182.96/46.76 YES 182.96/46.77 182.96/46.77 Problem: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(a(c(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 b(c(x1)) -> a(x1) 182.96/46.77 182.96/46.77 Proof: 182.96/46.77 String Reversal Processor: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 DP Processor: 182.96/46.77 DPs: 182.96/46.77 a#(a(x1)) -> b#(x1) 182.96/46.77 a#(a(x1)) -> a#(b(x1)) 182.96/46.77 a#(a(x1)) -> c#(a(b(x1))) 182.96/46.77 a#(a(x1)) -> b#(c(a(b(x1)))) 182.96/46.77 b#(x1) -> c#(x1) 182.96/46.77 c#(b(x1)) -> a#(x1) 182.96/46.77 TRS: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 TDG Processor: 182.96/46.77 DPs: 182.96/46.77 a#(a(x1)) -> b#(x1) 182.96/46.77 a#(a(x1)) -> a#(b(x1)) 182.96/46.77 a#(a(x1)) -> c#(a(b(x1))) 182.96/46.77 a#(a(x1)) -> b#(c(a(b(x1)))) 182.96/46.77 b#(x1) -> c#(x1) 182.96/46.77 c#(b(x1)) -> a#(x1) 182.96/46.77 TRS: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 graph: 182.96/46.77 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(c(a(b(x1)))) 182.96/46.77 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(a(b(x1))) 182.96/46.77 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1)) 182.96/46.77 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) 182.96/46.77 b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(x1) 182.96/46.77 a#(a(x1)) -> c#(a(b(x1))) -> c#(b(x1)) -> a#(x1) 182.96/46.77 a#(a(x1)) -> b#(c(a(b(x1)))) -> b#(x1) -> c#(x1) 182.96/46.77 a#(a(x1)) -> b#(x1) -> b#(x1) -> c#(x1) 182.96/46.77 a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(c(a(b(x1)))) 182.96/46.77 a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> c#(a(b(x1))) 182.96/46.77 a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) 182.96/46.77 a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1) 182.96/46.77 Arctic Interpretation Processor: 182.96/46.77 dimension: 2 182.96/46.77 usable rules: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 interpretation: 182.96/46.77 [c#](x0) = [-& 0 ]x0 + [0], 182.96/46.77 182.96/46.77 [b#](x0) = [-& 1 ]x0 + [0], 182.96/46.77 182.96/46.77 [a#](x0) = [0 0]x0 + [0], 182.96/46.77 182.96/46.77 [-& 1 ] [0] 182.96/46.77 [c](x0) = [-& 0 ]x0 + [0], 182.96/46.77 182.96/46.77 [0 1] [0] 182.96/46.77 [b](x0) = [0 1]x0 + [0], 182.96/46.77 182.96/46.77 [1 2] [1] 182.96/46.77 [a](x0) = [0 0]x0 + [0] 182.96/46.77 orientation: 182.96/46.77 a#(a(x1)) = [1 2]x1 + [1] >= [-& 1 ]x1 + [0] = b#(x1) 182.96/46.77 182.96/46.77 a#(a(x1)) = [1 2]x1 + [1] >= [0 1]x1 + [0] = a#(b(x1)) 182.96/46.77 182.96/46.77 a#(a(x1)) = [1 2]x1 + [1] >= [0 1]x1 + [0] = c#(a(b(x1))) 182.96/46.77 182.96/46.77 a#(a(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = b#(c(a(b(x1)))) 182.96/46.77 182.96/46.77 b#(x1) = [-& 1 ]x1 + [0] >= [-& 0 ]x1 + [0] = c#(x1) 182.96/46.77 182.96/46.77 c#(b(x1)) = [0 1]x1 + [0] >= [0 0]x1 + [0] = a#(x1) 182.96/46.77 182.96/46.77 [1 2] [1] 182.96/46.77 a(x1) = [0 0]x1 + [0] >= x1 = x1 182.96/46.77 182.96/46.77 [2 3] [2] [1 2] [1] 182.96/46.77 a(a(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = b(c(a(b(x1)))) 182.96/46.77 