190.57/48.45 YES 190.57/48.46 190.57/48.46 Problem: 190.57/48.46 a(x1) -> x1 190.57/48.46 a(b(x1)) -> b(c(b(a(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 190.57/48.46 Proof: 190.57/48.46 String Reversal Processor: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 DP Processor: 190.57/48.46 DPs: 190.57/48.46 b#(a(x1)) -> b#(x1) 190.57/48.46 b#(a(x1)) -> c#(b(x1)) 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 b#(a(x1)) -> a#(b(c(b(x1)))) 190.57/48.46 b#(x1) -> a#(x1) 190.57/48.46 TRS: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 TDG Processor: 190.57/48.46 DPs: 190.57/48.46 b#(a(x1)) -> b#(x1) 190.57/48.46 b#(a(x1)) -> c#(b(x1)) 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 b#(a(x1)) -> a#(b(c(b(x1)))) 190.57/48.46 b#(x1) -> a#(x1) 190.57/48.46 TRS: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 graph: 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) -> b#(x1) -> a#(x1) 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> a#(b(c(b(x1)))) 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> c#(b(x1)) 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> b#(x1) 190.57/48.46 b#(a(x1)) -> b#(x1) -> b#(x1) -> a#(x1) 190.57/48.46 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(c(b(x1)))) 190.57/48.46 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 190.57/48.46 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 190.57/48.46 SCC Processor: 190.57/48.46 #sccs: 1 190.57/48.46 #rules: 2 190.57/48.46 #arcs: 10/25 190.57/48.46 DPs: 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 b#(a(x1)) -> b#(x1) 190.57/48.46 TRS: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 Arctic Interpretation Processor: 190.57/48.46 dimension: 2 190.57/48.46 usable rules: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 interpretation: 190.57/48.46 [b#](x0) = [0 0]x0 + [-4], 190.57/48.46 190.57/48.46 [-3 0 ] [2] 190.57/48.46 [c](x0) = [-1 1 ]x0 + [3], 190.57/48.46 190.57/48.46 [2 1] [3] 190.57/48.46 [b](x0) = [0 0]x0 + [0], 190.57/48.46 190.57/48.46 [1 1 ] [3 ] 190.57/48.46 [a](x0) = [-& 0 ]x0 + [-&] 190.57/48.46 orientation: 190.57/48.46 b#(a(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = b#(c(b(x1))) 190.57/48.46 190.57/48.46 b#(a(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [-4] = b#(x1) 190.57/48.46 190.57/48.46 [1 1 ] [3 ] 190.57/48.46 a(x1) = [-& 0 ]x1 + [-&] >= x1 = x1 190.57/48.46 190.57/48.46 [3 3] [5] [3 3] [5] 190.57/48.46 b(a(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = a(b(c(b(x1)))) 190.57/48.46 190.57/48.46 [2 1] [3] [1 1 ] [3 ] 190.57/48.46 b(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 + [-&] = a(x1) 190.57/48.46 190.57/48.46 [0 2] [4] 190.57/48.46 c(c(c(x1))) = [1 3]x1 + [5] >= x1 = x1 190.57/48.46 problem: 190.57/48.46 DPs: 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 TRS: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 Restore Modifier: 190.57/48.46 DPs: 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 TRS: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 EDG Processor: 190.57/48.46 DPs: 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 TRS: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 graph: 190.57/48.46 b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> b#(c(b(x1))) 190.57/48.46 Arctic Interpretation Processor: 190.57/48.46 dimension: 2 190.57/48.46 usable rules: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 interpretation: 190.57/48.46 [b#](x0) = [0 -&]x0 + [0], 190.57/48.46 190.57/48.46 [-4 0 ] [0] 190.57/48.46 [c](x0) = [-1 1 ]x0 + [0], 190.57/48.46 190.57/48.46 [2 1] [1] 190.57/48.46 [b](x0) = [0 0]x0 + [0], 190.57/48.46 190.57/48.46 [1 1 ] [1] 190.57/48.46 [a](x0) = [-& 0 ]x0 + [0] 190.57/48.46 orientation: 190.57/48.46 b#(a(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(c(b(x1))) 190.57/48.46 190.57/48.46 [1 1 ] [1] 190.57/48.46 a(x1) = [-& 0 ]x1 + [0] >= x1 = x1 190.57/48.46 190.57/48.46 [3 3] [3] [3 3] [3] 190.57/48.46 b(a(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(b(c(b(x1)))) 190.57/48.46 190.57/48.46 [2 1] [1] [1 1 ] [1] 190.57/48.46 b(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = a(x1) 190.57/48.46 190.57/48.46 [0 2] [1] 190.57/48.46 c(c(c(x1))) = [1 3]x1 + [2] >= x1 = x1 190.57/48.46 problem: 190.57/48.46 DPs: 190.57/48.46 190.57/48.46 TRS: 190.57/48.46 a(x1) -> x1 190.57/48.46 b(a(x1)) -> a(b(c(b(x1)))) 190.57/48.46 b(x1) -> a(x1) 190.57/48.46 c(c(c(x1))) -> x1 190.57/48.46 Qed 190.57/48.46 EOF