263.73/47.03 YES 263.73/47.04 263.73/47.04 Problem: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 a(c(x1)) -> c(c(a(a(b(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 263.73/47.04 Proof: 263.73/47.04 String Reversal Processor: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 DP Processor: 263.73/47.04 DPs: 263.73/47.04 a#(x1) -> b#(x1) 263.73/47.04 c#(a(x1)) -> c#(x1) 263.73/47.04 c#(a(x1)) -> c#(c(x1)) 263.73/47.04 c#(a(x1)) -> a#(c(c(x1))) 263.73/47.04 c#(a(x1)) -> a#(a(c(c(x1)))) 263.73/47.04 c#(a(x1)) -> b#(a(a(c(c(x1))))) 263.73/47.04 TRS: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 TDG Processor: 263.73/47.04 DPs: 263.73/47.04 a#(x1) -> b#(x1) 263.73/47.04 c#(a(x1)) -> c#(x1) 263.73/47.04 c#(a(x1)) -> c#(c(x1)) 263.73/47.04 c#(a(x1)) -> a#(c(c(x1))) 263.73/47.04 c#(a(x1)) -> a#(a(c(c(x1)))) 263.73/47.04 c#(a(x1)) -> b#(a(a(c(c(x1))))) 263.73/47.04 TRS: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 graph: 263.73/47.04 c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> b#(a(a(c(c(x1))))) 263.73/47.04 c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(a(c(c(x1)))) 263.73/47.04 c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(c(c(x1))) 263.73/47.04 c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) 263.73/47.04 c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(x1) 263.73/47.04 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(a(c(c(x1))))) 263.73/47.04 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(c(c(x1)))) 263.73/47.04 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(c(x1))) 263.73/47.04 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(c(x1)) 263.73/47.04 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 263.73/47.04 c#(a(x1)) -> a#(c(c(x1))) -> a#(x1) -> b#(x1) 263.73/47.04 c#(a(x1)) -> a#(a(c(c(x1)))) -> a#(x1) -> b#(x1) 263.73/47.04 SCC Processor: 263.73/47.04 #sccs: 1 263.73/47.04 #rules: 2 263.73/47.04 #arcs: 12/36 263.73/47.04 DPs: 263.73/47.04 c#(a(x1)) -> c#(c(x1)) 263.73/47.04 c#(a(x1)) -> c#(x1) 263.73/47.04 TRS: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 Arctic Interpretation Processor: 263.73/47.04 dimension: 3 263.73/47.04 usable rules: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 interpretation: 263.73/47.04 [c#](x0) = [0 1 0]x0, 263.73/47.04 263.73/47.04 [0 1 1 ] [0] 263.73/47.04 [c](x0) = [-& 0 0 ]x0 + [0] 263.73/47.04 [-& 0 0 ] [0], 263.73/47.04 263.73/47.04 [-& 0 0 ] [0] 263.73/47.04 [b](x0) = [0 -& 0 ]x0 + [0] 263.73/47.04 [0 -& 0 ] [1], 263.73/47.04 263.73/47.04 [0 0 0] [0] 263.73/47.04 [a](x0) = [0 1 1]x0 + [0] 263.73/47.04 [0 0 0] [1] 263.73/47.04 orientation: 263.73/47.04 c#(a(x1)) = [1 2 2]x1 + [1] >= [0 1 1]x1 + [1] = c#(c(x1)) 263.73/47.04 263.73/47.04 c#(a(x1)) = [1 2 2]x1 + [1] >= [0 1 0]x1 = c#(x1) 263.73/47.04 263.73/47.04 [0 0 0] [0] 263.73/47.04 a(x1) = [0 1 1]x1 + [0] >= x1 = x1 263.73/47.04 [0 0 0] [1] 263.73/47.04 263.73/47.04 [0 0 0] [0] [-& 0 0 ] [0] 263.73/47.04 a(x1) = [0 1 1]x1 + [0] >= [0 -& 0 ]x1 + [0] = b(x1) 263.73/47.04 [0 0 0] [1] [0 -& 0 ] [1] 263.73/47.04 263.73/47.04 [1 2 2] [2] [1 2 2] [2] 263.73/47.04 c(a(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = b(a(a(c(c(x1))))) 263.73/47.04 [0 1 1] [1] [0 1 1] [1] 263.73/47.04 263.73/47.04 [0 -& 0 ] [1] 263.73/47.04 b(b(x1)) = [0 0 0 ]x1 + [1] >= x1 = x1 263.73/47.04 [0 0 0 ] [1] 263.73/47.04 problem: 263.73/47.04 DPs: 263.73/47.04 c#(a(x1)) -> c#(c(x1)) 263.73/47.04 TRS: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 Restore Modifier: 263.73/47.04 DPs: 263.73/47.04 c#(a(x1)) -> c#(c(x1)) 263.73/47.04 TRS: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 EDG Processor: 263.73/47.04 DPs: 263.73/47.04 c#(a(x1)) -> c#(c(x1)) 263.73/47.04 TRS: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 graph: 263.73/47.04 c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) 263.73/47.04 Arctic Interpretation Processor: 263.73/47.04 dimension: 2 263.73/47.04 usable rules: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 interpretation: 263.73/47.04 [c#](x0) = [2 0]x0 + [0], 263.73/47.04 263.73/47.04 [0 -&] [-&] 263.73/47.04 [c](x0) = [1 0 ]x0 + [0 ], 263.73/47.04 263.73/47.04 [-& 0 ] [0] 263.73/47.04 [b](x0) = [0 0 ]x0 + [0], 263.73/47.04 263.73/47.04 [1 0] [0] 263.73/47.04 [a](x0) = [0 0]x0 + [0] 263.73/47.04 orientation: 263.73/47.04 c#(a(x1)) = [3 2]x1 + [2] >= [2 0]x1 + [0] = c#(c(x1)) 263.73/47.04 263.73/47.04 [1 0] [0] 263.73/47.04 a(x1) = [0 0]x1 + [0] >= x1 = x1 263.73/47.04 263.73/47.04 [1 0] [0] [-& 0 ] [0] 263.73/47.04 a(x1) = [0 0]x1 + [0] >= [0 0 ]x1 + [0] = b(x1) 263.73/47.04 263.73/47.04 [1 0] [0] [1 0] [0] 263.73/47.04 c(a(x1)) = [2 1]x1 + [1] >= [2 1]x1 + [1] = b(a(a(c(c(x1))))) 263.73/47.04 263.73/47.04 [0 0] [0] 263.73/47.04 b(b(x1)) = [0 0]x1 + [0] >= x1 = x1 263.73/47.04 problem: 263.73/47.04 DPs: 263.73/47.04 263.73/47.04 TRS: 263.73/47.04 a(x1) -> x1 263.73/47.04 a(x1) -> b(x1) 263.73/47.04 c(a(x1)) -> b(a(a(c(c(x1))))) 263.73/47.04 b(b(x1)) -> x1 263.73/47.04 Qed 263.73/47.04 EOF