170.70/43.61 YES 170.70/43.61 170.70/43.61 Problem: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 a(b(x1)) -> b(a(c(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 170.70/43.61 Proof: 170.70/43.61 String Reversal Processor: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 DP Processor: 170.70/43.61 DPs: 170.70/43.61 a#(x1) -> b#(x1) 170.70/43.61 a#(x1) -> c#(x1) 170.70/43.61 b#(a(x1)) -> b#(x1) 170.70/43.61 b#(a(x1)) -> a#(b(x1)) 170.70/43.61 b#(a(x1)) -> c#(a(b(x1))) 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 TRS: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 TDG Processor: 170.70/43.61 DPs: 170.70/43.61 a#(x1) -> b#(x1) 170.70/43.61 a#(x1) -> c#(x1) 170.70/43.61 b#(a(x1)) -> b#(x1) 170.70/43.61 b#(a(x1)) -> a#(b(x1)) 170.70/43.61 b#(a(x1)) -> c#(a(b(x1))) 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 TRS: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 graph: 170.70/43.61 c#(c(x1)) -> a#(x1) -> a#(x1) -> c#(x1) 170.70/43.61 c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1) 170.70/43.61 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(x1) 170.70/43.61 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 170.70/43.61 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 170.70/43.61 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 170.70/43.61 b#(a(x1)) -> a#(b(x1)) -> a#(x1) -> c#(x1) 170.70/43.61 b#(a(x1)) -> a#(b(x1)) -> a#(x1) -> b#(x1) 170.70/43.61 a#(x1) -> c#(x1) -> c#(c(x1)) -> a#(x1) 170.70/43.61 a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 170.70/43.61 a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 170.70/43.61 a#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1) 170.70/43.61 Arctic Interpretation Processor: 170.70/43.61 dimension: 2 170.70/43.61 usable rules: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 interpretation: 170.70/43.61 [c#](x0) = [-& 0 ]x0 + [0], 170.70/43.61 170.70/43.61 [b#](x0) = [0 0]x0 + [1], 170.70/43.61 170.70/43.61 [a#](x0) = [0 0]x0 + [1], 170.70/43.61 170.70/43.61 [0 1] [0] 170.70/43.61 [c](x0) = [0 0]x0 + [1], 170.70/43.61 170.70/43.61 [0 0] [0] 170.70/43.61 [b](x0) = [0 0]x0 + [0], 170.70/43.61 170.70/43.61 [1 1] [2] 170.70/43.61 [a](x0) = [0 0]x0 + [1] 170.70/43.61 orientation: 170.70/43.61 a#(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b#(x1) 170.70/43.61 170.70/43.61 a#(x1) = [0 0]x1 + [1] >= [-& 0 ]x1 + [0] = c#(x1) 170.70/43.61 170.70/43.61 b#(a(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [1] = b#(x1) 170.70/43.61 170.70/43.61 b#(a(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [1] = a#(b(x1)) 170.70/43.61 170.70/43.61 b#(a(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [1] = c#(a(b(x1))) 170.70/43.61 170.70/43.61 c#(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a#(x1) 170.70/43.61 170.70/43.61 [1 1] [2] [0 0] [0] 170.70/43.61 a(x1) = [0 0]x1 + [1] >= [0 0]x1 + [0] = b(x1) 170.70/43.61 170.70/43.61 [1 1] [2] [0 1] [0] 170.70/43.61 a(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(x1) 170.70/43.61 170.70/43.61 [1 1] [2] [1 1] [2] 170.70/43.61 b(a(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = c(a(b(x1))) 170.70/43.61 170.70/43.61 [1 1] [2] [1 1] [2] 170.70/43.61 c(c(x1)) = [0 1]x1 + [1] >= [0 0]x1 + [1] = a(x1) 170.70/43.61 problem: 170.70/43.61 DPs: 170.70/43.61 a#(x1) -> b#(x1) 170.70/43.61 a#(x1) -> c#(x1) 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 TRS: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 Restore Modifier: 170.70/43.61 DPs: 170.70/43.61 a#(x1) -> b#(x1) 170.70/43.61 a#(x1) -> c#(x1) 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 TRS: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 EDG Processor: 170.70/43.61 DPs: 170.70/43.61 a#(x1) -> b#(x1) 170.70/43.61 a#(x1) -> c#(x1) 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 TRS: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 graph: 170.70/43.61 c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1) 170.70/43.61 c#(c(x1)) -> a#(x1) -> a#(x1) -> c#(x1) 170.70/43.61 a#(x1) -> c#(x1) -> c#(c(x1)) -> a#(x1) 170.70/43.61 SCC Processor: 170.70/43.61 #sccs: 1 170.70/43.61 #rules: 2 170.70/43.61 #arcs: 3/9 170.70/43.61 DPs: 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 a#(x1) -> c#(x1) 170.70/43.61 TRS: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 Usable Rule Processor: 170.70/43.61 DPs: 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 a#(x1) -> c#(x1) 170.70/43.61 TRS: 170.70/43.61 170.70/43.61 Arctic Interpretation Processor: 170.70/43.61 dimension: 4 170.70/43.61 usable rules: 170.70/43.61 170.70/43.61 interpretation: 170.70/43.61 [c#](x0) = [0 -& -& -&]x0, 170.70/43.61 170.70/43.61 [a#](x0) = [1 0 0 0]x0, 170.70/43.61 170.70/43.61 [1 0 0 0] [0] 170.70/43.61 [0 0 0 0] [0] 170.70/43.61 [c](x0) = [0 0 0 0]x0 + [0] 170.70/43.61 [0 0 0 0] [0] 170.70/43.61 orientation: 170.70/43.61 c#(c(x1)) = [1 0 0 0]x1 + [0] >= [1 0 0 0]x1 = a#(x1) 170.70/43.61 170.70/43.61 a#(x1) = [1 0 0 0]x1 >= [0 -& -& -&]x1 = c#(x1) 170.70/43.61 problem: 170.70/43.61 DPs: 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 TRS: 170.70/43.61 170.70/43.61 Restore Modifier: 170.70/43.61 DPs: 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 TRS: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 EDG Processor: 170.70/43.61 DPs: 170.70/43.61 c#(c(x1)) -> a#(x1) 170.70/43.61 TRS: 170.70/43.61 a(x1) -> b(x1) 170.70/43.61 a(x1) -> c(x1) 170.70/43.61 b(a(x1)) -> c(a(b(x1))) 170.70/43.61 c(c(x1)) -> a(x1) 170.70/43.61 graph: 170.70/43.61 170.70/43.61 SCC Processor: 170.70/43.61 #sccs: 0 170.70/43.61 #rules: 0 170.70/43.61 #arcs: 0/1 170.70/43.61 170.70/43.62 EOF