190.25/48.70 YES 190.45/48.71 190.45/48.71 Problem: 190.45/48.71 a(x1) -> x1 190.45/48.71 a(b(x1)) -> c(b(c(a(x1)))) 190.45/48.71 c(c(x1)) -> c(b(a(x1))) 190.45/48.71 190.45/48.71 Proof: 190.45/48.71 String Reversal Processor: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 DP Processor: 190.45/48.71 DPs: 190.45/48.71 b#(a(x1)) -> c#(x1) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> c#(b(c(x1))) 190.45/48.71 b#(a(x1)) -> a#(c(b(c(x1)))) 190.45/48.71 c#(c(x1)) -> b#(c(x1)) 190.45/48.71 c#(c(x1)) -> a#(b(c(x1))) 190.45/48.71 TRS: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 TDG Processor: 190.45/48.71 DPs: 190.45/48.71 b#(a(x1)) -> c#(x1) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> c#(b(c(x1))) 190.45/48.71 b#(a(x1)) -> a#(c(b(c(x1)))) 190.45/48.71 c#(c(x1)) -> b#(c(x1)) 190.45/48.71 c#(c(x1)) -> a#(b(c(x1))) 190.45/48.71 TRS: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 graph: 190.45/48.71 c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(b(c(x1)))) 190.45/48.71 c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(c(x1))) 190.45/48.71 c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) 190.45/48.71 c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1) 190.45/48.71 b#(a(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> a#(b(c(x1))) 190.45/48.71 b#(a(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(c(x1))) 190.45/48.71 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(b(c(x1)))) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(c(x1))) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1) 190.45/48.71 SCC Processor: 190.45/48.71 #sccs: 1 190.45/48.71 #rules: 4 190.45/48.71 #arcs: 12/36 190.45/48.71 DPs: 190.45/48.71 c#(c(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> c#(x1) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> c#(b(c(x1))) 190.45/48.71 TRS: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 Arctic Interpretation Processor: 190.45/48.71 dimension: 3 190.45/48.71 usable rules: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 interpretation: 190.45/48.71 [c#](x0) = [-& -& 0 ]x0 + [0], 190.45/48.71 190.45/48.71 [b#](x0) = [0 0 0]x0 + [0], 190.45/48.71 190.45/48.71 [-& -& 0 ] [0] 190.45/48.71 [c](x0) = [0 0 0 ]x0 + [1] 190.45/48.71 [0 0 1 ] [1], 190.45/48.71 190.45/48.71 [1 0 0 ] [0] 190.45/48.71 [b](x0) = [0 0 -&]x0 + [0] 190.45/48.71 [0 -& -&] [0], 190.45/48.71 190.45/48.71 [0 0 1 ] [1] 190.45/48.71 [a](x0) = [0 0 0 ]x0 + [1] 190.45/48.71 [-& 0 0 ] [1] 190.45/48.71 orientation: 190.45/48.71 c#(c(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = b#(c(x1)) 190.45/48.71 190.45/48.71 b#(a(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = c#(x1) 190.45/48.71 190.45/48.71 b#(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = b#(c(x1)) 190.45/48.71 190.45/48.71 b#(a(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = c#(b(c(x1))) 190.45/48.71 190.45/48.71 [0 0 1 ] [1] 190.45/48.71 a(x1) = [0 0 0 ]x1 + [1] >= x1 = x1 190.45/48.71 [-& 0 0 ] [1] 190.45/48.71 190.45/48.71 [1 1 2] [2] [1 1 2] [2] 190.45/48.71 b(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(c(b(c(x1)))) 190.45/48.71 [0 0 1] [1] [0 0 1] [1] 190.45/48.71 190.45/48.71 [0 0 1] [1] [0 0 1] [1] 190.45/48.71 c(c(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(b(c(x1))) 190.45/48.71 [1 1 2] [2] [0 0 0] [1] 190.45/48.71 problem: 190.45/48.71 DPs: 190.45/48.71 c#(c(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) 190.45/48.71 TRS: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 Restore Modifier: 190.45/48.71 DPs: 190.45/48.71 c#(c(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) 190.45/48.71 TRS: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 EDG Processor: 190.45/48.71 DPs: 190.45/48.71 c#(c(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) 190.45/48.71 TRS: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 graph: 190.45/48.71 c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) 190.45/48.71 b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) 190.45/48.71 SCC Processor: 190.45/48.71 #sccs: 1 190.45/48.71 #rules: 1 190.45/48.71 #arcs: 2/4 190.45/48.71 DPs: 190.45/48.71 b#(a(x1)) -> b#(c(x1)) 190.45/48.71 TRS: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 Arctic Interpretation Processor: 190.45/48.71 dimension: 3 190.45/48.71 usable rules: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 interpretation: 190.45/48.71 [b#](x0) = [-& 0 0 ]x0 + [0], 190.45/48.71 190.45/48.71 [1 0 0 ] [1] 190.45/48.71 [c](x0) = [0 0 -&]x0 + [0] 190.45/48.71 [0 -& -&] [0], 190.45/48.71 190.45/48.71 [-& -& 0 ] [0] 190.45/48.71 [b](x0) = [-& -& 0 ]x0 + [0] 190.45/48.71 [0 0 1 ] [0], 190.45/48.71 190.45/48.71 [0 1 0] [0] 190.45/48.71 [a](x0) = [0 0 0]x0 + [0] 190.45/48.71 [1 1 0] [1] 190.45/48.71 orientation: 190.45/48.71 b#(a(x1)) = [1 1 0]x1 + [1] >= [0 0 -&]x1 + [0] = b#(c(x1)) 190.45/48.71 190.45/48.71 [0 1 0] [0] 190.45/48.71 a(x1) = [0 0 0]x1 + [0] >= x1 = x1 190.45/48.71 [1 1 0] [1] 190.45/48.71 190.45/48.71 [1 1 0] [1] [1 0 0] [1] 190.45/48.71 b(a(x1)) = [1 1 0]x1 + [1] >= [1 0 0]x1 + [1] = a(c(b(c(x1)))) 190.45/48.71 [2 2 1] [2] [2 1 1] [2] 190.45/48.71 190.45/48.71 [2 1 1] [2] [1 0 0] [1] 190.45/48.71 c(c(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = a(b(c(x1))) 190.45/48.71 [1 0 0] [1] [1 0 0] [1] 190.45/48.71 problem: 190.45/48.71 DPs: 190.45/48.71 190.45/48.71 TRS: 190.45/48.71 a(x1) -> x1 190.45/48.71 b(a(x1)) -> a(c(b(c(x1)))) 190.45/48.71 c(c(x1)) -> a(b(c(x1))) 190.45/48.71 Qed 190.45/48.72 EOF