175.58/44.86 YES 175.58/44.87 175.58/44.87 Problem: 175.58/44.87 a(a(x1)) -> x1 175.58/44.87 a(b(x1)) -> x1 175.58/44.87 b(b(a(x1))) -> a(b(a(b(b(x1))))) 175.58/44.87 175.58/44.87 Proof: 175.58/44.87 DP Processor: 175.58/44.87 DPs: 175.58/44.87 b#(b(a(x1))) -> b#(x1) 175.58/44.87 b#(b(a(x1))) -> b#(b(x1)) 175.58/44.87 b#(b(a(x1))) -> a#(b(b(x1))) 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) 175.58/44.87 b#(b(a(x1))) -> a#(b(a(b(b(x1))))) 175.58/44.87 TRS: 175.58/44.87 a(a(x1)) -> x1 175.58/44.87 a(b(x1)) -> x1 175.58/44.87 b(b(a(x1))) -> a(b(a(b(b(x1))))) 175.58/44.87 TDG Processor: 175.58/44.87 DPs: 175.58/44.87 b#(b(a(x1))) -> b#(x1) 175.58/44.87 b#(b(a(x1))) -> b#(b(x1)) 175.58/44.87 b#(b(a(x1))) -> a#(b(b(x1))) 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) 175.58/44.87 b#(b(a(x1))) -> a#(b(a(b(b(x1))))) 175.58/44.87 TRS: 175.58/44.87 a(a(x1)) -> x1 175.58/44.87 a(b(x1)) -> x1 175.58/44.87 b(b(a(x1))) -> a(b(a(b(b(x1))))) 175.58/44.87 graph: 175.58/44.87 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(b(a(b(b(x1))))) 175.58/44.87 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) 175.58/44.87 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(b(b(x1))) 175.58/44.87 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1)) 175.58/44.87 b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1) 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) -> 175.58/44.87 b#(b(a(x1))) -> a#(b(a(b(b(x1))))) 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) -> 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> a#(b(b(x1))) 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(x1)) 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(x1) 175.58/44.87 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(b(a(b(b(x1))))) 175.58/44.87 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) 175.58/44.87 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(b(b(x1))) 175.58/44.87 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1)) 175.58/44.87 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1) 175.58/44.87 SCC Processor: 175.58/44.87 #sccs: 1 175.58/44.87 #rules: 3 175.58/44.87 #arcs: 15/25 175.58/44.87 DPs: 175.58/44.87 b#(b(a(x1))) -> b#(b(x1)) 175.58/44.87 b#(b(a(x1))) -> b#(x1) 175.58/44.87 b#(b(a(x1))) -> b#(a(b(b(x1)))) 175.58/44.87 TRS: 175.58/44.87 a(a(x1)) -> x1 175.58/44.87 a(b(x1)) -> x1 175.58/44.87 b(b(a(x1))) -> a(b(a(b(b(x1))))) 175.58/44.87 Arctic Interpretation Processor: 175.58/44.87 dimension: 2 175.58/44.87 usable rules: 175.58/44.87 a(a(x1)) -> x1 175.58/44.87 a(b(x1)) -> x1 175.58/44.87 b(b(a(x1))) -> a(b(a(b(b(x1))))) 175.58/44.87 interpretation: 175.58/44.87 [b#](x0) = [1 0]x0 + [0], 175.58/44.87 175.58/44.87 [-& 0 ] [0] 175.58/44.87 [b](x0) = [0 -&]x0 + [0], 175.58/44.87 175.58/44.87 [-& 0 ] [0] 175.58/44.87 [a](x0) = [0 1 ]x0 + [1] 175.58/44.87 orientation: 175.58/44.87 b#(b(a(x1))) = [1 2]x1 + [2] >= [0 1]x1 + [1] = b#(b(x1)) 175.58/44.87 175.58/44.87 b#(b(a(x1))) = [1 2]x1 + [2] >= [1 0]x1 + [0] = b#(x1) 175.58/44.87 175.58/44.87 b#(b(a(x1))) = [1 2]x1 + [2] >= [0 1]x1 + [1] = b#(a(b(b(x1)))) 175.58/44.87 175.58/44.87 [0 1] [1] 175.58/44.87 a(a(x1)) = [1 2]x1 + [2] >= x1 = x1 175.58/44.87 175.58/44.87 [0 -&] [0] 175.58/44.87 a(b(x1)) = [1 0 ]x1 + [1] >= x1 = x1 175.58/44.87 175.58/44.87 [-& 0 ] [0] [-& 0 ] [0] 175.58/44.87 b(b(a(x1))) = [0 1 ]x1 + [1] >= [0 1 ]x1 + [1] = a(b(a(b(b(x1))))) 175.58/44.87 problem: 175.58/44.87 DPs: 175.58/44.87 b#(b(a(x1))) -> b#(x1) 175.58/44.87 TRS: 175.58/44.87 a(a(x1)) -> x1 175.58/44.87 a(b(x1)) -> x1 175.58/44.87 b(b(a(x1))) -> a(b(a(b(b(x1))))) 175.58/44.87 Restore Modifier: 175.58/44.87 DPs: 175.58/44.87 b#(b(a(x1))) -> b#(x1) 175.58/44.87 TRS: 175.58/44.87 a(a(x1)) -> x1 175.58/44.87 a(b(x1)) -> x1 175.58/44.87 b(b(a(x1))) -> a(b(a(b(b(x1))))) 175.58/44.87 EDG Processor: 175.58/44.87 DPs: 175.58/44.87 b#(b(a(x1))) -> b#(x1) 175.58/44.87 TRS: 175.58/44.87 a(a(x1)) -> x1 175.58/44.87 a(b(x1)) -> x1 175.58/44.87 b(b(a(x1))) -> a(b(a(b(b(x1))))) 175.58/44.87 graph: 175.58/44.87 b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1) 175.58/44.87 Usable Rule Processor: 175.58/44.87 DPs: 175.58/44.87 b#(b(a(x1))) -> b#(x1) 175.58/44.87 TRS: 175.58/44.87 175.58/44.87 Arctic Interpretation Processor: 175.58/44.87 dimension: 1 175.58/44.87 usable rules: 175.58/44.87 175.58/44.87 interpretation: 175.58/44.87 [b#](x0) = 6x0, 175.58/44.87 175.58/44.87 [b](x0) = 1x0 + 12, 175.58/44.87 175.58/44.87 [a](x0) = x0 + 9 175.58/44.87 orientation: 175.58/44.87 b#(b(a(x1))) = 7x1 + 18 >= 6x1 = b#(x1) 175.58/44.87 problem: 175.58/44.87 DPs: 175.58/44.87 175.58/44.87 TRS: 175.58/44.87 175.58/44.87 Qed 175.58/44.87 EOF