182.80/46.71 YES 182.80/46.72 182.80/46.72 Problem: 182.80/46.72 a(x1) -> x1 182.80/46.72 a(a(b(x1))) -> c(c(a(c(x1)))) 182.80/46.72 c(c(x1)) -> b(a(x1)) 182.80/46.72 182.80/46.72 Proof: 182.80/46.72 String Reversal Processor: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 DP Processor: 182.80/46.72 DPs: 182.80/46.72 b#(a(a(x1))) -> c#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(c(x1)) 182.80/46.72 b#(a(a(x1))) -> a#(c(c(x1))) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 c#(c(x1)) -> b#(x1) 182.80/46.72 c#(c(x1)) -> a#(b(x1)) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 TDG Processor: 182.80/46.72 DPs: 182.80/46.72 b#(a(a(x1))) -> c#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(c(x1)) 182.80/46.72 b#(a(a(x1))) -> a#(c(c(x1))) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 c#(c(x1)) -> b#(x1) 182.80/46.72 c#(c(x1)) -> a#(b(x1)) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 graph: 182.80/46.72 c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(c(c(x1))) 182.80/46.72 c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(c(x1)) 182.80/46.72 c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(c(x1)) -> c#(c(x1)) -> a#(b(x1)) 182.80/46.72 b#(a(a(x1))) -> c#(c(x1)) -> c#(c(x1)) -> b#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> a#(b(x1)) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> b#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(x1)) 182.80/46.72 b#(a(a(x1))) -> c#(x1) -> c#(c(x1)) -> b#(x1) 182.80/46.72 SCC Processor: 182.80/46.72 #sccs: 1 182.80/46.72 #rules: 4 182.80/46.72 #arcs: 10/36 182.80/46.72 DPs: 182.80/46.72 c#(c(x1)) -> b#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(c(x1)) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 Arctic Interpretation Processor: 182.80/46.72 dimension: 2 182.80/46.72 usable rules: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 interpretation: 182.80/46.72 [c#](x0) = [0 0]x0 + [0], 182.80/46.72 182.80/46.72 [b#](x0) = [0 0]x0, 182.80/46.72 182.80/46.72 [0 0] [-&] 182.80/46.72 [c](x0) = [1 0]x0 + [0 ], 182.80/46.72 182.80/46.72 [0 0] 182.80/46.72 [b](x0) = [0 0]x0, 182.80/46.72 182.80/46.72 [0 0] [0 ] 182.80/46.72 [a](x0) = [1 1]x0 + [-&] 182.80/46.72 orientation: 182.80/46.72 c#(c(x1)) = [1 0]x1 + [0] >= [0 0]x1 = b#(x1) 182.80/46.72 182.80/46.72 b#(a(a(x1))) = [2 2]x1 + [1] >= [0 0]x1 + [0] = c#(x1) 182.80/46.72 182.80/46.72 b#(a(a(x1))) = [2 2]x1 + [1] >= [1 0]x1 + [0] = c#(c(x1)) 182.80/46.72 182.80/46.72 b#(a(a(x1))) = [2 2]x1 + [1] >= [2 2]x1 + [1] = c#(a(c(c(x1)))) 182.80/46.72 182.80/46.72 [0 0] [0 ] 182.80/46.72 a(x1) = [1 1]x1 + [-&] >= x1 = x1 182.80/46.72 182.80/46.72 [2 2] [1] [2 2] [1] 182.80/46.72 b(a(a(x1))) = [2 2]x1 + [1] >= [2 2]x1 + [1] = c(a(c(c(x1)))) 182.80/46.72 182.80/46.72 [1 0] [0] [0 0] [0 ] 182.80/46.72 c(c(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [-&] = a(b(x1)) 182.80/46.72 problem: 182.80/46.72 DPs: 182.80/46.72 c#(c(x1)) -> b#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 Restore Modifier: 182.80/46.72 DPs: 182.80/46.72 c#(c(x1)) -> b#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 EDG Processor: 182.80/46.72 DPs: 182.80/46.72 c#(c(x1)) -> b#(x1) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 graph: 182.80/46.72 c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> b#(x1) 182.80/46.72 Arctic Interpretation Processor: 182.80/46.72 dimension: 2 182.80/46.72 usable rules: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 interpretation: 182.80/46.72 [c#](x0) = [3 2]x0, 182.80/46.72 182.80/46.72 [b#](x0) = [0 2]x0, 182.80/46.72 182.80/46.72 [0 0 ] 182.80/46.72 [c](x0) = [1 -&]x0, 182.80/46.72 182.80/46.72 [0 0] 182.80/46.72 [b](x0) = [0 0]x0, 182.80/46.72 182.80/46.72 [0 0] 182.80/46.72 [a](x0) = [1 1]x0 182.80/46.72 orientation: 182.80/46.72 c#(c(x1)) = [3 3]x1 >= [0 2]x1 = b#(x1) 182.80/46.72 182.80/46.72 b#(a(a(x1))) = [4 4]x1 >= [4 4]x1 = c#(a(c(c(x1)))) 182.80/46.72 182.80/46.72 [0 0] 182.80/46.72 a(x1) = [1 1]x1 >= x1 = x1 182.80/46.72 182.80/46.72 [2 2] [2 2] 182.80/46.72 b(a(a(x1))) = [2 2]x1 >= [2 2]x1 = c(a(c(c(x1)))) 182.80/46.72 182.80/46.72 [1 0] [0 0] 182.80/46.72 c(c(x1)) = [1 1]x1 >= [1 1]x1 = a(b(x1)) 182.80/46.72 problem: 182.80/46.72 DPs: 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 Restore Modifier: 182.80/46.72 DPs: 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 EDG Processor: 182.80/46.72 DPs: 182.80/46.72 b#(a(a(x1))) -> c#(a(c(c(x1)))) 182.80/46.72 TRS: 182.80/46.72 a(x1) -> x1 182.80/46.72 b(a(a(x1))) -> c(a(c(c(x1)))) 182.80/46.72 c(c(x1)) -> a(b(x1)) 182.80/46.72 graph: 182.80/46.72 182.80/46.72 SCC Processor: 182.80/46.72 #sccs: 0 182.80/46.72 #rules: 0 182.80/46.72 #arcs: 0/1 182.80/46.72 182.80/46.72 EOF