190.28/48.62 YES 190.28/48.63 190.28/48.63 Problem: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(b(c(a(x1)))) 190.28/48.63 190.28/48.63 Proof: 190.28/48.63 String Reversal Processor: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 DP Processor: 190.28/48.63 DPs: 190.28/48.63 a#(x1) -> b#(x1) 190.28/48.63 b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(x1) 190.28/48.63 c#(a(c(x1))) -> b#(a(x1)) 190.28/48.63 c#(a(c(x1))) -> c#(b(a(x1))) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 TRS: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 TDG Processor: 190.28/48.63 DPs: 190.28/48.63 a#(x1) -> b#(x1) 190.28/48.63 b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(x1) 190.28/48.63 c#(a(c(x1))) -> b#(a(x1)) 190.28/48.63 c#(a(c(x1))) -> c#(b(a(x1))) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 TRS: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 graph: 190.28/48.63 c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> c#(b(a(x1))) 190.28/48.63 c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> b#(a(x1)) 190.28/48.63 c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> a#(x1) 190.28/48.63 c#(a(c(x1))) -> b#(a(x1)) -> b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) -> a#(x1) -> b#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 190.28/48.63 b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> c#(b(a(x1))) 190.28/48.63 b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> b#(a(x1)) 190.28/48.63 b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(x1) 190.28/48.63 a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1) 190.28/48.63 Arctic Interpretation Processor: 190.28/48.63 dimension: 1 190.28/48.63 usable rules: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 interpretation: 190.28/48.63 [c#](x0) = 15x0, 190.28/48.63 190.28/48.63 [b#](x0) = 14x0, 190.28/48.63 190.28/48.63 [a#](x0) = 14x0, 190.28/48.63 190.28/48.63 [c](x0) = 2x0, 190.28/48.63 190.28/48.63 [b](x0) = 1x0, 190.28/48.63 190.28/48.63 [a](x0) = 1x0 190.28/48.63 orientation: 190.28/48.63 a#(x1) = 14x1 >= 14x1 = b#(x1) 190.28/48.63 190.28/48.63 b#(b(x1)) = 15x1 >= 15x1 = c#(x1) 190.28/48.63 190.28/48.63 c#(a(c(x1))) = 18x1 >= 14x1 = a#(x1) 190.28/48.63 190.28/48.63 c#(a(c(x1))) = 18x1 >= 15x1 = b#(a(x1)) 190.28/48.63 190.28/48.63 c#(a(c(x1))) = 18x1 >= 17x1 = c#(b(a(x1))) 190.28/48.63 190.28/48.63 c#(a(c(x1))) = 18x1 >= 18x1 = a#(c(b(a(x1)))) 190.28/48.63 190.28/48.63 a(x1) = 1x1 >= 1x1 = b(x1) 190.28/48.63 190.28/48.63 b(b(x1)) = 2x1 >= 2x1 = c(x1) 190.28/48.63 190.28/48.63 c(a(c(x1))) = 5x1 >= 5x1 = a(c(b(a(x1)))) 190.28/48.63 problem: 190.28/48.63 DPs: 190.28/48.63 a#(x1) -> b#(x1) 190.28/48.63 b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 TRS: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 Restore Modifier: 190.28/48.63 DPs: 190.28/48.63 a#(x1) -> b#(x1) 190.28/48.63 b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 TRS: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 EDG Processor: 190.28/48.63 DPs: 190.28/48.63 a#(x1) -> b#(x1) 190.28/48.63 b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 TRS: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 graph: 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) -> a#(x1) -> b#(x1) 190.28/48.63 b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1) 190.28/48.63 Arctic Interpretation Processor: 190.28/48.63 dimension: 3 190.28/48.63 usable rules: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 interpretation: 190.28/48.63 [c#](x0) = [1 0 0]x0 + [0], 190.28/48.63 190.28/48.63 [b#](x0) = [-& 0 0 ]x0 + [0], 190.28/48.63 190.28/48.63 [a#](x0) = [0 1 1]x0 + [1], 190.28/48.63 190.28/48.63 [1 -& 0 ] [-&] 190.28/48.63 [c](x0) = [1 -& 1 ]x0 + [0 ] 190.28/48.63 [0 -& 1 ] [1 ], 190.28/48.63 190.28/48.63 [0 -& 1 ] [1] 190.28/48.63 [b](x0) = [1 0 0 ]x0 + [0] 190.28/48.63 [0 -& -&] [0], 190.28/48.63 190.28/48.63 [1 -& 1 ] [1] 190.28/48.63 [a](x0) = [1 0 0 ]x0 + [0] 190.28/48.63 [0 -& -&] [0] 190.28/48.63 orientation: 190.28/48.63 a#(x1) = [0 1 1]x1 + [1] >= [-& 0 0 ]x1 + [0] = b#(x1) 190.28/48.63 190.28/48.63 b#(b(x1)) = [1 0 0]x1 + [0] >= [1 0 0]x1 + [0] = c#(x1) 190.28/48.63 190.28/48.63 c#(a(c(x1))) = [3 -& 3 ]x1 + [3] >= [3 -& 3 ]x1 + [3] = a#(c(b(a(x1)))) 190.28/48.63 190.28/48.63 [1 -& 1 ] [1] [0 -& 1 ] [1] 190.28/48.63 a(x1) = [1 0 0 ]x1 + [0] >= [1 0 0 ]x1 + [0] = b(x1) 190.28/48.63 [0 -& -&] [0] [0 -& -&] [0] 190.28/48.63 190.28/48.63 [1 -& 1 ] [1] [1 -& 0 ] [-&] 190.28/48.63 b(b(x1)) = [1 0 2 ]x1 + [2] >= [1 -& 1 ]x1 + [0 ] = c(x1) 190.28/48.63 [0 -& 1 ] [1] [0 -& 1 ] [1 ] 190.28/48.63 190.28/48.63 [3 -& 3 ] [3] [3 -& 3 ] [3] 190.28/48.63 c(a(c(x1))) = [3 -& 3 ]x1 + [3] >= [3 -& 3 ]x1 + [3] = a(c(b(a(x1)))) 190.28/48.63 [2 -& 2 ] [2] [2 -& 2 ] [2] 190.28/48.63 problem: 190.28/48.63 DPs: 190.28/48.63 b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 TRS: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 Restore Modifier: 190.28/48.63 DPs: 190.28/48.63 b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 TRS: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 EDG Processor: 190.28/48.63 DPs: 190.28/48.63 b#(b(x1)) -> c#(x1) 190.28/48.63 c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 TRS: 190.28/48.63 a(x1) -> b(x1) 190.28/48.63 b(b(x1)) -> c(x1) 190.28/48.63 c(a(c(x1))) -> a(c(b(a(x1)))) 190.28/48.63 graph: 190.28/48.63 b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(c(b(a(x1)))) 190.28/48.63 SCC Processor: 190.28/48.63 #sccs: 0 190.28/48.63 #rules: 0 190.28/48.63 #arcs: 1/4 190.28/48.63 190.28/48.64 EOF