180.10/45.89 YES 180.10/45.90 180.10/45.90 Problem: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 180.10/45.90 Proof: 180.10/45.90 DP Processor: 180.10/45.90 DPs: 180.10/45.90 a#(x1) -> c#(x1) 180.10/45.90 a#(x1) -> b#(c(x1)) 180.10/45.90 c#(c(b(x1))) -> c#(x1) 180.10/45.90 c#(c(b(x1))) -> a#(c(x1)) 180.10/45.90 c#(c(b(x1))) -> a#(a(c(x1))) 180.10/45.90 c#(c(b(x1))) -> a#(a(a(c(x1)))) 180.10/45.90 TRS: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 TDG Processor: 180.10/45.90 DPs: 180.10/45.90 a#(x1) -> c#(x1) 180.10/45.90 a#(x1) -> b#(c(x1)) 180.10/45.90 c#(c(b(x1))) -> c#(x1) 180.10/45.90 c#(c(b(x1))) -> a#(c(x1)) 180.10/45.90 c#(c(b(x1))) -> a#(a(c(x1))) 180.10/45.90 c#(c(b(x1))) -> a#(a(a(c(x1)))) 180.10/45.90 TRS: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 graph: 180.10/45.90 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(a(a(c(x1)))) 180.10/45.90 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(a(c(x1))) 180.10/45.90 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1)) 180.10/45.90 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 180.10/45.90 c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> b#(c(x1)) 180.10/45.90 c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> c#(x1) 180.10/45.90 c#(c(b(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(c(x1)) 180.10/45.90 c#(c(b(x1))) -> a#(a(c(x1))) -> a#(x1) -> c#(x1) 180.10/45.90 c#(c(b(x1))) -> a#(a(a(c(x1)))) -> a#(x1) -> b#(c(x1)) 180.10/45.90 c#(c(b(x1))) -> a#(a(a(c(x1)))) -> a#(x1) -> c#(x1) 180.10/45.90 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(a(a(c(x1)))) 180.10/45.90 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(a(c(x1))) 180.10/45.90 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1)) 180.10/45.90 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 180.10/45.90 SCC Processor: 180.10/45.90 #sccs: 1 180.10/45.90 #rules: 5 180.10/45.90 #arcs: 14/36 180.10/45.90 DPs: 180.10/45.90 c#(c(b(x1))) -> c#(x1) 180.10/45.90 c#(c(b(x1))) -> a#(c(x1)) 180.10/45.90 a#(x1) -> c#(x1) 180.10/45.90 c#(c(b(x1))) -> a#(a(c(x1))) 180.10/45.90 c#(c(b(x1))) -> a#(a(a(c(x1)))) 180.10/45.90 TRS: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 Arctic Interpretation Processor: 180.10/45.90 dimension: 2 180.10/45.90 usable rules: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 interpretation: 180.10/45.90 [c#](x0) = [0 -&]x0, 180.10/45.90 180.10/45.90 [a#](x0) = [0 -&]x0 + [0], 180.10/45.90 180.10/45.90 [-& 0 ] [0] 180.10/45.90 [b](x0) = [0 1 ]x0 + [2], 180.10/45.90 180.10/45.90 [-& 0 ] [0] 180.10/45.90 [c](x0) = [0 -&]x0 + [0], 180.10/45.90 180.10/45.90 [0 -&] [0] 180.10/45.90 [a](x0) = [1 0 ]x0 + [2] 180.10/45.90 orientation: 180.10/45.90 c#(c(b(x1))) = [0 1]x1 + [2] >= [0 -&]x1 = c#(x1) 180.10/45.90 180.10/45.90 c#(c(b(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [0] = a#(c(x1)) 180.10/45.90 180.10/45.90 a#(x1) = [0 -&]x1 + [0] >= [0 -&]x1 = c#(x1) 180.10/45.90 180.10/45.90 c#(c(b(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [0] = a#(a(c(x1))) 180.10/45.90 180.10/45.90 c#(c(b(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [0] = a#(a(a(c(x1)))) 180.10/45.90 180.10/45.90 [0 -&] [0] [0 -&] [0] 180.10/45.90 a(x1) = [1 0 ]x1 + [2] >= [1 0 ]x1 + [2] = b(c(x1)) 180.10/45.90 180.10/45.90 [0 1] [2] 180.10/45.90 b(b(x1)) = [1 2]x1 + [3] >= x1 = x1 180.10/45.90 180.10/45.90 [-& 0 ] [0] [-& 0 ] [0] 180.10/45.90 c(c(b(x1))) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = a(a(a(c(x1)))) 180.10/45.90 problem: 180.10/45.90 DPs: 180.10/45.90 c#(c(b(x1))) -> c#(x1) 180.10/45.90 a#(x1) -> c#(x1) 180.10/45.90 TRS: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 Restore Modifier: 180.10/45.90 DPs: 180.10/45.90 c#(c(b(x1))) -> c#(x1) 180.10/45.90 a#(x1) -> c#(x1) 180.10/45.90 TRS: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 EDG Processor: 180.10/45.90 DPs: 180.10/45.90 c#(c(b(x1))) -> c#(x1) 180.10/45.90 a#(x1) -> c#(x1) 180.10/45.90 TRS: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 graph: 180.10/45.90 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 180.10/45.90 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 180.10/45.90 SCC Processor: 180.10/45.90 #sccs: 1 180.10/45.90 #rules: 1 180.10/45.90 #arcs: 2/4 180.10/45.90 DPs: 180.10/45.90 c#(c(b(x1))) -> c#(x1) 180.10/45.90 TRS: 180.10/45.90 a(x1) -> b(c(x1)) 180.10/45.90 b(b(x1)) -> x1 180.10/45.90 c(c(b(x1))) -> a(a(a(c(x1)))) 180.10/45.90 Usable Rule Processor: 180.10/45.90 DPs: 180.10/45.90 c#(c(b(x1))) -> c#(x1) 180.10/45.90 TRS: 180.10/45.90 180.10/45.90 Arctic Interpretation Processor: 180.10/45.90 dimension: 1 180.10/45.90 usable rules: 180.10/45.90 180.10/45.90 interpretation: 180.10/45.90 [c#](x0) = 6x0, 180.10/45.90 180.10/45.90 [b](x0) = x0 + 9, 180.10/45.90 180.10/45.90 [c](x0) = 1x0 + 12 180.10/45.90 orientation: 180.10/45.90 c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1) 180.10/45.90 problem: 180.10/45.90 DPs: 180.10/45.90 180.10/45.90 TRS: 180.10/45.90 180.10/45.90 Qed 180.10/45.91 EOF