185.32/47.38 YES 185.32/47.39 185.32/47.39 Problem: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 185.32/47.39 Proof: 185.32/47.39 DP Processor: 185.32/47.39 DPs: 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 a#(x1) -> b#(c(x1)) 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> c#(c(x1)) 185.32/47.39 c#(c(b(x1))) -> b#(c(c(x1))) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 TDG Processor: 185.32/47.39 DPs: 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 a#(x1) -> b#(c(x1)) 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> c#(c(x1)) 185.32/47.39 c#(c(b(x1))) -> b#(c(c(x1))) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 graph: 185.32/47.39 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(c(c(x1))) 185.32/47.39 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1)) 185.32/47.39 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> b#(c(c(x1))) 185.32/47.39 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1)) 185.32/47.39 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) -> a#(x1) -> b#(c(x1)) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) -> a#(x1) -> c#(x1) 185.32/47.39 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> b#(c(c(x1))) 185.32/47.39 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1)) 185.32/47.39 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 185.32/47.39 SCC Processor: 185.32/47.39 #sccs: 1 185.32/47.39 #rules: 4 185.32/47.39 #arcs: 14/36 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(c(x1)) 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 Arctic Interpretation Processor: 185.32/47.39 dimension: 2 185.32/47.39 usable rules: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 interpretation: 185.32/47.39 [c#](x0) = [1 0]x0 + [0], 185.32/47.39 185.32/47.39 [a#](x0) = [1 1]x0 + [0], 185.32/47.39 185.32/47.39 [-& 0 ] [2] 185.32/47.39 [b](x0) = [0 1 ]x0 + [3], 185.32/47.39 185.32/47.39 [-& 0 ] [0] 185.32/47.39 [c](x0) = [0 -&]x0 + [0], 185.32/47.39 185.32/47.39 [0 -&] [2] 185.32/47.39 [a](x0) = [1 0 ]x0 + [3] 185.32/47.39 orientation: 185.32/47.39 c#(c(b(x1))) = [1 2]x1 + [4] >= [0 1]x1 + [1] = c#(c(x1)) 185.32/47.39 185.32/47.39 c#(c(b(x1))) = [1 2]x1 + [4] >= [1 0]x1 + [0] = c#(x1) 185.32/47.39 185.32/47.39 c#(c(b(x1))) = [1 2]x1 + [4] >= [1 2]x1 + [4] = a#(b(c(c(x1)))) 185.32/47.39 185.32/47.39 a#(x1) = [1 1]x1 + [0] >= [1 0]x1 + [0] = c#(x1) 185.32/47.39 185.32/47.39 [0 -&] [2] [0 -&] [2] 185.32/47.39 a(x1) = [1 0 ]x1 + [3] >= [1 0 ]x1 + [3] = b(c(x1)) 185.32/47.39 185.32/47.39 [0 1] [3] 185.32/47.39 b(b(x1)) = [1 2]x1 + [4] >= x1 = x1 185.32/47.39 185.32/47.39 [-& 0 ] [2] [-& 0 ] [2] 185.32/47.39 c(c(b(x1))) = [0 1 ]x1 + [3] >= [0 1 ]x1 + [3] = a(b(c(c(x1)))) 185.32/47.39 problem: 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 Restore Modifier: 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 EDG Processor: 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 graph: 185.32/47.39 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 185.32/47.39 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 c#(c(b(x1))) -> a#(b(c(c(x1)))) -> a#(x1) -> c#(x1) 185.32/47.39 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 185.32/47.39 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(b(c(c(x1)))) 185.32/47.39 Arctic Interpretation Processor: 185.32/47.39 dimension: 2 185.32/47.39 usable rules: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 interpretation: 185.32/47.39 [c#](x0) = [2 0]x0, 185.32/47.39 185.32/47.39 [a#](x0) = [2 1]x0 + [0], 185.32/47.39 185.32/47.39 [-& 0 ] [0] 185.32/47.39 [b](x0) = [0 1 ]x0 + [3], 185.32/47.39 185.32/47.39 [-& 0 ] [0] 185.32/47.39 [c](x0) = [0 -&]x0 + [0], 185.32/47.39 185.32/47.39 [0 -&] [0] 185.32/47.39 [a](x0) = [1 0 ]x0 + [3] 185.32/47.39 orientation: 185.32/47.39 c#(c(b(x1))) = [2 3]x1 + [5] >= [2 0]x1 = c#(x1) 185.32/47.39 185.32/47.39 c#(c(b(x1))) = [2 3]x1 + [5] >= [1 2]x1 + [4] = a#(b(c(c(x1)))) 185.32/47.39 185.32/47.39 a#(x1) = [2 1]x1 + [0] >= [2 0]x1 = c#(x1) 185.32/47.39 185.32/47.39 [0 -&] [0] [0 -&] [0] 185.32/47.39 a(x1) = [1 0 ]x1 + [3] >= [1 0 ]x1 + [3] = b(c(x1)) 185.32/47.39 185.32/47.39 [0 1] [3] 185.32/47.39 b(b(x1)) = [1 2]x1 + [4] >= x1 = x1 185.32/47.39 185.32/47.39 [-& 0 ] [0] [-& 0 ] [0] 185.32/47.39 c(c(b(x1))) = [0 1 ]x1 + [3] >= [0 1 ]x1 + [3] = a(b(c(c(x1)))) 185.32/47.39 problem: 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 Restore Modifier: 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 EDG Processor: 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 a#(x1) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 graph: 185.32/47.39 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 185.32/47.39 a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 185.32/47.39 SCC Processor: 185.32/47.39 #sccs: 1 185.32/47.39 #rules: 1 185.32/47.39 #arcs: 2/4 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 a(x1) -> b(c(x1)) 185.32/47.39 b(b(x1)) -> x1 185.32/47.39 c(c(b(x1))) -> a(b(c(c(x1)))) 185.32/47.39 Usable Rule Processor: 185.32/47.39 DPs: 185.32/47.39 c#(c(b(x1))) -> c#(x1) 185.32/47.39 TRS: 185.32/47.39 185.32/47.39 Arctic Interpretation Processor: 185.32/47.39 dimension: 1 185.32/47.39 usable rules: 185.32/47.39 185.32/47.39 interpretation: 185.32/47.39 [c#](x0) = 6x0, 185.32/47.39 185.32/47.39 [b](x0) = x0 + 9, 185.32/47.39 185.32/47.39 [c](x0) = 1x0 + 12 185.32/47.39 orientation: 185.32/47.39 c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1) 185.32/47.39 problem: 185.32/47.39 DPs: 185.32/47.39 185.32/47.39 TRS: 185.32/47.39 185.32/47.39 Qed 185.32/47.40 EOF