182.04/46.55 YES 182.04/46.56 182.04/46.56 Problem: 182.04/46.56 a(a(x1)) -> b(c(x1)) 182.04/46.56 a(b(x1)) -> c(a(x1)) 182.04/46.56 c(c(x1)) -> a(b(x1)) 182.04/46.56 182.04/46.56 Proof: 182.04/46.56 String Reversal Processor: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 DP Processor: 182.04/46.56 DPs: 182.04/46.56 a#(a(x1)) -> b#(x1) 182.04/46.56 a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> c#(x1) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) 182.04/46.56 c#(c(x1)) -> a#(x1) 182.04/46.56 c#(c(x1)) -> b#(a(x1)) 182.04/46.56 TRS: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 TDG Processor: 182.04/46.56 DPs: 182.04/46.56 a#(a(x1)) -> b#(x1) 182.04/46.56 a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> c#(x1) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) 182.04/46.56 c#(c(x1)) -> a#(x1) 182.04/46.56 c#(c(x1)) -> b#(a(x1)) 182.04/46.56 TRS: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 graph: 182.04/46.56 c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1)) 182.04/46.56 c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> c#(x1) 182.04/46.56 c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1)) 182.04/46.56 c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) 182.04/46.56 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(a(x1)) 182.04/46.56 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(x1) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1) 182.04/46.56 a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1)) 182.04/46.56 a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1) 182.04/46.56 a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(x1)) 182.04/46.56 a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1) 182.04/46.56 Arctic Interpretation Processor: 182.04/46.56 dimension: 1 182.04/46.56 usable rules: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 interpretation: 182.04/46.56 [c#](x0) = 14x0, 182.04/46.56 182.04/46.56 [b#](x0) = 14x0 + 1, 182.04/46.56 182.04/46.56 [a#](x0) = 14x0 + 0, 182.04/46.56 182.04/46.56 [b](x0) = 2x0 + 9, 182.04/46.56 182.04/46.56 [c](x0) = 2x0 + 9, 182.04/46.56 182.04/46.56 [a](x0) = 2x0 + 9 182.04/46.56 orientation: 182.04/46.56 a#(a(x1)) = 16x1 + 23 >= 14x1 + 1 = b#(x1) 182.04/46.56 182.04/46.56 a#(a(x1)) = 16x1 + 23 >= 16x1 + 23 = c#(b(x1)) 182.04/46.56 182.04/46.56 b#(a(x1)) = 16x1 + 23 >= 14x1 = c#(x1) 182.04/46.56 182.04/46.56 b#(a(x1)) = 16x1 + 23 >= 16x1 + 23 = a#(c(x1)) 182.04/46.56 182.04/46.56 c#(c(x1)) = 16x1 + 23 >= 14x1 + 0 = a#(x1) 182.04/46.56 182.04/46.56 c#(c(x1)) = 16x1 + 23 >= 16x1 + 23 = b#(a(x1)) 182.04/46.56 182.04/46.56 a(a(x1)) = 4x1 + 11 >= 4x1 + 11 = c(b(x1)) 182.04/46.56 182.04/46.56 b(a(x1)) = 4x1 + 11 >= 4x1 + 11 = a(c(x1)) 182.04/46.56 182.04/46.56 c(c(x1)) = 4x1 + 11 >= 4x1 + 11 = b(a(x1)) 182.04/46.56 problem: 182.04/46.56 DPs: 182.04/46.56 a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) 182.04/46.56 c#(c(x1)) -> b#(a(x1)) 182.04/46.56 TRS: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 Restore Modifier: 182.04/46.56 DPs: 182.04/46.56 a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) 182.04/46.56 c#(c(x1)) -> b#(a(x1)) 182.04/46.56 TRS: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 EDG Processor: 182.04/46.56 DPs: 182.04/46.56 a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) 182.04/46.56 c#(c(x1)) -> b#(a(x1)) 182.04/46.56 TRS: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 graph: 182.04/46.56 c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1)) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1)) 182.04/46.56 a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1)) 182.04/46.56 Arctic Interpretation Processor: 182.04/46.56 dimension: 3 182.04/46.56 usable rules: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 interpretation: 182.04/46.56 [c#](x0) = [0 0 1]x0 + [0], 182.04/46.56 182.04/46.56 [b#](x0) = [-& 0 0 ]x0 + [0], 182.04/46.56 182.04/46.56 [a#](x0) = [0 0 0]x0 + [0], 182.04/46.56 182.04/46.56 [0 1 1 ] [0] 182.04/46.56 [b](x0) = [-& 1 1 ]x0 + [0] 182.04/46.56 [-& 0 0 ] [0], 182.04/46.56 182.04/46.56 [0 0 1] [0] 182.04/46.56 [c](x0) = [0 0 1]x0 + [0] 182.04/46.56 [0 0 1] [0], 182.04/46.56 182.04/46.56 [0 1 0] [1 ] 182.04/46.56 [a](x0) = [0 0 1]x0 + [-&] 182.04/46.56 [0 0 0] [0 ] 182.04/46.56 orientation: 182.04/46.56 a#(a(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = c#(b(x1)) 182.04/46.56 182.04/46.56 b#(a(x1)) = [0 0 1]x1 + [0] >= [0 0 1]x1 + [0] = a#(c(x1)) 182.04/46.56 182.04/46.56 c#(c(x1)) = [1 1 2]x1 + [1] >= [0 0 1]x1 + [0] = b#(a(x1)) 182.04/46.56 182.04/46.56 [1 1 2] [1] [0 1 1] [1] 182.04/46.56 a(a(x1)) = [1 1 1]x1 + [1] >= [0 1 1]x1 + [1] = c(b(x1)) 182.04/46.56 [0 1 1] [1] [0 1 1] [1] 182.04/46.56 182.04/46.56 [1 1 2] [1] [1 1 2] [1] 182.04/46.56 b(a(x1)) = [1 1 2]x1 + [1] >= [1 1 2]x1 + [1] = a(c(x1)) 182.04/46.56 [0 0 1] [0] [0 0 1] [0] 182.04/46.56 182.04/46.56 [1 1 2] [1] [1 1 2] [1] 182.04/46.56 c(c(x1)) = [1 1 2]x1 + [1] >= [1 1 2]x1 + [1] = b(a(x1)) 182.04/46.56 [1 1 2] [1] [0 0 1] [0] 182.04/46.56 problem: 182.04/46.56 DPs: 182.04/46.56 a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) 182.04/46.56 TRS: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 Restore Modifier: 182.04/46.56 DPs: 182.04/46.56 a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) 182.04/46.56 TRS: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 EDG Processor: 182.04/46.56 DPs: 182.04/46.56 a#(a(x1)) -> c#(b(x1)) 182.04/46.56 b#(a(x1)) -> a#(c(x1)) 182.04/46.56 TRS: 182.04/46.56 a(a(x1)) -> c(b(x1)) 182.04/46.56 b(a(x1)) -> a(c(x1)) 182.04/46.56 c(c(x1)) -> b(a(x1)) 182.04/46.56 graph: 182.04/46.56 b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1)) 182.04/46.56 SCC Processor: 182.04/46.56 #sccs: 0 182.04/46.56 #rules: 0 182.04/46.56 #arcs: 1/4 182.04/46.56 182.04/46.56 EOF