179.83/45.94 YES 179.83/45.95 179.83/45.95 Problem: 179.83/45.95 a(x1) -> x1 179.83/45.95 a(b(x1)) -> b(a(c(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> b(b(a(x1))) 179.83/45.95 179.83/45.95 Proof: 179.83/45.95 String Reversal Processor: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 DP Processor: 179.83/45.95 DPs: 179.83/45.95 b#(a(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> a#(b(x1)) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 c#(c(x1)) -> b#(x1) 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 c#(c(x1)) -> a#(b(b(x1))) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 TDG Processor: 179.83/45.95 DPs: 179.83/45.95 b#(a(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> a#(b(x1)) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 c#(c(x1)) -> b#(x1) 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 c#(c(x1)) -> a#(b(b(x1))) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 graph: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 c#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(x1)) 179.83/45.95 c#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1) 179.83/45.95 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 179.83/45.95 c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(b(b(x1))) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> b#(b(x1)) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 179.83/45.95 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 179.83/45.95 SCC Processor: 179.83/45.95 #sccs: 1 179.83/45.95 #rules: 4 179.83/45.95 #arcs: 12/36 179.83/45.95 DPs: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 b#(a(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 c#(c(x1)) -> b#(x1) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 Arctic Interpretation Processor: 179.83/45.95 dimension: 2 179.83/45.95 usable rules: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 interpretation: 179.83/45.95 [c#](x0) = [-& 0 ]x0 + [0], 179.83/45.95 179.83/45.95 [b#](x0) = [-& 0 ]x0 + [2], 179.83/45.95 179.83/45.95 [-& 1 ] [0] 179.83/45.95 [c](x0) = [0 1 ]x0 + [3], 179.83/45.95 179.83/45.95 [0 0] [-&] 179.83/45.95 [b](x0) = [0 0]x0 + [2 ], 179.83/45.95 179.83/45.95 [1 1] [3] 179.83/45.95 [a](x0) = [0 0]x0 + [0] 179.83/45.95 orientation: 179.83/45.95 c#(c(x1)) = [0 1]x1 + [3] >= [0 0]x1 + [2] = b#(b(x1)) 179.83/45.95 179.83/45.95 b#(a(x1)) = [0 0]x1 + [2] >= [-& 0 ]x1 + [2] = b#(x1) 179.83/45.95 179.83/45.95 b#(a(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [2] = c#(a(b(x1))) 179.83/45.95 179.83/45.95 c#(c(x1)) = [0 1]x1 + [3] >= [-& 0 ]x1 + [2] = b#(x1) 179.83/45.95 179.83/45.95 [1 1] [3] 179.83/45.95 a(x1) = [0 0]x1 + [0] >= x1 = x1 179.83/45.95 179.83/45.95 [1 1] [3] [1 1] [3] 179.83/45.95 b(a(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = c(a(b(x1))) 179.83/45.95 179.83/45.95 [0 0] [-&] 179.83/45.95 b(x1) = [0 0]x1 + [2 ] >= x1 = x1 179.83/45.95 179.83/45.95 [1 2] [4] [1 1] [3] 179.83/45.95 c(c(x1)) = [1 2]x1 + [4] >= [0 0]x1 + [2] = a(b(b(x1))) 179.83/45.95 problem: 179.83/45.95 DPs: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 b#(a(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 Restore Modifier: 179.83/45.95 DPs: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 b#(a(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 EDG Processor: 179.83/45.95 DPs: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 b#(a(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 graph: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1) 179.83/45.95 c#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> b#(b(x1)) 179.83/45.95 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 179.83/45.95 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 179.83/45.95 Arctic Interpretation Processor: 179.83/45.95 dimension: 2 179.83/45.95 usable rules: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 interpretation: 179.83/45.95 [c#](x0) = [2 1]x0 + [0], 179.83/45.95 179.83/45.95 [b#](x0) = [0 2]x0 + [0], 179.83/45.95 179.83/45.95 [-& 0 ] [0] 179.83/45.95 [c](x0) = [1 0 ]x0 + [0], 179.83/45.95 179.83/45.95 [0 0] [0] 179.83/45.95 [b](x0) = [0 0]x0 + [0], 179.83/45.95 179.83/45.95 [0 0] [0] 179.83/45.95 [a](x0) = [1 1]x0 + [1] 179.83/45.95 orientation: 179.83/45.95 c#(c(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = b#(b(x1)) 179.83/45.95 179.83/45.95 b#(a(x1)) = [3 3]x1 + [3] >= [0 2]x1 + [0] = b#(x1) 179.83/45.95 179.83/45.95 b#(a(x1)) = [3 3]x1 + [3] >= [2 2]x1 + [2] = c#(a(b(x1))) 179.83/45.95 179.83/45.95 [0 0] [0] 179.83/45.95 a(x1) = [1 1]x1 + [1] >= x1 = x1 179.83/45.95 179.83/45.95 [1 1] [1] [1 1] [1] 179.83/45.95 b(a(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = c(a(b(x1))) 179.83/45.95 179.83/45.95 [0 0] [0] 179.83/45.95 b(x1) = [0 0]x1 + [0] >= x1 = x1 179.83/45.95 179.83/45.95 [1 0] [0] [0 0] [0] 179.83/45.95 c(c(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(b(b(x1))) 179.83/45.95 problem: 179.83/45.95 DPs: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 Restore Modifier: 179.83/45.95 DPs: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 EDG Processor: 179.83/45.95 DPs: 179.83/45.95 c#(c(x1)) -> b#(b(x1)) 179.83/45.95 TRS: 179.83/45.95 a(x1) -> x1 179.83/45.95 b(a(x1)) -> c(a(b(x1))) 179.83/45.95 b(x1) -> x1 179.83/45.95 c(c(x1)) -> a(b(b(x1))) 179.83/45.95 graph: 179.83/45.95 179.83/45.95 SCC Processor: 179.83/45.95 #sccs: 0 179.83/45.95 #rules: 0 179.83/45.95 #arcs: 0/1 179.83/45.95 179.83/45.96 EOF