170.66/43.61 YES 170.66/43.62 170.66/43.62 Problem: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 170.66/43.62 Proof: 170.66/43.62 DP Processor: 170.66/43.62 DPs: 170.66/43.62 a#(x1) -> c#(x1) 170.66/43.62 a#(x1) -> b#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 TRS: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 TDG Processor: 170.66/43.62 DPs: 170.66/43.62 a#(x1) -> c#(x1) 170.66/43.62 a#(x1) -> b#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 TRS: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 graph: 170.66/43.62 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> b#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> a#(a(c(x1))) -> a#(x1) -> c#(x1) 170.66/43.62 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 170.66/43.62 SCC Processor: 170.66/43.62 #sccs: 1 170.66/43.62 #rules: 4 170.66/43.62 #arcs: 10/25 170.66/43.62 DPs: 170.66/43.62 c#(c(b(x1))) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 a#(x1) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 TRS: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 Arctic Interpretation Processor: 170.66/43.62 dimension: 2 170.66/43.62 usable rules: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 interpretation: 170.66/43.62 [c#](x0) = [0 -&]x0 + [0], 170.66/43.62 170.66/43.62 [a#](x0) = [1 0]x0 + [1], 170.66/43.62 170.66/43.62 [-& 0 ] [0] 170.66/43.62 [b](x0) = [0 1 ]x0 + [2], 170.66/43.62 170.66/43.62 [-& 0 ] [0 ] 170.66/43.62 [c](x0) = [0 -&]x0 + [-&], 170.66/43.62 170.66/43.62 [0 -&] [0] 170.66/43.62 [a](x0) = [1 0 ]x0 + [2] 170.66/43.62 orientation: 170.66/43.62 c#(c(b(x1))) = [0 1]x1 + [2] >= [0 -&]x1 + [0] = c#(x1) 170.66/43.62 170.66/43.62 c#(c(b(x1))) = [0 1]x1 + [2] >= [0 1]x1 + [1] = a#(c(x1)) 170.66/43.62 170.66/43.62 a#(x1) = [1 0]x1 + [1] >= [0 -&]x1 + [0] = c#(x1) 170.66/43.62 170.66/43.62 c#(c(b(x1))) = [0 1]x1 + [2] >= [0 1]x1 + [2] = a#(a(c(x1))) 170.66/43.62 170.66/43.62 [0 -&] [0] [0 -&] [0] 170.66/43.62 a(x1) = [1 0 ]x1 + [2] >= [1 0 ]x1 + [2] = b(c(x1)) 170.66/43.62 170.66/43.62 [0 1] [2] 170.66/43.62 b(b(x1)) = [1 2]x1 + [3] >= x1 = x1 170.66/43.62 170.66/43.62 [-& 0 ] [0] [-& 0 ] [0] 170.66/43.62 c(c(b(x1))) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = a(a(c(x1))) 170.66/43.62 problem: 170.66/43.62 DPs: 170.66/43.62 c#(c(b(x1))) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 TRS: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 Restore Modifier: 170.66/43.62 DPs: 170.66/43.62 c#(c(b(x1))) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 TRS: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 EDG Processor: 170.66/43.62 DPs: 170.66/43.62 c#(c(b(x1))) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 TRS: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 graph: 170.66/43.62 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 170.66/43.62 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1)) 170.66/43.62 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(a(c(x1))) 170.66/43.62 SCC Processor: 170.66/43.62 #sccs: 1 170.66/43.62 #rules: 1 170.66/43.62 #arcs: 3/9 170.66/43.62 DPs: 170.66/43.62 c#(c(b(x1))) -> c#(x1) 170.66/43.62 TRS: 170.66/43.62 a(x1) -> b(c(x1)) 170.66/43.62 b(b(x1)) -> x1 170.66/43.62 c(c(b(x1))) -> a(a(c(x1))) 170.66/43.62 Usable Rule Processor: 170.66/43.62 DPs: 170.66/43.62 c#(c(b(x1))) -> c#(x1) 170.66/43.62 TRS: 170.66/43.62 170.66/43.62 Arctic Interpretation Processor: 170.66/43.62 dimension: 1 170.66/43.62 usable rules: 170.66/43.62 170.66/43.62 interpretation: 170.66/43.62 [c#](x0) = 6x0, 170.66/43.62 170.66/43.62 [b](x0) = x0 + 9, 170.66/43.62 170.66/43.62 [c](x0) = 1x0 + 12 170.66/43.62 orientation: 170.66/43.62 c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1) 170.66/43.62 problem: 170.66/43.62 DPs: 170.66/43.62 170.66/43.62 TRS: 170.66/43.62 170.66/43.62 Qed 170.66/43.62 EOF