199.54/44.48 YES 199.54/44.49 199.54/44.49 Problem: 199.54/44.49 a(x1) -> x1 199.54/44.49 a(b(x1)) -> b(a(c(a(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 199.54/44.49 Proof: 199.54/44.49 String Reversal Processor: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 DP Processor: 199.54/44.49 DPs: 199.54/44.49 b#(a(x1)) -> b#(x1) 199.54/44.49 b#(a(x1)) -> a#(b(x1)) 199.54/44.49 b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 b#(a(x1)) -> a#(c(a(b(x1)))) 199.54/44.49 c#(c(c(x1))) -> b#(x1) 199.54/44.49 TRS: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 TDG Processor: 199.54/44.49 DPs: 199.54/44.49 b#(a(x1)) -> b#(x1) 199.54/44.49 b#(a(x1)) -> a#(b(x1)) 199.54/44.49 b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 b#(a(x1)) -> a#(c(a(b(x1)))) 199.54/44.49 c#(c(c(x1))) -> b#(x1) 199.54/44.49 TRS: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 graph: 199.54/44.49 c#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> a#(c(a(b(x1)))) 199.54/44.49 c#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 c#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 199.54/44.49 c#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> b#(x1) 199.54/44.49 b#(a(x1)) -> c#(a(b(x1))) -> c#(c(c(x1))) -> b#(x1) 199.54/44.49 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(a(b(x1)))) 199.54/44.49 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 199.54/44.49 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 199.54/44.49 SCC Processor: 199.54/44.49 #sccs: 1 199.54/44.49 #rules: 3 199.54/44.49 #arcs: 9/25 199.54/44.49 DPs: 199.54/44.49 c#(c(c(x1))) -> b#(x1) 199.54/44.49 b#(a(x1)) -> b#(x1) 199.54/44.49 b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 TRS: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 Arctic Interpretation Processor: 199.54/44.49 dimension: 2 199.54/44.49 usable rules: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 interpretation: 199.54/44.49 [c#](x0) = [-& 1 ]x0 + [2], 199.54/44.49 199.54/44.49 [b#](x0) = [0 3]x0 + [0], 199.54/44.49 199.54/44.49 [-& 0 ] [0 ] 199.54/44.49 [c](x0) = [0 2 ]x0 + [-&], 199.54/44.49 199.54/44.49 [2 -&] [-&] 199.54/44.49 [b](x0) = [2 0 ]x0 + [1 ], 199.54/44.49 199.54/44.49 [2 0] [2] 199.54/44.49 [a](x0) = [0 0]x0 + [2] 199.54/44.49 orientation: 199.54/44.49 c#(c(c(x1))) = [3 5]x1 + [2] >= [0 3]x1 + [0] = b#(x1) 199.54/44.49 199.54/44.49 b#(a(x1)) = [3 3]x1 + [5] >= [0 3]x1 + [0] = b#(x1) 199.54/44.49 199.54/44.49 b#(a(x1)) = [3 3]x1 + [5] >= [3 1]x1 + [3] = c#(a(b(x1))) 199.54/44.49 199.54/44.49 [2 0] [2] 199.54/44.49 a(x1) = [0 0]x1 + [2] >= x1 = x1 199.54/44.49 199.54/44.49 [4 2] [4] [4 2] [4] 199.54/44.49 b(a(x1)) = [4 2]x1 + [4] >= [4 2]x1 + [4] = a(c(a(b(x1)))) 199.54/44.49 199.54/44.49 [2 -&] [-&] 199.54/44.49 b(x1) = [2 0 ]x1 + [1 ] >= x1 = x1 199.54/44.49 199.54/44.49 [2 4] [0] [2 -&] [-&] 199.54/44.49 c(c(c(x1))) = [4 6]x1 + [2] >= [2 0 ]x1 + [1 ] = b(x1) 199.54/44.49 problem: 199.54/44.49 DPs: 199.54/44.49 b#(a(x1)) -> b#(x1) 199.54/44.49 b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 TRS: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 Restore Modifier: 199.54/44.49 DPs: 199.54/44.49 b#(a(x1)) -> b#(x1) 199.54/44.49 b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 TRS: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 EDG Processor: 199.54/44.49 DPs: 199.54/44.49 b#(a(x1)) -> b#(x1) 199.54/44.49 b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 TRS: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 graph: 199.54/44.49 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 199.54/44.49 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1))) 199.54/44.49 SCC Processor: 199.54/44.49 #sccs: 1 199.54/44.49 #rules: 1 199.54/44.49 #arcs: 2/4 199.54/44.49 DPs: 199.54/44.49 b#(a(x1)) -> b#(x1) 199.54/44.49 TRS: 199.54/44.49 a(x1) -> x1 199.54/44.49 b(a(x1)) -> a(c(a(b(x1)))) 199.54/44.49 b(x1) -> x1 199.54/44.49 c(c(c(x1))) -> b(x1) 199.54/44.49 Usable Rule Processor: 199.54/44.49 DPs: 199.54/44.49 b#(a(x1)) -> b#(x1) 199.54/44.49 TRS: 199.54/44.49 199.54/44.49 Arctic Interpretation Processor: 199.54/44.49 dimension: 4 199.54/44.49 usable rules: 199.54/44.49 199.54/44.49 interpretation: 199.54/44.49 [b#](x0) = [0 -& -& -&]x0, 199.54/44.49 199.54/44.49 [1 0 0 0] [0] 199.54/44.49 [0 0 0 0] [0] 199.54/44.49 [a](x0) = [1 0 0 0]x0 + [0] 199.54/44.49 [0 0 0 0] [0] 199.54/44.49 orientation: 199.54/44.49 b#(a(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = b#(x1) 199.54/44.49 problem: 199.54/44.49 DPs: 199.54/44.49 199.54/44.49 TRS: 199.54/44.49 199.54/44.49 Qed 199.54/44.50 EOF