180.10/46.02 YES 180.10/46.03 180.10/46.03 Problem: 180.10/46.03 a(x1) -> b(x1) 180.10/46.03 a(a(c(x1))) -> c(a(c(a(a(x1))))) 180.10/46.03 c(c(x1)) -> x1 180.10/46.03 180.10/46.03 Proof: 180.10/46.03 DP Processor: 180.10/46.03 DPs: 180.10/46.03 a#(a(c(x1))) -> a#(x1) 180.10/46.03 a#(a(c(x1))) -> a#(a(x1)) 180.10/46.03 a#(a(c(x1))) -> c#(a(a(x1))) 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) 180.10/46.03 a#(a(c(x1))) -> c#(a(c(a(a(x1))))) 180.10/46.03 TRS: 180.10/46.03 a(x1) -> b(x1) 180.10/46.03 a(a(c(x1))) -> c(a(c(a(a(x1))))) 180.10/46.03 c(c(x1)) -> x1 180.10/46.03 TDG Processor: 180.10/46.03 DPs: 180.10/46.03 a#(a(c(x1))) -> a#(x1) 180.10/46.03 a#(a(c(x1))) -> a#(a(x1)) 180.10/46.03 a#(a(c(x1))) -> c#(a(a(x1))) 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) 180.10/46.03 a#(a(c(x1))) -> c#(a(c(a(a(x1))))) 180.10/46.03 TRS: 180.10/46.03 a(x1) -> b(x1) 180.10/46.03 a(a(c(x1))) -> c(a(c(a(a(x1))))) 180.10/46.03 c(c(x1)) -> x1 180.10/46.03 graph: 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) -> 180.10/46.03 a#(a(c(x1))) -> c#(a(c(a(a(x1))))) 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) -> 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) -> a#(a(c(x1))) -> c#(a(a(x1))) 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) -> a#(a(c(x1))) -> a#(a(x1)) 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) -> a#(a(c(x1))) -> a#(x1) 180.10/46.03 a#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> c#(a(c(a(a(x1))))) 180.10/46.03 a#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(c(a(a(x1)))) 180.10/46.03 a#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> c#(a(a(x1))) 180.10/46.03 a#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(a(x1)) 180.10/46.03 a#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(x1) 180.10/46.03 a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> c#(a(c(a(a(x1))))) 180.10/46.03 a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(c(a(a(x1)))) 180.10/46.03 a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> c#(a(a(x1))) 180.10/46.03 a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(a(x1)) 180.10/46.03 a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(x1) 180.10/46.03 SCC Processor: 180.10/46.03 #sccs: 1 180.10/46.03 #rules: 3 180.10/46.03 #arcs: 15/25 180.10/46.03 DPs: 180.10/46.03 a#(a(c(x1))) -> a#(c(a(a(x1)))) 180.10/46.03 a#(a(c(x1))) -> a#(x1) 180.10/46.03 a#(a(c(x1))) -> a#(a(x1)) 180.10/46.03 TRS: 180.10/46.03 a(x1) -> b(x1) 180.10/46.03 a(a(c(x1))) -> c(a(c(a(a(x1))))) 180.10/46.03 c(c(x1)) -> x1 180.10/46.03 Arctic Interpretation Processor: 180.10/46.03 dimension: 2 180.10/46.03 usable rules: 180.10/46.03 a(x1) -> b(x1) 180.10/46.03 a(a(c(x1))) -> c(a(c(a(a(x1))))) 180.10/46.03 c(c(x1)) -> x1 180.10/46.03 interpretation: 180.10/46.03 [a#](x0) = [1 0]x0 + [0], 180.10/46.03 180.10/46.03 [-& 0 ] [1] 180.10/46.03 [c](x0) = [0 1 ]x0 + [2], 180.10/46.03 180.10/46.03 [-& 0 ] [0] 180.10/46.03 [b](x0) = [-& -&]x0 + [0], 180.10/46.03 180.10/46.03 [-& 0 ] [0] 180.10/46.03 [a](x0) = [0 -&]x0 + [0] 180.10/46.03 orientation: 180.10/46.03 a#(a(c(x1))) = [1 2]x1 + [3] >= [0 1]x1 + [2] = a#(c(a(a(x1)))) 180.10/46.03 180.10/46.03 a#(a(c(x1))) = [1 2]x1 + [3] >= [1 0]x1 + [0] = a#(x1) 180.10/46.03 180.10/46.03 a#(a(c(x1))) = [1 2]x1 + [3] >= [0 1]x1 + [1] = a#(a(x1)) 180.10/46.03 180.10/46.03 [-& 0 ] [0] [-& 0 ] [0] 180.10/46.03 a(x1) = [0 -&]x1 + [0] >= [-& -&]x1 + [0] = b(x1) 180.10/46.03 180.10/46.03 [-& 0 ] [1] [-& 0 ] [1] 180.10/46.03 a(a(c(x1))) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = c(a(c(a(a(x1))))) 180.10/46.03 180.10/46.03 [0 1] [2] 180.10/46.03 c(c(x1)) = [1 2]x1 + [3] >= x1 = x1 180.10/46.03 problem: 180.10/46.03 DPs: 180.10/46.03 a#(a(c(x1))) -> a#(x1) 180.10/46.03 TRS: 180.10/46.03 a(x1) -> b(x1) 180.10/46.03 a(a(c(x1))) -> c(a(c(a(a(x1))))) 180.10/46.03 c(c(x1)) -> x1 180.10/46.03 Restore Modifier: 180.10/46.03 DPs: 180.10/46.03 a#(a(c(x1))) -> a#(x1) 180.10/46.03 TRS: 180.10/46.03 a(x1) -> b(x1) 180.10/46.03 a(a(c(x1))) -> c(a(c(a(a(x1))))) 180.10/46.03 c(c(x1)) -> x1 180.10/46.03 EDG Processor: 180.10/46.03 DPs: 180.10/46.03 a#(a(c(x1))) -> a#(x1) 180.10/46.03 TRS: 180.10/46.03 a(x1) -> b(x1) 180.10/46.03 a(a(c(x1))) -> c(a(c(a(a(x1))))) 180.10/46.03 c(c(x1)) -> x1 180.10/46.03 graph: 180.10/46.03 a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(x1) 180.10/46.03 Usable Rule Processor: 180.10/46.03 DPs: 180.10/46.03 a#(a(c(x1))) -> a#(x1) 180.10/46.03 TRS: 180.10/46.03 180.10/46.03 Arctic Interpretation Processor: 180.10/46.03 dimension: 1 180.10/46.03 usable rules: 180.10/46.03 180.10/46.03 interpretation: 180.10/46.03 [a#](x0) = 6x0, 180.10/46.03 180.10/46.03 [c](x0) = x0 + 9, 180.10/46.03 180.10/46.03 [a](x0) = 1x0 + 12 180.10/46.03 orientation: 180.10/46.03 a#(a(c(x1))) = 7x1 + 18 >= 6x1 = a#(x1) 180.10/46.03 problem: 180.10/46.03 DPs: 180.10/46.03 180.10/46.03 TRS: 180.10/46.03 180.10/46.03 Qed 180.10/46.03 EOF