178.13/45.55 YES 178.13/45.56 178.13/45.56 Problem: 178.13/45.56 a(x1) -> b(c(x1)) 178.13/45.56 a(b(x1)) -> c(a(x1)) 178.13/45.56 c(c(c(x1))) -> a(b(x1)) 178.13/45.56 178.13/45.56 Proof: 178.13/45.56 String Reversal Processor: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 DP Processor: 178.13/45.56 DPs: 178.13/45.56 a#(x1) -> b#(x1) 178.13/45.56 a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> c#(x1) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) 178.13/45.56 c#(c(c(x1))) -> a#(x1) 178.13/45.56 c#(c(c(x1))) -> b#(a(x1)) 178.13/45.56 TRS: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 TDG Processor: 178.13/45.56 DPs: 178.13/45.56 a#(x1) -> b#(x1) 178.13/45.56 a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> c#(x1) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) 178.13/45.56 c#(c(c(x1))) -> a#(x1) 178.13/45.56 c#(c(c(x1))) -> b#(a(x1)) 178.13/45.56 TRS: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 graph: 178.13/45.56 c#(c(c(x1))) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1)) 178.13/45.56 c#(c(c(x1))) -> b#(a(x1)) -> b#(a(x1)) -> c#(x1) 178.13/45.56 c#(c(c(x1))) -> a#(x1) -> a#(x1) -> c#(b(x1)) 178.13/45.56 c#(c(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 178.13/45.56 b#(a(x1)) -> c#(x1) -> c#(c(c(x1))) -> b#(a(x1)) 178.13/45.56 b#(a(x1)) -> c#(x1) -> c#(c(c(x1))) -> a#(x1) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> b#(x1) 178.13/45.56 a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(a(x1)) 178.13/45.56 a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(x1) 178.13/45.56 a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(c(x1)) 178.13/45.56 a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(x1) 178.13/45.56 Arctic Interpretation Processor: 178.13/45.56 dimension: 1 178.13/45.56 usable rules: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 interpretation: 178.13/45.56 [c#](x0) = x0, 178.13/45.56 178.13/45.56 [b#](x0) = x0, 178.13/45.56 178.13/45.56 [a#](x0) = 1x0, 178.13/45.56 178.13/45.56 [b](x0) = 1x0, 178.13/45.56 178.13/45.56 [c](x0) = 1x0, 178.13/45.56 178.13/45.56 [a](x0) = 2x0 178.13/45.56 orientation: 178.13/45.56 a#(x1) = 1x1 >= x1 = b#(x1) 178.13/45.56 178.13/45.56 a#(x1) = 1x1 >= 1x1 = c#(b(x1)) 178.13/45.56 178.13/45.56 b#(a(x1)) = 2x1 >= x1 = c#(x1) 178.13/45.56 178.13/45.56 b#(a(x1)) = 2x1 >= 2x1 = a#(c(x1)) 178.13/45.56 178.13/45.56 c#(c(c(x1))) = 2x1 >= 1x1 = a#(x1) 178.13/45.56 178.13/45.56 c#(c(c(x1))) = 2x1 >= 2x1 = b#(a(x1)) 178.13/45.56 178.13/45.56 a(x1) = 2x1 >= 2x1 = c(b(x1)) 178.13/45.56 178.13/45.56 b(a(x1)) = 3x1 >= 3x1 = a(c(x1)) 178.13/45.56 178.13/45.56 c(c(c(x1))) = 3x1 >= 3x1 = b(a(x1)) 178.13/45.56 problem: 178.13/45.56 DPs: 178.13/45.56 a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) 178.13/45.56 c#(c(c(x1))) -> b#(a(x1)) 178.13/45.56 TRS: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 Restore Modifier: 178.13/45.56 DPs: 178.13/45.56 a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) 178.13/45.56 c#(c(c(x1))) -> b#(a(x1)) 178.13/45.56 TRS: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 EDG Processor: 178.13/45.56 DPs: 178.13/45.56 a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) 178.13/45.56 c#(c(c(x1))) -> b#(a(x1)) 178.13/45.56 TRS: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 graph: 178.13/45.56 c#(c(c(x1))) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1)) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> c#(b(x1)) 178.13/45.56 a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(a(x1)) 178.13/45.56 Arctic Interpretation Processor: 178.13/45.56 dimension: 2 178.13/45.56 usable rules: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 interpretation: 178.13/45.56 [c#](x0) = [0 0]x0 + [0], 178.13/45.56 178.13/45.56 [b#](x0) = [0 -&]x0 + [0], 178.13/45.56 178.13/45.56 [a#](x0) = [2 0]x0 + [0], 178.13/45.56 178.13/45.56 [2 -&] [-&] 178.13/45.56 [b](x0) = [0 -&]x0 + [0 ], 178.13/45.56 178.13/45.56 [-& 0 ] [0] 178.13/45.56 [c](x0) = [0 2 ]x0 + [2], 178.13/45.56 178.13/45.56 [0 2 ] [2] 178.13/45.56 [a](x0) = [2 -&]x0 + [2] 178.13/45.56 orientation: 178.13/45.56 a#(x1) = [2 0]x1 + [0] >= [2 -&]x1 + [0] = c#(b(x1)) 178.13/45.56 178.13/45.56 b#(a(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = a#(c(x1)) 178.13/45.56 178.13/45.56 c#(c(c(x1))) = [2 4]x1 + [4] >= [0 2]x1 + [2] = b#(a(x1)) 178.13/45.56 178.13/45.56 [0 2 ] [2] [0 -&] [0] 178.13/45.56 a(x1) = [2 -&]x1 + [2] >= [2 -&]x1 + [2] = c(b(x1)) 178.13/45.56 178.13/45.56 [2 4] [4] [2 4 ] [4] 178.13/45.56 b(a(x1)) = [0 2]x1 + [2] >= [-& 2 ]x1 + [2] = a(c(x1)) 178.13/45.56 178.13/45.56 [2 4] [4] [2 4] [4] 178.13/45.56 c(c(c(x1))) = [4 6]x1 + [6] >= [0 2]x1 + [2] = b(a(x1)) 178.13/45.56 problem: 178.13/45.56 DPs: 178.13/45.56 a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) 178.13/45.56 TRS: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 Restore Modifier: 178.13/45.56 DPs: 178.13/45.56 a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) 178.13/45.56 TRS: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 EDG Processor: 178.13/45.56 DPs: 178.13/45.56 a#(x1) -> c#(b(x1)) 178.13/45.56 b#(a(x1)) -> a#(c(x1)) 178.13/45.56 TRS: 178.13/45.56 a(x1) -> c(b(x1)) 178.13/45.56 b(a(x1)) -> a(c(x1)) 178.13/45.56 c(c(c(x1))) -> b(a(x1)) 178.13/45.56 graph: 178.13/45.56 b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> c#(b(x1)) 178.13/45.56 SCC Processor: 178.13/45.56 #sccs: 0 178.13/45.56 #rules: 0 178.13/45.56 #arcs: 1/4 178.13/45.56 178.13/45.56 EOF