187.07/47.74 YES 187.07/47.75 187.07/47.75 Problem: 187.07/47.75 a(x1) -> x1 187.07/47.75 a(b(x1)) -> b(c(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(c(b(a(x1)))) 187.07/47.75 187.07/47.75 Proof: 187.07/47.75 String Reversal Processor: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 DP Processor: 187.07/47.75 DPs: 187.07/47.75 b#(a(x1)) -> b#(x1) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 c#(c(x1)) -> a#(x1) 187.07/47.75 c#(c(x1)) -> c#(a(x1)) 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 c#(c(x1)) -> a#(b(c(a(x1)))) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 TDG Processor: 187.07/47.75 DPs: 187.07/47.75 b#(a(x1)) -> b#(x1) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 c#(c(x1)) -> a#(x1) 187.07/47.75 c#(c(x1)) -> c#(a(x1)) 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 c#(c(x1)) -> a#(b(c(a(x1)))) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 graph: 187.07/47.75 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(b(c(a(x1)))) 187.07/47.75 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) 187.07/47.75 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1) 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(b(x1)) 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(x1) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(b(c(a(x1)))) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(a(x1)) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1) 187.07/47.75 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 187.07/47.75 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 187.07/47.75 SCC Processor: 187.07/47.75 #sccs: 1 187.07/47.75 #rules: 4 187.07/47.75 #arcs: 12/36 187.07/47.75 DPs: 187.07/47.75 c#(c(x1)) -> c#(a(x1)) 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 b#(a(x1)) -> b#(x1) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 Arctic Interpretation Processor: 187.07/47.75 dimension: 2 187.07/47.75 usable rules: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 interpretation: 187.07/47.75 [c#](x0) = [-& 2 ]x0 + [0], 187.07/47.75 187.07/47.75 [b#](x0) = [0 2]x0 + [0], 187.07/47.75 187.07/47.75 [-& 2 ] [0] 187.07/47.75 [c](x0) = [-& 2 ]x0 + [3], 187.07/47.75 187.07/47.75 [0 0] [2] 187.07/47.75 [b](x0) = [0 0]x0 + [0], 187.07/47.75 187.07/47.75 [2 2 ] [3] 187.07/47.75 [a](x0) = [-& 0 ]x0 + [1] 187.07/47.75 orientation: 187.07/47.75 c#(c(x1)) = [-& 4 ]x1 + [5] >= [-& 2 ]x1 + [3] = c#(a(x1)) 187.07/47.75 187.07/47.75 c#(c(x1)) = [-& 4 ]x1 + [5] >= [-& 4 ]x1 + [5] = b#(c(a(x1))) 187.07/47.75 187.07/47.75 b#(a(x1)) = [2 2]x1 + [3] >= [0 2]x1 + [0] = b#(x1) 187.07/47.75 187.07/47.75 b#(a(x1)) = [2 2]x1 + [3] >= [2 2]x1 + [2] = c#(b(x1)) 187.07/47.75 187.07/47.75 [2 2 ] [3] 187.07/47.75 a(x1) = [-& 0 ]x1 + [1] >= x1 = x1 187.07/47.75 187.07/47.75 [2 2] [3] [2 2] [2] 187.07/47.75 b(a(x1)) = [2 2]x1 + [3] >= [2 2]x1 + [3] = c(b(x1)) 187.07/47.75 187.07/47.75 [0 0] [2] 187.07/47.75 b(x1) = [0 0]x1 + [0] >= x1 = x1 187.07/47.75 187.07/47.75 [-& 4 ] [5] [-& 4 ] [5] 187.07/47.75 c(c(x1)) = [-& 4 ]x1 + [5] >= [-& 2 ]x1 + [3] = a(b(c(a(x1)))) 187.07/47.75 problem: 187.07/47.75 DPs: 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 b#(a(x1)) -> b#(x1) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 Restore Modifier: 187.07/47.75 DPs: 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 b#(a(x1)) -> b#(x1) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 EDG Processor: 187.07/47.75 DPs: 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 b#(a(x1)) -> b#(x1) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 graph: 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(x1) 187.07/47.75 c#(c(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(b(x1)) 187.07/47.75 b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(c(a(x1))) 187.07/47.75 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 187.07/47.75 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 187.07/47.75 Arctic Interpretation Processor: 187.07/47.75 dimension: 2 187.07/47.75 usable rules: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 interpretation: 187.07/47.75 [c#](x0) = [-& 0 ]x0 + [0], 187.07/47.75 187.07/47.75 [b#](x0) = [0 -&]x0, 187.07/47.75 187.07/47.75 [-& 0 ] [0] 187.07/47.75 [c](x0) = [-& 2 ]x0 + [2], 187.07/47.75 187.07/47.75 [0 -&] [0] 187.07/47.75 [b](x0) = [2 0 ]x0 + [0], 187.07/47.75 187.07/47.75 [2 0 ] [0] 187.07/47.75 [a](x0) = [-& 0 ]x0 + [0] 187.07/47.75 orientation: 187.07/47.75 c#(c(x1)) = [-& 2 ]x1 + [2] >= [-& 0 ]x1 + [0] = b#(c(a(x1))) 187.07/47.75 187.07/47.75 b#(a(x1)) = [2 0]x1 + [0] >= [0 -&]x1 = b#(x1) 187.07/47.75 187.07/47.75 b#(a(x1)) = [2 0]x1 + [0] >= [2 0]x1 + [0] = c#(b(x1)) 187.07/47.75 187.07/47.75 [2 0 ] [0] 187.07/47.75 a(x1) = [-& 0 ]x1 + [0] >= x1 = x1 187.07/47.75 187.07/47.75 [2 0] [0] [2 0] [0] 187.07/47.75 b(a(x1)) = [4 2]x1 + [2] >= [4 2]x1 + [2] = c(b(x1)) 187.07/47.75 187.07/47.75 [0 -&] [0] 187.07/47.75 b(x1) = [2 0 ]x1 + [0] >= x1 = x1 187.07/47.75 187.07/47.75 [-& 2 ] [2] [-& 2 ] [2] 187.07/47.75 c(c(x1)) = [-& 4 ]x1 + [4] >= [-& 2 ]x1 + [2] = a(b(c(a(x1)))) 187.07/47.75 problem: 187.07/47.75 DPs: 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 Restore Modifier: 187.07/47.75 DPs: 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 EDG Processor: 187.07/47.75 DPs: 187.07/47.75 b#(a(x1)) -> c#(b(x1)) 187.07/47.75 TRS: 187.07/47.75 a(x1) -> x1 187.07/47.75 b(a(x1)) -> c(b(x1)) 187.07/47.75 b(x1) -> x1 187.07/47.75 c(c(x1)) -> a(b(c(a(x1)))) 187.07/47.75 graph: 187.07/47.75 187.07/47.75 SCC Processor: 187.07/47.75 #sccs: 0 187.07/47.75 #rules: 0 187.07/47.75 #arcs: 0/1 187.07/47.75 187.17/47.75 EOF