177.09/45.30 YES 177.09/45.31 177.09/45.31 Problem: 177.09/45.31 a(b(b(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 b(b(a(x1))) -> a(b(a(x1))) 177.09/45.31 177.09/45.31 Proof: 177.09/45.31 String Reversal Processor: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 DP Processor: 177.09/45.31 DPs: 177.09/45.31 a#(a(x1)) -> b#(x1) 177.09/45.31 a#(a(x1)) -> b#(b(x1)) 177.09/45.31 a#(a(x1)) -> b#(b(b(x1))) 177.09/45.31 a#(b(b(x1))) -> a#(x1) 177.09/45.31 a#(b(b(x1))) -> b#(a(x1)) 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 TRS: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 TDG Processor: 177.09/45.31 DPs: 177.09/45.31 a#(a(x1)) -> b#(x1) 177.09/45.31 a#(a(x1)) -> b#(b(x1)) 177.09/45.31 a#(a(x1)) -> b#(b(b(x1))) 177.09/45.31 a#(b(b(x1))) -> a#(x1) 177.09/45.31 a#(b(b(x1))) -> b#(a(x1)) 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 TRS: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 graph: 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) -> b#(a(x1)) 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) -> a#(x1) 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(b(b(x1))) 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(b(x1)) 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(x1) 177.09/45.31 a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(a(x1)) 177.09/45.31 a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1) 177.09/45.31 a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(b(x1))) 177.09/45.31 a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(x1)) 177.09/45.31 a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1) 177.09/45.31 SCC Processor: 177.09/45.31 #sccs: 1 177.09/45.31 #rules: 2 177.09/45.31 #arcs: 12/36 177.09/45.31 DPs: 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 a#(b(b(x1))) -> a#(x1) 177.09/45.31 TRS: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 Arctic Interpretation Processor: 177.09/45.31 dimension: 2 177.09/45.31 usable rules: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 interpretation: 177.09/45.31 [a#](x0) = [-& 0 ]x0 + [0], 177.09/45.31 177.09/45.31 [-& 2 ] [0] 177.09/45.31 [a](x0) = [0 2 ]x0 + [1], 177.09/45.31 177.09/45.31 [0 2 ] [1] 177.09/45.31 [b](x0) = [0 -&]x0 + [0] 177.09/45.31 orientation: 177.09/45.31 a#(b(b(x1))) = [0 2]x1 + [1] >= [-& 2 ]x1 + [0] = a#(b(a(x1))) 177.09/45.31 177.09/45.31 a#(b(b(x1))) = [0 2]x1 + [1] >= [-& 0 ]x1 + [0] = a#(x1) 177.09/45.31 177.09/45.31 [2 4] [3] [-& 2 ] [0] 177.09/45.31 b(b(a(x1))) = [2 4]x1 + [3] >= [0 2 ]x1 + [1] = a(x1) 177.09/45.31 177.09/45.31 [2 4] [3] [2 4] [3] 177.09/45.31 a(a(x1)) = [2 4]x1 + [3] >= [2 2]x1 + [2] = b(b(b(x1))) 177.09/45.31 177.09/45.31 [2 4] [3] [-& 4 ] [2] 177.09/45.31 a(b(b(x1))) = [2 4]x1 + [3] >= [2 4 ]x1 + [3] = a(b(a(x1))) 177.09/45.31 problem: 177.09/45.31 DPs: 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 TRS: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 Restore Modifier: 177.09/45.31 DPs: 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 TRS: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 EDG Processor: 177.09/45.31 DPs: 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 TRS: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 graph: 177.09/45.31 a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1))) 177.09/45.31 Arctic Interpretation Processor: 177.09/45.31 dimension: 2 177.09/45.31 usable rules: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 interpretation: 177.09/45.31 [a#](x0) = [-& 0 ]x0 + [0], 177.09/45.31 177.09/45.31 [-& 0 ] [0] 177.09/45.31 [a](x0) = [0 2 ]x0 + [2], 177.09/45.31 177.09/45.31 [-& 1 ] [1 ] 177.09/45.31 [b](x0) = [0 -&]x0 + [-&] 177.09/45.31 orientation: 177.09/45.31 a#(b(b(x1))) = [-& 1 ]x1 + [1] >= [-& 0 ]x1 + [0] = a#(b(a(x1))) 177.09/45.31 177.09/45.31 [-& 1 ] [1] [-& 0 ] [0] 177.09/45.31 b(b(a(x1))) = [1 3 ]x1 + [3] >= [0 2 ]x1 + [2] = a(x1) 177.09/45.31 177.09/45.31 [0 2] [2] [-& 2 ] [2] 177.09/45.31 a(a(x1)) = [2 4]x1 + [4] >= [1 -&]x1 + [1] = b(b(b(x1))) 177.09/45.31 177.09/45.31 [-& 1 ] [1] [-& 0 ] [0] 177.09/45.31 a(b(b(x1))) = [1 3 ]x1 + [3] >= [1 3 ]x1 + [3] = a(b(a(x1))) 177.09/45.31 problem: 177.09/45.31 DPs: 177.09/45.31 177.09/45.31 TRS: 177.09/45.31 b(b(a(x1))) -> a(x1) 177.09/45.31 a(a(x1)) -> b(b(b(x1))) 177.09/45.31 a(b(b(x1))) -> a(b(a(x1))) 177.09/45.31 Qed 177.09/45.31 EOF