181.16/46.30 YES 181.16/46.31 181.16/46.31 Problem: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 a(b(x1)) -> c(c(x1)) 181.16/46.31 b(c(x1)) -> a(a(x1)) 181.16/46.31 181.16/46.31 Proof: 181.16/46.31 String Reversal Processor: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 DP Processor: 181.16/46.31 DPs: 181.16/46.31 a#(a(x1)) -> b#(x1) 181.16/46.31 a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(x1) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(x1) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 TDG Processor: 181.16/46.31 DPs: 181.16/46.31 a#(a(x1)) -> b#(x1) 181.16/46.31 a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(x1) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(x1) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 graph: 181.16/46.31 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(b(x1)) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1) 181.16/46.31 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(b(x1)) 181.16/46.31 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 181.16/46.31 b#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(x1)) 181.16/46.31 b#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 181.16/46.31 a#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(c(x1)) 181.16/46.31 a#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(x1) 181.16/46.31 a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(c(x1)) 181.16/46.31 a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1) 181.16/46.31 Arctic Interpretation Processor: 181.16/46.31 dimension: 1 181.16/46.31 usable rules: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 interpretation: 181.16/46.31 [c#](x0) = x0, 181.16/46.31 181.16/46.31 [b#](x0) = x0, 181.16/46.31 181.16/46.31 [a#](x0) = x0 + 0, 181.16/46.31 181.16/46.31 [c](x0) = 1x0, 181.16/46.31 181.16/46.31 [b](x0) = 1x0 + 0, 181.16/46.31 181.16/46.31 [a](x0) = 1x0 + 0 181.16/46.31 orientation: 181.16/46.31 a#(a(x1)) = 1x1 + 0 >= x1 = b#(x1) 181.16/46.31 181.16/46.31 a#(a(x1)) = 1x1 + 0 >= 1x1 + 0 = b#(b(x1)) 181.16/46.31 181.16/46.31 b#(a(x1)) = 1x1 + 0 >= x1 = c#(x1) 181.16/46.31 181.16/46.31 b#(a(x1)) = 1x1 + 0 >= 1x1 = c#(c(x1)) 181.16/46.31 181.16/46.31 c#(b(x1)) = 1x1 + 0 >= x1 + 0 = a#(x1) 181.16/46.31 181.16/46.31 c#(b(x1)) = 1x1 + 0 >= 1x1 + 0 = a#(a(x1)) 181.16/46.31 181.16/46.31 a(a(x1)) = 2x1 + 1 >= 2x1 + 1 = b(b(x1)) 181.16/46.31 181.16/46.31 b(a(x1)) = 2x1 + 1 >= 2x1 = c(c(x1)) 181.16/46.31 181.16/46.31 c(b(x1)) = 2x1 + 1 >= 2x1 + 1 = a(a(x1)) 181.16/46.31 problem: 181.16/46.31 DPs: 181.16/46.31 a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(x1) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 Restore Modifier: 181.16/46.31 DPs: 181.16/46.31 a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(x1) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 EDG Processor: 181.16/46.31 DPs: 181.16/46.31 a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(x1) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 graph: 181.16/46.31 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(b(x1)) 181.16/46.31 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1)) 181.16/46.31 a#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(c(x1)) 181.16/46.31 Arctic Interpretation Processor: 181.16/46.31 dimension: 1 181.16/46.31 usable rules: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 