182.96/46.77 [0 1] [0] [-& 1 ] [0] 182.96/46.77 b(x1) = [0 1]x1 + [0] >= [-& 0 ]x1 + [0] = c(x1) 182.96/46.77 182.96/46.77 [1 2] [1] [1 2] [1] 182.96/46.77 c(b(x1)) = [0 1]x1 + [0] >= [0 0]x1 + [0] = a(x1) 182.96/46.77 problem: 182.96/46.77 DPs: 182.96/46.77 a#(a(x1)) -> b#(c(a(b(x1)))) 182.96/46.77 b#(x1) -> c#(x1) 182.96/46.77 c#(b(x1)) -> a#(x1) 182.96/46.77 TRS: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 Restore Modifier: 182.96/46.77 DPs: 182.96/46.77 a#(a(x1)) -> b#(c(a(b(x1)))) 182.96/46.77 b#(x1) -> c#(x1) 182.96/46.77 c#(b(x1)) -> a#(x1) 182.96/46.77 TRS: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 EDG Processor: 182.96/46.77 DPs: 182.96/46.77 a#(a(x1)) -> b#(c(a(b(x1)))) 182.96/46.77 b#(x1) -> c#(x1) 182.96/46.77 c#(b(x1)) -> a#(x1) 182.96/46.77 TRS: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 graph: 182.96/46.77 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(c(a(b(x1)))) 182.96/46.77 b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(x1) 182.96/46.77 a#(a(x1)) -> b#(c(a(b(x1)))) -> b#(x1) -> c#(x1) 182.96/46.77 Arctic Interpretation Processor: 182.96/46.77 dimension: 2 182.96/46.77 usable rules: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 interpretation: 182.96/46.77 [c#](x0) = [0 3]x0 + [0], 182.96/46.77 182.96/46.77 [b#](x0) = [0 3]x0 + [0], 182.96/46.77 182.96/46.77 [a#](x0) = [3 0]x0, 182.96/46.77 182.96/46.77 [-& 1 ] [0 ] 182.96/46.77 [c](x0) = [-& 0 ]x0 + [-&], 182.96/46.77 182.96/46.77 [-& 1 ] [0] 182.96/46.77 [b](x0) = [0 1 ]x0 + [0], 182.96/46.77 182.96/46.77 [1 2] [1 ] 182.96/46.77 [a](x0) = [0 0]x0 + [-&] 182.96/46.77 orientation: 182.96/46.77 a#(a(x1)) = [4 5]x1 + [4] >= [3 4]x1 + [3] = b#(c(a(b(x1)))) 182.96/46.77 182.96/46.77 b#(x1) = [0 3]x1 + [0] >= [0 3]x1 + [0] = c#(x1) 182.96/46.77 182.96/46.77 c#(b(x1)) = [3 4]x1 + [3] >= [3 0]x1 = a#(x1) 182.96/46.77 182.96/46.77 [1 2] [1 ] 182.96/46.77 a(x1) = [0 0]x1 + [-&] >= x1 = x1 182.96/46.77 182.96/46.77 [2 3] [2] [1 2] [1] 182.96/46.77 a(a(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = b(c(a(b(x1)))) 182.96/46.77 182.96/46.77 [-& 1 ] [0] [-& 1 ] [0 ] 182.96/46.77 b(x1) = [0 1 ]x1 + [0] >= [-& 0 ]x1 + [-&] = c(x1) 182.96/46.77 182.96/46.77 [1 2] [1] [1 2] [1 ] 182.96/46.77 c(b(x1)) = [0 1]x1 + [0] >= [0 0]x1 + [-&] = a(x1) 182.96/46.77 problem: 182.96/46.77 DPs: 182.96/46.77 b#(x1) -> c#(x1) 182.96/46.77 c#(b(x1)) -> a#(x1) 182.96/46.77 TRS: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 Restore Modifier: 182.96/46.77 DPs: 182.96/46.77 b#(x1) -> c#(x1) 182.96/46.77 c#(b(x1)) -> a#(x1) 182.96/46.77 TRS: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 EDG Processor: 182.96/46.77 DPs: 182.96/46.77 b#(x1) -> c#(x1) 182.96/46.77 c#(b(x1)) -> a#(x1) 182.96/46.77 TRS: 182.96/46.77 a(x1) -> x1 182.96/46.77 a(a(x1)) -> b(c(a(b(x1)))) 182.96/46.77 b(x1) -> c(x1) 182.96/46.77 c(b(x1)) -> a(x1) 182.96/46.77 graph: 182.96/46.77 b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(x1) 182.96/46.77 SCC Processor: 182.96/46.77 #sccs: 0 182.96/46.77 #rules: 0 182.96/46.77 #arcs: 1/4 182.96/46.77 182.96/46.77 EOF