176.08/45.02 YES 176.39/45.03 176.39/45.03 Problem: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 176.39/45.03 Proof: 176.39/45.03 DP Processor: 176.39/45.03 DPs: 176.39/45.03 a#(x1) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 b#(b(c(x1))) -> c#(a(b(x1))) 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) 176.39/45.03 b#(b(c(x1))) -> c#(b(c(a(b(x1))))) 176.39/45.03 TRS: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 TDG Processor: 176.39/45.03 DPs: 176.39/45.03 a#(x1) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 b#(b(c(x1))) -> c#(a(b(x1))) 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) 176.39/45.03 b#(b(c(x1))) -> c#(b(c(a(b(x1))))) 176.39/45.03 TRS: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 graph: 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) -> 176.39/45.03 b#(b(c(x1))) -> c#(b(c(a(b(x1))))) 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) -> 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) -> b#(b(c(x1))) -> c#(a(b(x1))) 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) -> b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) -> b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(b(c(a(b(x1))))) 176.39/45.03 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(c(a(b(x1)))) 176.39/45.03 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(b(x1))) 176.39/45.03 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> a#(b(x1)) -> a#(x1) -> b#(x1) 176.39/45.03 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(b(c(a(b(x1))))) 176.39/45.03 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(c(a(b(x1)))) 176.39/45.03 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(b(x1))) 176.39/45.03 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 176.39/45.03 SCC Processor: 176.39/45.03 #sccs: 1 176.39/45.03 #rules: 4 176.39/45.03 #arcs: 16/36 176.39/45.03 DPs: 176.39/45.03 b#(b(c(x1))) -> b#(c(a(b(x1)))) 176.39/45.03 b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 a#(x1) -> b#(x1) 176.39/45.03 TRS: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 Arctic Interpretation Processor: 176.39/45.03 dimension: 2 176.39/45.03 usable rules: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 interpretation: 176.39/45.03 [b#](x0) = [1 0]x0, 176.39/45.03 176.39/45.03 [a#](x0) = [2 1]x0 + [0], 176.39/45.03 176.39/45.03 [-& 0 ] [1] 176.39/45.03 [c](x0) = [0 2 ]x0 + [3], 176.39/45.03 176.39/45.03 [-& 0 ] [0 ] 176.39/45.03 [b](x0) = [0 -&]x0 + [-&], 176.39/45.03 176.39/45.03 [0 0 ] [0] 176.39/45.03 [a](x0) = [0 -&]x0 + [0] 176.39/45.03 orientation: 176.39/45.03 b#(b(c(x1))) = [1 3]x1 + [4] >= [0 2]x1 + [3] = b#(c(a(b(x1)))) 176.39/45.03 176.39/45.03 b#(b(c(x1))) = [1 3]x1 + [4] >= [1 0]x1 = b#(x1) 176.39/45.03 176.39/45.03 b#(b(c(x1))) = [1 3]x1 + [4] >= [1 2]x1 + [2] = a#(b(x1)) 176.39/45.03 176.39/45.03 a#(x1) = [2 1]x1 + [0] >= [1 0]x1 = b#(x1) 176.39/45.03 176.39/45.03 [0 0 ] [0] [-& 0 ] [0 ] 176.39/45.03 a(x1) = [0 -&]x1 + [0] >= [0 -&]x1 + [-&] = b(x1) 176.39/45.03 176.39/45.03 [-& 0 ] [1] [-& 0 ] [1] 176.39/45.03 b(b(c(x1))) = [0 2 ]x1 + [3] >= [0 2 ]x1 + [3] = c(b(c(a(b(x1))))) 176.39/45.03 176.39/45.03 [0 2] [3] 176.39/45.03 c(c(x1)) = [2 4]x1 + [5] >= x1 = x1 176.39/45.03 problem: 176.39/45.03 DPs: 176.39/45.03 b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 TRS: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 Restore Modifier: 176.39/45.03 DPs: 176.39/45.03 b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 TRS: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 EDG Processor: 176.39/45.03 DPs: 176.39/45.03 b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 TRS: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 graph: 176.39/45.03 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 176.39/45.03 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(b(x1)) 176.39/45.03 SCC Processor: 176.39/45.03 #sccs: 1 176.39/45.03 #rules: 1 176.39/45.03 #arcs: 2/4 176.39/45.03 DPs: 176.39/45.03 b#(b(c(x1))) -> b#(x1) 176.39/45.03 TRS: 176.39/45.03 a(x1) -> b(x1) 176.39/45.03 b(b(c(x1))) -> c(b(c(a(b(x1))))) 176.39/45.03 c(c(x1)) -> x1 176.39/45.03 Usable Rule Processor: 176.39/45.03 DPs: 176.39/45.03 b#(b(c(x1))) -> b#(x1) 176.39/45.03 TRS: 176.39/45.03 176.39/45.03 Arctic Interpretation Processor: 176.39/45.03 dimension: 1 176.39/45.03 usable rules: 176.39/45.03 176.39/45.03 interpretation: 176.39/45.03 [b#](x0) = 6x0, 176.39/45.03 176.39/45.03 [c](x0) = x0 + 9, 176.39/45.03 176.39/45.03 [b](x0) = 1x0 + 12 176.39/45.03 orientation: 176.39/45.03 b#(b(c(x1))) = 7x1 + 18 >= 6x1 = b#(x1) 176.39/45.03 problem: 176.39/45.03 DPs: 176.39/45.03 176.39/45.03 TRS: 176.39/45.03 176.39/45.03 Qed 176.39/45.03 EOF