interpretation: 181.16/46.31 [c#](x0) = x0 + 0, 181.16/46.31 181.16/46.31 [b#](x0) = x0 + 8, 181.16/46.31 181.16/46.31 [a#](x0) = x0, 181.16/46.31 181.16/46.31 [c](x0) = 8x0, 181.16/46.31 181.16/46.31 [b](x0) = 8x0 + 8, 181.16/46.31 181.16/46.31 [a](x0) = 8x0 + 8 181.16/46.31 orientation: 181.16/46.31 a#(a(x1)) = 8x1 + 8 >= 8x1 + 8 = b#(b(x1)) 181.16/46.31 181.16/46.31 b#(a(x1)) = 8x1 + 8 >= 8x1 + 0 = c#(c(x1)) 181.16/46.31 181.16/46.31 c#(b(x1)) = 8x1 + 8 >= x1 = a#(x1) 181.16/46.31 181.16/46.31 c#(b(x1)) = 8x1 + 8 >= 8x1 + 8 = a#(a(x1)) 181.16/46.31 181.16/46.31 a(a(x1)) = 16x1 + 16 >= 16x1 + 16 = b(b(x1)) 181.16/46.31 181.16/46.31 b(a(x1)) = 16x1 + 16 >= 16x1 = c(c(x1)) 181.16/46.31 181.16/46.31 c(b(x1)) = 16x1 + 16 >= 16x1 + 16 = a(a(x1)) 181.16/46.31 problem: 181.16/46.31 DPs: 181.16/46.31 a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 Restore Modifier: 181.16/46.31 DPs: 181.16/46.31 a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 EDG Processor: 181.16/46.31 DPs: 181.16/46.31 a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 graph: 181.16/46.31 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(b(x1)) 181.16/46.31 b#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1)) 181.16/46.31 a#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(c(x1)) 181.16/46.31 Arctic Interpretation Processor: 181.16/46.31 dimension: 3 181.16/46.31 usable rules: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 interpretation: 181.16/46.31 [c#](x0) = [1 0 0]x0 + [0], 181.16/46.31 181.16/46.31 [b#](x0) = [0 0 0]x0 + [0], 181.16/46.31 181.16/46.31 [a#](x0) = [1 1 0]x0 + [0], 181.16/46.31 181.16/46.31 [0 -& -&] [-&] 181.16/46.31 [c](x0) = [1 0 0 ]x0 + [-&] 181.16/46.31 [1 0 0 ] [0 ], 181.16/46.31 181.16/46.31 [0 0 0] [0] 181.16/46.31 [b](x0) = [0 0 0]x0 + [0] 181.16/46.31 [0 0 0] [0], 181.16/46.31 181.16/46.31 [-& 0 -&] [0] 181.16/46.31 [a](x0) = [0 0 0 ]x0 + [0] 181.16/46.31 [1 0 0 ] [0] 181.16/46.31 orientation: 181.16/46.31 a#(a(x1)) = [1 1 1]x1 + [1] >= [0 0 0]x1 + [0] = b#(b(x1)) 181.16/46.31 181.16/46.31 b#(a(x1)) = [1 0 0]x1 + [0] >= [1 0 0]x1 + [0] = c#(c(x1)) 181.16/46.31 181.16/46.31 c#(b(x1)) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = a#(a(x1)) 181.16/46.31 181.16/46.31 [0 0 0] [0] [0 0 0] [0] 181.16/46.31 a(a(x1)) = [1 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(b(x1)) 181.16/46.31 [1 1 0] [1] [0 0 0] [0] 181.16/46.31 181.16/46.31 [1 0 0] [0] [0 -& -&] [-&] 181.16/46.31 b(a(x1)) = [1 0 0]x1 + [0] >= [1 0 0 ]x1 + [0 ] = c(c(x1)) 181.16/46.31 [1 0 0] [0] [1 0 0 ] [0 ] 181.16/46.31 181.16/46.31 [0 0 0] [0] [0 0 0] [0] 181.16/46.31 c(b(x1)) = [1 1 1]x1 + [1] >= [1 0 0]x1 + [0] = a(a(x1)) 181.16/46.31 [1 1 1] [1] [1 1 0] [1] 181.16/46.31 problem: 181.16/46.31 DPs: 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 Restore Modifier: 181.16/46.31 DPs: 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 EDG Processor: 181.16/46.31 DPs: 181.16/46.31 b#(a(x1)) -> c#(c(x1)) 181.16/46.31 c#(b(x1)) -> a#(a(x1)) 181.16/46.31 TRS: 181.16/46.31 a(a(x1)) -> b(b(x1)) 181.16/46.31 b(a(x1)) -> c(c(x1)) 181.16/46.31 c(b(x1)) -> a(a(x1)) 181.16/46.31 graph: 181.16/46.31 b#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1)) 181.16/46.31 SCC Processor: 181.16/46.31 #sccs: 0 181.16/46.31 #rules: 0 181.16/46.31 #arcs: 1/4 181.16/46.31 181.16/46.32 EOF