185.54/47.41 YES 185.71/47.42 185.71/47.42 Problem: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(b(c(a(x1)))) 185.71/47.42 c(b(x1)) -> a(b(a(x1))) 185.71/47.42 185.71/47.42 Proof: 185.71/47.42 String Reversal Processor: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 DP Processor: 185.71/47.42 DPs: 185.71/47.42 a#(a(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> a#(c(b(a(x1)))) 185.71/47.42 b#(c(x1)) -> a#(x1) 185.71/47.42 b#(c(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> a#(b(a(x1))) 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 TDG Processor: 185.71/47.42 DPs: 185.71/47.42 a#(a(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> a#(c(b(a(x1)))) 185.71/47.42 b#(c(x1)) -> a#(x1) 185.71/47.42 b#(c(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> a#(b(a(x1))) 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 graph: 185.71/47.42 b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(a(x1))) 185.71/47.42 b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) 185.71/47.42 b#(c(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(c(b(a(x1)))) 185.71/47.42 b#(c(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(a(x1)))) 185.71/47.42 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(a(x1))) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) 185.71/47.42 a#(a(x1)) -> a#(c(b(a(x1)))) -> a#(a(x1)) -> a#(c(b(a(x1)))) 185.71/47.42 a#(a(x1)) -> a#(c(b(a(x1)))) -> a#(a(x1)) -> b#(a(x1)) 185.71/47.42 EDG Processor: 185.71/47.42 DPs: 185.71/47.42 a#(a(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> a#(c(b(a(x1)))) 185.71/47.42 b#(c(x1)) -> a#(x1) 185.71/47.42 b#(c(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> a#(b(a(x1))) 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 graph: 185.71/47.42 b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) 185.71/47.42 b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(a(x1))) 185.71/47.42 b#(c(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(c(b(a(x1)))) 185.71/47.42 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(a(x1)))) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(a(x1))) 185.71/47.42 SCC Processor: 185.71/47.42 #sccs: 1 185.71/47.42 #rules: 4 185.71/47.42 #arcs: 10/25 185.71/47.42 DPs: 185.71/47.42 b#(c(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> a#(b(a(x1))) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) 185.71/47.42 b#(c(x1)) -> a#(x1) 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 Arctic Interpretation Processor: 185.71/47.42 dimension: 2 185.71/47.42 usable rules: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 interpretation: 185.71/47.42 [b#](x0) = [1 1]x0 + [0], 185.71/47.42 185.71/47.42 [a#](x0) = [0 1]x0, 185.71/47.42 185.71/47.42 [0 -&] [2] 185.71/47.42 [b](x0) = [0 -&]x0 + [2], 185.71/47.42 185.71/47.42 [1 1] [3] 185.71/47.42 [c](x0) = [1 0]x0 + [0], 185.71/47.42 185.71/47.42 [0 0] [0] 185.71/47.42 [a](x0) = [1 1]x0 + [3] 185.71/47.42 orientation: 185.71/47.42 b#(c(x1)) = [2 2]x1 + [4] >= [2 2]x1 + [4] = b#(a(x1)) 185.71/47.42 185.71/47.42 b#(c(x1)) = [2 2]x1 + [4] >= [1 1]x1 + [3] = a#(b(a(x1))) 185.71/47.42 185.71/47.42 a#(a(x1)) = [2 2]x1 + [4] >= [2 2]x1 + [4] = b#(a(x1)) 185.71/47.42 185.71/47.42 b#(c(x1)) = [2 2]x1 + [4] >= [0 1]x1 = a#(x1) 185.71/47.42 185.71/47.42 [0 0] [0] 185.71/47.42 a(x1) = [1 1]x1 + [3] >= x1 = x1 185.71/47.42 185.71/47.42 [1 1] [3] [1 1] [3] 185.71/47.42 a(a(x1)) = [2 2]x1 + [4] >= [2 2]x1 + [4] = a(c(b(a(x1)))) 185.71/47.42 185.71/47.42 [1 1] [3] [0 0] [2] 185.71/47.42 b(c(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = a(b(a(x1))) 185.71/47.42 problem: 185.71/47.42 DPs: 185.71/47.42 b#(c(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 Restore Modifier: 185.71/47.42 DPs: 185.71/47.42 b#(c(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 EDG Processor: 185.71/47.42 DPs: 185.71/47.42 b#(c(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 graph: 185.71/47.42 b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) 185.71/47.42 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) 185.71/47.42 SCC Processor: 185.71/47.42 #sccs: 1 185.71/47.42 #rules: 1 185.71/47.42 #arcs: 2/4 185.71/47.42 DPs: 185.71/47.42 b#(c(x1)) -> b#(a(x1)) 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 Arctic Interpretation Processor: 185.71/47.42 dimension: 3 185.71/47.42 usable rules: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 interpretation: 185.71/47.42 [b#](x0) = [0 1 0]x0 + [0], 185.71/47.42 185.71/47.42 [0 1 0 ] [0] 185.71/47.42 [b](x0) = [-& 0 -&]x0 + [0] 185.71/47.42 [-& 0 -&] [0], 185.71/47.42 185.71/47.42 [1 0 0] [0] 185.71/47.42 [c](x0) = [0 1 1]x0 + [1] 185.71/47.42 [0 0 0] [0], 185.71/47.42 185.71/47.42 [0 0 1 ] [0] 185.71/47.42 [a](x0) = [-& 0 0 ]x0 + [0] 185.71/47.42 [0 1 1 ] [1] 185.71/47.42 orientation: 185.71/47.42 b#(c(x1)) = [1 2 2]x1 + [2] >= [0 1 1]x1 + [1] = b#(a(x1)) 185.71/47.42 185.71/47.42 [0 0 1 ] [0] 185.71/47.42 a(x1) = [-& 0 0 ]x1 + [0] >= x1 = x1 185.71/47.42 [0 1 1 ] [1] 185.71/47.42 185.71/47.42 [1 2 2] [2] [1 2 2] [2] 185.71/47.42 a(a(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = a(c(b(a(x1)))) 185.71/47.42 [1 2 2] [2] [1 2 2] [2] 185.71/47.42 185.71/47.42 [1 2 2] [2] [0 1 1 ] [1] 185.71/47.42 b(c(x1)) = [0 1 1]x1 + [1] >= [-& 0 0 ]x1 + [0] = a(b(a(x1))) 185.71/47.42 [0 1 1] [1] [0 1 1 ] [1] 185.71/47.42 problem: 185.71/47.42 DPs: 185.71/47.42 185.71/47.42 TRS: 185.71/47.42 a(x1) -> x1 185.71/47.42 a(a(x1)) -> a(c(b(a(x1)))) 185.71/47.42 b(c(x1)) -> a(b(a(x1))) 185.71/47.42 Qed 185.71/47.43 EOF