179.03/45.78 YES 179.03/45.79 179.03/45.79 Problem: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 a(b(x1)) -> b(a(c(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 179.03/45.79 Proof: 179.03/45.79 String Reversal Processor: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 DP Processor: 179.03/45.79 DPs: 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 b#(a(x1)) -> b#(x1) 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 c#(c(x1)) -> a#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 TDG Processor: 179.03/45.79 DPs: 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 b#(a(x1)) -> b#(x1) 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 c#(c(x1)) -> a#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 graph: 179.03/45.79 c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1) 179.03/45.79 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(x1) 179.03/45.79 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 179.03/45.79 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 179.03/45.79 b#(a(x1)) -> a#(b(x1)) -> a#(x1) -> b#(x1) 179.03/45.79 a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 179.03/45.79 a#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1) 179.03/45.79 Arctic Interpretation Processor: 179.03/45.79 dimension: 2 179.03/45.79 usable rules: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 interpretation: 179.03/45.79 [c#](x0) = [-& 0 ]x0 + [0], 179.03/45.79 179.03/45.79 [b#](x0) = [0 0]x0, 179.03/45.79 179.03/45.79 [a#](x0) = [0 0]x0, 179.03/45.79 179.03/45.79 [0 0] [-&] 179.03/45.79 [c](x0) = [1 1]x0 + [0 ], 179.03/45.79 179.03/45.79 [0 -&] [-&] 179.03/45.79 [b](x0) = [1 0 ]x0 + [0 ], 179.03/45.79 179.03/45.79 [1 0] [0] 179.03/45.79 [a](x0) = [1 0]x0 + [0] 179.03/45.79 orientation: 179.03/45.79 a#(x1) = [0 0]x1 >= [0 0]x1 = b#(x1) 179.03/45.79 179.03/45.79 b#(a(x1)) = [1 0]x1 + [0] >= [0 0]x1 = b#(x1) 179.03/45.79 179.03/45.79 b#(a(x1)) = [1 0]x1 + [0] >= [1 0]x1 + [0] = a#(b(x1)) 179.03/45.79 179.03/45.79 b#(a(x1)) = [1 0]x1 + [0] >= [1 0]x1 + [0] = c#(a(b(x1))) 179.03/45.79 179.03/45.79 c#(c(x1)) = [1 1]x1 + [0] >= [0 0]x1 = a#(x1) 179.03/45.79 179.03/45.79 [1 0] [0] 179.03/45.79 a(x1) = [1 0]x1 + [0] >= x1 = x1 179.03/45.79 179.03/45.79 [1 0] [0] [0 -&] [-&] 179.03/45.79 a(x1) = [1 0]x1 + [0] >= [1 0 ]x1 + [0 ] = b(x1) 179.03/45.79 179.03/45.79 [1 0] [0] [1 0] [0] 179.03/45.79 b(a(x1)) = [2 1]x1 + [1] >= [2 1]x1 + [1] = c(a(b(x1))) 179.03/45.79 179.03/45.79 [0 -&] [-&] 179.03/45.79 b(x1) = [1 0 ]x1 + [0 ] >= x1 = x1 179.03/45.79 179.03/45.79 [1 1] [0] [1 0] [0] 179.03/45.79 c(c(x1)) = [2 2]x1 + [1] >= [1 0]x1 + [0] = a(x1) 179.03/45.79 problem: 179.03/45.79 DPs: 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 b#(a(x1)) -> b#(x1) 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 Restore Modifier: 179.03/45.79 DPs: 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 b#(a(x1)) -> b#(x1) 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 EDG Processor: 179.03/45.79 DPs: 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 b#(a(x1)) -> b#(x1) 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 graph: 179.03/45.79 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 179.03/45.79 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 179.03/45.79 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 b#(a(x1)) -> a#(b(x1)) -> a#(x1) -> b#(x1) 179.03/45.79 a#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1) 179.03/45.79 a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 179.03/45.79 a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 