181.96/46.48 YES 182.04/46.49 182.04/46.49 Problem: 182.04/46.49 a(x1) -> x1 182.04/46.49 a(b(b(x1))) -> b(b(b(c(a(a(x1)))))) 182.04/46.49 b(c(x1)) -> x1 182.04/46.49 182.04/46.49 Proof: 182.04/46.49 String Reversal Processor: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 DP Processor: 182.04/46.49 DPs: 182.04/46.49 b#(b(a(x1))) -> b#(x1) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) 182.04/46.49 b#(b(a(x1))) -> c#(b(b(b(x1)))) 182.04/46.49 b#(b(a(x1))) -> a#(c(b(b(b(x1))))) 182.04/46.49 b#(b(a(x1))) -> a#(a(c(b(b(b(x1)))))) 182.04/46.49 TRS: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 TDG Processor: 182.04/46.49 DPs: 182.04/46.49 b#(b(a(x1))) -> b#(x1) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) 182.04/46.49 b#(b(a(x1))) -> c#(b(b(b(x1)))) 182.04/46.49 b#(b(a(x1))) -> a#(c(b(b(b(x1))))) 182.04/46.49 b#(b(a(x1))) -> a#(a(c(b(b(b(x1)))))) 182.04/46.49 TRS: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 graph: 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) -> 182.04/46.49 b#(b(a(x1))) -> a#(a(c(b(b(b(x1)))))) 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> a#(c(b(b(b(x1))))) 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> c#(b(b(b(x1)))) 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(b(b(x1))) 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(x1) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(a(c(b(b(b(x1)))))) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(c(b(b(b(x1))))) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> c#(b(b(b(x1)))) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(b(x1))) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1) 182.04/46.49 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(a(c(b(b(b(x1)))))) 182.04/46.49 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(c(b(b(b(x1))))) 182.04/46.49 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> c#(b(b(b(x1)))) 182.04/46.49 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(b(x1))) 182.04/46.49 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1) 182.04/46.49 SCC Processor: 182.04/46.49 #sccs: 1 182.04/46.49 #rules: 3 182.04/46.49 #arcs: 18/36 182.04/46.49 DPs: 182.04/46.49 b#(b(a(x1))) -> b#(b(b(x1))) 182.04/46.49 b#(b(a(x1))) -> b#(x1) 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 TRS: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 Arctic Interpretation Processor: 182.04/46.49 dimension: 2 182.04/46.49 usable rules: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 interpretation: 182.04/46.49 [b#](x0) = [1 0]x0 + [0], 182.04/46.49 182.04/46.49 [-& 0 ] [0] 182.04/46.49 [c](x0) = [0 0 ]x0 + [3], 182.04/46.49 182.04/46.49 [-& 0 ] [2] 182.04/46.49 [b](x0) = [0 -&]x0 + [0], 182.04/46.49 182.04/46.49 [0 -&] [0] 182.04/46.49 [a](x0) = [1 0 ]x0 + [3] 182.04/46.49 orientation: 182.04/46.49 b#(b(a(x1))) = [2 1]x1 + [4] >= [1 0]x1 + [3] = b#(b(b(x1))) 182.04/46.49 182.04/46.49 b#(b(a(x1))) = [2 1]x1 + [4] >= [1 0]x1 + [0] = b#(x1) 182.04/46.49 182.04/46.49 b#(b(a(x1))) = [2 1]x1 + [4] >= [0 1]x1 + [3] = b#(b(x1)) 182.04/46.49 182.04/46.49 [0 -&] [0] 182.04/46.49 a(x1) = [1 0 ]x1 + [3] >= x1 = x1 182.04/46.49 182.04/46.49 [0 -&] [2] [0 -&] [2] 182.04/46.49 b(b(a(x1))) = [1 0 ]x1 + [3] >= [1 0 ]x1 + [3] = a(a(c(b(b(b(x1)))))) 182.04/46.49 182.04/46.49 [0 -&] [0] 182.04/46.49 c(b(x1)) = [0 0 ]x1 + [3] >= x1 = x1 182.04/46.49 problem: 182.04/46.49 DPs: 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 TRS: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 Restore Modifier: 182.04/46.49 DPs: 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 TRS: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 EDG Processor: 182.04/46.49 DPs: 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 TRS: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 graph: 182.04/46.49 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1)) 182.04/46.49 Matrix Interpretation Processor: dim=1 182.04/46.49 182.04/46.49 usable rules: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 interpretation: 182.04/46.49 [b#](x0) = 2x0, 182.04/46.49 182.04/46.49 [c](x0) = 1/2x0 + 1, 182.04/46.49 182.04/46.49 [b](x0) = 2x0, 182.04/46.49 182.04/46.49 [a](x0) = x0 + 1/2 182.04/46.49 orientation: 182.04/46.49 b#(b(a(x1))) = 4x1 + 2 >= 4x1 = b#(b(x1)) 182.04/46.49 182.04/46.49 a(x1) = x1 + 1/2 >= x1 = x1 182.04/46.49 182.04/46.49 b(b(a(x1))) = 4x1 + 2 >= 4x1 + 2 = a(a(c(b(b(b(x1)))))) 182.04/46.49 182.04/46.49 c(b(x1)) = x1 + 1 >= x1 = x1 182.04/46.49 problem: 182.04/46.49 DPs: 182.04/46.49 182.04/46.49 TRS: 182.04/46.49 a(x1) -> x1 182.04/46.49 b(b(a(x1))) -> a(a(c(b(b(b(x1)))))) 182.04/46.49 c(b(x1)) -> x1 182.04/46.49 Qed 182.04/46.49 EOF