178.90/45.75 YES 179.24/45.75 179.24/45.75 Problem: 179.24/45.75 a(b(x1)) -> x1 179.24/45.75 b(c(x1)) -> a(a(x1)) 179.24/45.75 c(a(x1)) -> b(b(c(c(x1)))) 179.24/45.75 179.24/45.75 Proof: 179.24/45.75 String Reversal Processor: 179.24/45.75 b(a(x1)) -> x1 179.24/45.75 c(b(x1)) -> a(a(x1)) 179.24/45.75 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.75 DP Processor: 179.24/45.75 DPs: 179.24/45.75 c#(b(x1)) -> a#(x1) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) 179.24/45.75 a#(c(x1)) -> b#(x1) 179.24/45.75 a#(c(x1)) -> b#(b(x1)) 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 a#(c(x1)) -> c#(c(b(b(x1)))) 179.24/45.75 TRS: 179.24/45.75 b(a(x1)) -> x1 179.24/45.75 c(b(x1)) -> a(a(x1)) 179.24/45.75 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.75 TDG Processor: 179.24/45.75 DPs: 179.24/45.75 c#(b(x1)) -> a#(x1) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) 179.24/45.75 a#(c(x1)) -> b#(x1) 179.24/45.75 a#(c(x1)) -> b#(b(x1)) 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 a#(c(x1)) -> c#(c(b(b(x1)))) 179.24/45.75 TRS: 179.24/45.75 b(a(x1)) -> x1 179.24/45.75 c(b(x1)) -> a(a(x1)) 179.24/45.75 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.75 graph: 179.24/45.75 a#(c(x1)) -> c#(c(b(b(x1)))) -> c#(b(x1)) -> a#(a(x1)) 179.24/45.75 a#(c(x1)) -> c#(c(b(b(x1)))) -> c#(b(x1)) -> a#(x1) 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(a(x1)) 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(c(b(b(x1)))) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1)) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1) 179.24/45.75 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(b(b(x1)))) 179.24/45.75 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1)) 179.24/45.75 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1) 179.24/45.75 EDG Processor: 179.24/45.75 DPs: 179.24/45.75 c#(b(x1)) -> a#(x1) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) 179.24/45.75 a#(c(x1)) -> b#(x1) 179.24/45.75 a#(c(x1)) -> b#(b(x1)) 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 a#(c(x1)) -> c#(c(b(b(x1)))) 179.24/45.75 TRS: 179.24/45.75 b(a(x1)) -> x1 179.24/45.75 c(b(x1)) -> a(a(x1)) 179.24/45.75 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.75 graph: 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1) 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(a(x1)) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1)) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(c(b(b(x1)))) 179.24/45.75 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1) 179.24/45.75 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1)) 179.24/45.75 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(b(b(x1)))) 179.24/45.75 SCC Processor: 179.24/45.75 #sccs: 1 179.24/45.75 #rules: 3 179.24/45.75 #arcs: 10/36 179.24/45.75 DPs: 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 c#(b(x1)) -> a#(a(x1)) 179.24/45.75 c#(b(x1)) -> a#(x1) 179.24/45.75 TRS: 179.24/45.75 b(a(x1)) -> x1 179.24/45.75 c(b(x1)) -> a(a(x1)) 179.24/45.75 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.75 Arctic Interpretation Processor: 179.24/45.75 dimension: 2 179.24/45.75 usable rules: 179.24/45.75 b(a(x1)) -> x1 179.24/45.75 c(b(x1)) -> a(a(x1)) 179.24/45.75 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.75 interpretation: 179.24/45.75 [a#](x0) = [0 1]x0 + [0], 179.24/45.75 179.24/45.75 [c#](x0) = [1 2]x0 + [3], 179.24/45.75 179.24/45.75 [1 2] [3] 179.24/45.75 [c](x0) = [0 1]x0 + [2], 179.24/45.75 179.24/45.75 [1 0 ] [2 ] 179.24/45.75 [a](x0) = [0 -&]x0 + [-&], 179.24/45.75 179.24/45.75 [-& 0 ] [0] 179.24/45.75 [b](x0) = [0 -&]x0 + [0] 179.24/45.75 orientation: 179.24/45.75 a#(c(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = c#(b(b(x1))) 179.24/45.75 179.24/45.75 c#(b(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = a#(a(x1)) 179.24/45.75 179.24/45.75 c#(b(x1)) = [2 1]x1 + [3] >= [0 1]x1 + [0] = a#(x1) 179.24/45.75 179.24/45.75 [0 -&] [0] 179.24/45.75 b(a(x1)) = [1 0 ]x1 + [2] >= x1 = x1 179.24/45.75 179.24/45.75 [2 1] [3] [2 1] [3] 179.24/45.75 c(b(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = a(a(x1)) 179.24/45.75 179.24/45.75 [2 3] [4] [2 3] [4] 179.24/45.75 a(c(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = c(c(b(b(x1)))) 179.24/45.75 problem: 179.24/45.75 DPs: 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 c#(b(x1)) -> a#(x1) 179.24/45.75 TRS: 179.24/45.75 b(a(x1)) -> x1 179.24/45.75 c(b(x1)) -> a(a(x1)) 179.24/45.75 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.75 Restore Modifier: 179.24/45.75 DPs: 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) 179.24/45.75 c#(b(x1)) -> a#(x1) 179.24/45.75 TRS: 179.24/45.75 b(a(x1)) -> x1 179.24/45.75 c(b(x1)) -> a(a(x1)) 179.24/45.75 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.75 EDG Processor: 179.24/45.75 DPs: 179.24/45.75 a#(c(x1)) -> c#(b(b(x1))) 179.24/45.76 c#(b(x1)) -> a#(x1) 179.24/45.76 TRS: 179.24/45.76 b(a(x1)) -> x1 179.24/45.76 c(b(x1)) -> a(a(x1)) 179.24/45.76 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.76 graph: 179.24/45.76 a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1) 179.24/45.76 c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1))) 179.24/45.76 Usable Rule Processor: 179.24/45.76 DPs: 179.24/45.76 a#(c(x1)) -> c#(b(b(x1))) 179.24/45.76 c#(b(x1)) -> a#(x1) 179.24/45.76 TRS: 179.24/45.76 b(a(x1)) -> x1 179.24/45.76 Arctic Interpretation Processor: 179.24/45.76 dimension: 1 179.24/45.76 usable rules: 179.24/45.76 b(a(x1)) -> x1 179.24/45.76 interpretation: 179.24/45.76 [a#](x0) = 10x0, 179.24/45.76 179.24/45.76 [c#](x0) = x0 + 7, 179.24/45.76 179.24/45.76 [c](x0) = 11x0 + 7, 179.24/45.76 179.24/45.76 [a](x0) = 10x0 + 12, 179.24/45.76 179.24/45.76 [b](x0) = 10x0 + 6 179.24/45.76 orientation: 179.24/45.76 a#(c(x1)) = 21x1 + 17 >= 20x1 + 16 = c#(b(b(x1))) 179.24/45.76 179.24/45.76 c#(b(x1)) = 10x1 + 7 >= 10x1 = a#(x1) 179.24/45.76 179.24/45.76 b(a(x1)) = 20x1 + 22 >= x1 = x1 179.24/45.76 problem: 179.24/45.76 DPs: 179.24/45.76 c#(b(x1)) -> a#(x1) 179.24/45.76 TRS: 179.24/45.76 b(a(x1)) -> x1 179.24/45.76 Restore Modifier: 179.24/45.76 DPs: 179.24/45.76 c#(b(x1)) -> a#(x1) 179.24/45.76 TRS: 179.24/45.76 b(a(x1)) -> x1 179.24/45.76 c(b(x1)) -> a(a(x1)) 179.24/45.76 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.76 EDG Processor: 179.24/45.76 DPs: 179.24/45.76 c#(b(x1)) -> a#(x1) 179.24/45.76 TRS: 179.24/45.76 b(a(x1)) -> x1 179.24/45.76 c(b(x1)) -> a(a(x1)) 179.24/45.76 a(c(x1)) -> c(c(b(b(x1)))) 179.24/45.76 graph: 179.24/45.76 179.24/45.76 SCC Processor: 179.24/45.76 #sccs: 0 179.24/45.76 #rules: 0 179.24/45.76 #arcs: 0/1 179.24/45.76 179.24/45.76 EOF