179.03/45.79 SCC Processor: 179.03/45.79 #sccs: 1 179.03/45.79 #rules: 3 179.03/45.79 #arcs: 7/16 179.03/45.79 DPs: 179.03/45.79 b#(a(x1)) -> b#(x1) 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 Arctic Interpretation Processor: 179.03/45.79 dimension: 2 179.03/45.79 usable rules: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 interpretation: 179.03/45.79 [b#](x0) = [0 1]x0 + [0], 179.03/45.79 179.03/45.79 [a#](x0) = [0 1]x0 + [3], 179.03/45.79 179.03/45.79 [1 1] [0] 179.03/45.79 [c](x0) = [0 0]x0 + [2], 179.03/45.79 179.03/45.79 [0 1 ] [0] 179.03/45.79 [b](x0) = [-& 0 ]x0 + [1], 179.03/45.79 179.03/45.79 [0 1] [0] 179.03/45.79 [a](x0) = [0 1]x0 + [2] 179.03/45.79 orientation: 179.03/45.79 b#(a(x1)) = [1 2]x1 + [3] >= [0 1]x1 + [0] = b#(x1) 179.03/45.79 179.03/45.79 b#(a(x1)) = [1 2]x1 + [3] >= [0 1]x1 + [3] = a#(b(x1)) 179.03/45.79 179.03/45.79 a#(x1) = [0 1]x1 + [3] >= [0 1]x1 + [0] = b#(x1) 179.03/45.79 179.03/45.79 [0 1] [0] 179.03/45.79 a(x1) = [0 1]x1 + [2] >= x1 = x1 179.03/45.79 179.03/45.79 [0 1] [0] [0 1 ] [0] 179.03/45.79 a(x1) = [0 1]x1 + [2] >= [-& 0 ]x1 + [1] = b(x1) 179.03/45.79 179.03/45.79 [1 2] [3] [1 2] [3] 179.03/45.79 b(a(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = c(a(b(x1))) 179.03/45.79 179.03/45.79 [0 1 ] [0] 179.03/45.79 b(x1) = [-& 0 ]x1 + [1] >= x1 = x1 179.03/45.79 179.03/45.79 [2 2] [3] [0 1] [0] 179.03/45.79 c(c(x1)) = [1 1]x1 + [2] >= [0 1]x1 + [2] = a(x1) 179.03/45.79 problem: 179.03/45.79 DPs: 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 Restore Modifier: 179.03/45.79 DPs: 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 EDG Processor: 179.03/45.79 DPs: 179.03/45.79 b#(a(x1)) -> a#(b(x1)) 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 graph: 179.03/45.79 b#(a(x1)) -> a#(b(x1)) -> a#(x1) -> b#(x1) 179.03/45.79 a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 179.03/45.79 Arctic Interpretation Processor: 179.03/45.79 dimension: 2 179.03/45.79 usable rules: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 interpretation: 179.03/45.79 [b#](x0) = [0 0]x0, 179.03/45.79 179.03/45.79 [a#](x0) = [0 0]x0, 179.03/45.79 179.03/45.79 [-& 0 ] [0 ] 179.03/45.79 [c](x0) = [2 0 ]x0 + [-&], 179.03/45.79 179.03/45.79 [0 0] 179.03/45.79 [b](x0) = [0 0]x0, 179.03/45.79 179.03/45.79 [0 0] [-&] 179.03/45.79 [a](x0) = [2 2]x0 + [0 ] 179.03/45.79 orientation: 179.03/45.79 b#(a(x1)) = [2 2]x1 + [0] >= [0 0]x1 = a#(b(x1)) 179.03/45.79 179.03/45.79 a#(x1) = [0 0]x1 >= [0 0]x1 = b#(x1) 179.03/45.79 179.03/45.79 [0 0] [-&] 179.03/45.79 a(x1) = [2 2]x1 + [0 ] >= x1 = x1 179.03/45.79 179.03/45.79 [0 0] [-&] [0 0] 179.03/45.79 a(x1) = [2 2]x1 + [0 ] >= [0 0]x1 = b(x1) 179.03/45.79 179.03/45.79 [2 2] [0] [2 2] [0] 179.03/45.79 b(a(x1)) = [2 2]x1 + [0] >= [2 2]x1 + [0] = c(a(b(x1))) 179.03/45.79 179.03/45.79 [0 0] 179.03/45.79 b(x1) = [0 0]x1 >= x1 = x1 179.03/45.79 179.03/45.79 [2 0] [0] [0 0] [-&] 179.03/45.79 c(c(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [0 ] = a(x1) 179.03/45.79 problem: 179.03/45.79 DPs: 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 Restore Modifier: 179.03/45.79 DPs: 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 EDG Processor: 179.03/45.79 DPs: 179.03/45.79 a#(x1) -> b#(x1) 179.03/45.79 TRS: 179.03/45.79 a(x1) -> x1 179.03/45.79 a(x1) -> b(x1) 179.03/45.79 b(a(x1)) -> c(a(b(x1))) 179.03/45.79 b(x1) -> x1 179.03/45.79 c(c(x1)) -> a(x1) 179.03/45.79 graph: 179.03/45.79 179.03/45.79 SCC Processor: 179.03/45.79 #sccs: 0 179.03/45.79 #rules: 0 179.03/45.79 #arcs: 0/1 179.03/45.79 179.03/45.80 EOF