174.18/44.48 YES 174.18/44.49 174.18/44.49 Problem: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 174.18/44.49 Proof: 174.18/44.49 DP Processor: 174.18/44.49 DPs: 174.18/44.49 a#(x1) -> c#(x1) 174.18/44.49 a#(x1) -> b#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 TRS: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 TDG Processor: 174.18/44.49 DPs: 174.18/44.49 a#(x1) -> c#(x1) 174.18/44.49 a#(x1) -> b#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 TRS: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 graph: 174.18/44.49 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> b#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> a#(a(c(x1))) -> a#(x1) -> c#(x1) 174.18/44.49 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 174.18/44.49 SCC Processor: 174.18/44.49 #sccs: 1 174.18/44.49 #rules: 4 174.18/44.49 #arcs: 10/25 174.18/44.49 DPs: 174.18/44.49 c#(c(b(x1))) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 a#(x1) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 TRS: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 Arctic Interpretation Processor: 174.18/44.49 dimension: 2 174.18/44.49 usable rules: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 interpretation: 174.18/44.49 [c#](x0) = [0 -&]x0 + [0], 174.18/44.49 174.18/44.49 [a#](x0) = [1 0]x0 + [2], 174.18/44.49 174.18/44.49 [-& 0 ] [1] 174.18/44.49 [b](x0) = [0 1 ]x0 + [2], 174.18/44.49 174.18/44.49 [-& 0 ] [0] 174.18/44.49 [c](x0) = [0 -&]x0 + [1], 174.18/44.49 174.18/44.49 [0 -&] [1] 174.18/44.49 [a](x0) = [1 0 ]x0 + [2] 174.18/44.49 orientation: 174.18/44.49 c#(c(b(x1))) = [0 1]x1 + [2] >= [0 -&]x1 + [0] = c#(x1) 174.18/44.49 174.18/44.49 c#(c(b(x1))) = [0 1]x1 + [2] >= [0 1]x1 + [2] = a#(c(x1)) 174.18/44.49 174.18/44.49 a#(x1) = [1 0]x1 + [2] >= [0 -&]x1 + [0] = c#(x1) 174.18/44.49 174.18/44.49 c#(c(b(x1))) = [0 1]x1 + [2] >= [0 1]x1 + [2] = a#(a(c(x1))) 174.18/44.49 174.18/44.49 [0 -&] [1] 174.18/44.49 a(x1) = [1 0 ]x1 + [2] >= x1 = x1 174.18/44.49 174.18/44.49 [0 -&] [1] [0 -&] [1] 174.18/44.49 a(x1) = [1 0 ]x1 + [2] >= [1 0 ]x1 + [2] = b(c(x1)) 174.18/44.49 174.18/44.49 [0 1] [2] 174.18/44.49 b(b(x1)) = [1 2]x1 + [3] >= x1 = x1 174.18/44.49 174.18/44.49 [-& 0 ] [1] [-& 0 ] [1] 174.18/44.49 c(c(b(x1))) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = a(a(c(x1))) 174.18/44.49 problem: 174.18/44.49 DPs: 174.18/44.49 c#(c(b(x1))) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 TRS: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 Restore Modifier: 174.18/44.49 DPs: 174.18/44.49 c#(c(b(x1))) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 TRS: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 EDG Processor: 174.18/44.49 DPs: 174.18/44.49 c#(c(b(x1))) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 TRS: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 graph: 174.18/44.49 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 174.18/44.49 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1)) 174.18/44.49 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(a(c(x1))) 174.18/44.49 SCC Processor: 174.18/44.49 #sccs: 1 174.18/44.49 #rules: 1 174.18/44.49 #arcs: 3/9 174.18/44.49 DPs: 174.18/44.49 c#(c(b(x1))) -> c#(x1) 174.18/44.49 TRS: 174.18/44.49 a(x1) -> x1 174.18/44.49 a(x1) -> b(c(x1)) 174.18/44.49 b(b(x1)) -> x1 174.18/44.49 c(c(b(x1))) -> a(a(c(x1))) 174.18/44.49 Usable Rule Processor: 174.18/44.49 DPs: 174.18/44.49 c#(c(b(x1))) -> c#(x1) 174.18/44.49 TRS: 174.18/44.49 174.18/44.49 Arctic Interpretation Processor: 174.18/44.49 dimension: 1 174.18/44.49 usable rules: 174.18/44.49 174.18/44.49 interpretation: 174.18/44.49 [c#](x0) = 6x0, 174.18/44.49 174.18/44.49 [b](x0) = x0 + 9, 174.18/44.49 174.18/44.49 [c](x0) = 1x0 + 12 174.18/44.49 orientation: 174.18/44.49 c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1) 174.18/44.49 problem: 174.18/44.49 DPs: 174.18/44.49 174.18/44.49 TRS: 174.18/44.49 174.18/44.49 Qed 174.18/44.49 EOF