63 182.41/46.63 [a#](x0) = x0 + 0, 182.41/46.63 182.41/46.63 [c](x0) = 8x0 + 9, 182.41/46.63 182.41/46.63 [a](x0) = 8x0 + 8 182.41/46.63 orientation: 182.41/46.63 a#(a(a(x1))) = 16x1 + 16 >= 8x1 + 8 = c#(a(x1)) 182.41/46.63 182.41/46.63 a#(a(a(x1))) = 16x1 + 16 >= 16x1 + 16 = c#(c(a(x1))) 182.41/46.63 182.41/46.63 a#(c(a(x1))) = 16x1 + 16 >= 16x1 + 16 = c#(c(a(x1))) 182.41/46.63 182.41/46.63 c#(a(c(x1))) = 16x1 + 17 >= 16x1 + 17 = a#(a(c(x1))) 182.41/46.63 182.41/46.63 a(a(a(x1))) = 24x1 + 24 >= 24x1 + 24 = c(c(a(x1))) 182.41/46.63 182.41/46.63 a(c(a(x1))) = 24x1 + 24 >= 24x1 + 24 = c(c(a(x1))) 182.41/46.63 182.41/46.63 c(a(c(x1))) = 24x1 + 25 >= 24x1 + 25 = a(a(c(x1))) 182.41/46.63 problem: 182.41/46.63 DPs: 182.41/46.63 a#(a(a(x1))) -> c#(c(a(x1))) 182.41/46.63 a#(c(a(x1))) -> c#(c(a(x1))) 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 TRS: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 Restore Modifier: 182.41/46.63 DPs: 182.41/46.63 a#(a(a(x1))) -> c#(c(a(x1))) 182.41/46.63 a#(c(a(x1))) -> c#(c(a(x1))) 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 TRS: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 EDG Processor: 182.41/46.63 DPs: 182.41/46.63 a#(a(a(x1))) -> c#(c(a(x1))) 182.41/46.63 a#(c(a(x1))) -> c#(c(a(x1))) 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 TRS: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 graph: 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) -> a#(a(a(x1))) -> c#(c(a(x1))) 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) -> a#(c(a(x1))) -> c#(c(a(x1))) 182.41/46.63 a#(c(a(x1))) -> c#(c(a(x1))) -> c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 a#(a(a(x1))) -> c#(c(a(x1))) -> c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 Arctic Interpretation Processor: 182.41/46.63 dimension: 2 182.41/46.63 usable rules: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 interpretation: 182.41/46.63 [c#](x0) = [1 0]x0 + [0], 182.41/46.63 182.41/46.63 [a#](x0) = [2 0]x0 + [0], 182.41/46.63 182.41/46.63 [0 2 ] 182.41/46.63 [c](x0) = [-& 0 ]x0, 182.41/46.63 182.41/46.63 [0 2] [-&] 182.41/46.63 [a](x0) = [2 0]x0 + [0 ] 182.41/46.63 orientation: 182.41/46.63 a#(a(a(x1))) = [6 4]x1 + [4] >= [5 3]x1 + [3] = c#(c(a(x1))) 182.41/46.63 182.41/46.63 a#(c(a(x1))) = [6 4]x1 + [4] >= [5 3]x1 + [3] = c#(c(a(x1))) 182.41/46.63 182.41/46.63 c#(a(c(x1))) = [2 4]x1 + [0] >= [2 4]x1 + [0] = a#(a(c(x1))) 182.41/46.63 182.41/46.63 [4 6] [2] [4 2] [2] 182.41/46.63 a(a(a(x1))) = [6 4]x1 + [4] >= [2 0]x1 + [0] = c(c(a(x1))) 182.41/46.63 182.41/46.63 [4 2] [2] [4 2] [2] 182.41/46.63 a(c(a(x1))) = [6 4]x1 + [4] >= [2 0]x1 + [0] = c(c(a(x1))) 182.41/46.63 182.41/46.63 [4 6] [2] [4 6] [2] 182.41/46.63 c(a(c(x1))) = [2 4]x1 + [0] >= [2 4]x1 + [0] = a(a(c(x1))) 182.41/46.63 problem: 182.41/46.63 DPs: 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 TRS: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 Restore Modifier: 182.41/46.63 DPs: 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 TRS: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 EDG Processor: 182.41/46.63 DPs: 182.41/46.63 c#(a(c(x1))) -> a#(a(c(x1))) 182.41/46.63 TRS: 182.41/46.63 a(a(a(x1))) -> c(c(a(x1))) 182.41/46.63 a(c(a(x1))) -> c(c(a(x1))) 182.41/46.63 c(a(c(x1))) -> a(a(c(x1))) 182.41/46.63 graph: 182.41/46.63 182.41/46.63 SCC Processor: 182.41/46.63 #sccs: 0 182.41/46.63 #rules: 0 182.41/46.63 #arcs: 0/1 182.41/46.63 182.72/46.64 EOF