186.63/47.57 YES 186.63/47.57 186.63/47.57 Problem: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 186.63/47.57 Proof: 186.63/47.57 DP Processor: 186.63/47.57 DPs: 186.63/47.57 a#(x1) -> b#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 b#(b(c(x1))) -> c#(a(a(x1))) 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) 186.63/47.57 b#(b(c(x1))) -> c#(b(c(a(a(x1))))) 186.63/47.57 TRS: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 TDG Processor: 186.63/47.57 DPs: 186.63/47.57 a#(x1) -> b#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 b#(b(c(x1))) -> c#(a(a(x1))) 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) 186.63/47.57 b#(b(c(x1))) -> c#(b(c(a(a(x1))))) 186.63/47.57 TRS: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 graph: 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) -> 186.63/47.57 b#(b(c(x1))) -> c#(b(c(a(a(x1))))) 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) -> 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) -> b#(b(c(x1))) -> c#(a(a(x1))) 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) -> b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) -> b#(b(c(x1))) -> a#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 186.63/47.57 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(b(c(a(a(x1))))) 186.63/47.57 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(c(a(a(x1)))) 186.63/47.57 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(a(x1))) 186.63/47.57 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 186.63/47.57 SCC Processor: 186.63/47.57 #sccs: 1 186.63/47.57 #rules: 4 186.63/47.57 #arcs: 12/36 186.63/47.57 DPs: 186.63/47.57 b#(b(c(x1))) -> b#(c(a(a(x1)))) 186.63/47.57 b#(b(c(x1))) -> a#(x1) 186.63/47.57 a#(x1) -> b#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 TRS: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 Arctic Interpretation Processor: 186.63/47.57 dimension: 2 186.63/47.57 usable rules: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 interpretation: 186.63/47.57 [b#](x0) = [0 -&]x0 + [0], 186.63/47.57 186.63/47.57 [a#](x0) = [0 0]x0 + [0], 186.63/47.57 186.63/47.57 [-& 0 ] [0] 186.63/47.57 [c](x0) = [0 1 ]x0 + [2], 186.63/47.57 186.63/47.57 [-& 0 ] [0 ] 186.63/47.57 [b](x0) = [0 -&]x0 + [-&], 186.63/47.57 186.63/47.57 [-& 0 ] [0] 186.63/47.57 [a](x0) = [0 -&]x0 + [0] 186.63/47.57 orientation: 186.63/47.57 b#(b(c(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [0] = b#(c(a(a(x1)))) 186.63/47.57 186.63/47.57 b#(b(c(x1))) = [0 1]x1 + [2] >= [0 0]x1 + [0] = a#(x1) 186.63/47.57 186.63/47.57 a#(x1) = [0 0]x1 + [0] >= [0 -&]x1 + [0] = b#(x1) 186.63/47.57 186.63/47.57 b#(b(c(x1))) = [0 1]x1 + [2] >= [0 0]x1 + [0] = a#(a(x1)) 186.63/47.57 186.63/47.57 [-& 0 ] [0] [-& 0 ] [0 ] 186.63/47.57 a(x1) = [0 -&]x1 + [0] >= [0 -&]x1 + [-&] = b(x1) 186.63/47.57 186.63/47.57 [-& 0 ] [0] [-& 0 ] [0] 186.63/47.57 b(b(c(x1))) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = c(b(c(a(a(x1))))) 186.63/47.57 186.63/47.57 [0 1] [2] 186.63/47.57 c(c(x1)) = [1 2]x1 + [3] >= x1 = x1 186.63/47.57 problem: 186.63/47.57 DPs: 186.63/47.57 b#(b(c(x1))) -> a#(x1) 186.63/47.57 a#(x1) -> b#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 TRS: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 Restore Modifier: 186.63/47.57 DPs: 186.63/47.57 b#(b(c(x1))) -> a#(x1) 186.63/47.57 a#(x1) -> b#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 TRS: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 EDG Processor: 186.63/47.57 DPs: 186.63/47.57 b#(b(c(x1))) -> a#(x1) 186.63/47.57 a#(x1) -> b#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 TRS: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 graph: 186.63/47.57 b#(b(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1) 186.63/47.57 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 186.63/47.57 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 186.63/47.57 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(a(x1)) 186.63/47.57 Arctic Interpretation Processor: 186.63/47.57 dimension: 2 186.63/47.57 usable rules: 186.63/47.57 a(x1) -> b(x1) 186.63/47.57 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.57 c(c(x1)) -> x1 186.63/47.57 interpretation: 186.63/47.57 [b#](x0) = [1 0]x0 + [0], 186.63/47.57 186.63/47.57 [a#](x0) = [1 0]x0 + [0], 186.63/47.57 186.63/47.57 [-& 0 ] [0] 186.63/47.57 [c](x0) = [0 1 ]x0 + [1], 186.63/47.57 186.63/47.57 [-& 0 ] [0] 186.63/47.57 [b](x0) = [0 -&]x0 + [0], 186.63/47.57 186.63/47.58 [-& 0 ] [0] 186.63/47.58 [a](x0) = [0 -&]x0 + [0] 186.63/47.58 orientation: 186.63/47.58 b#(b(c(x1))) = [1 2]x1 + [2] >= [1 0]x1 + [0] = a#(x1) 186.63/47.58 186.63/47.58 a#(x1) = [1 0]x1 + [0] >= [1 0]x1 + [0] = b#(x1) 186.63/47.58 186.63/47.58 b#(b(c(x1))) = [1 2]x1 + [2] >= [0 1]x1 + [1] = a#(a(x1)) 186.63/47.58 186.63/47.58 [-& 0 ] [0] [-& 0 ] [0] 186.63/47.58 a(x1) = [0 -&]x1 + [0] >= [0 -&]x1 + [0] = b(x1) 186.63/47.58 186.63/47.58 [-& 0 ] [0] [-& 0 ] [0] 186.63/47.58 b(b(c(x1))) = [0 1 ]x1 + [1] >= [0 1 ]x1 + [1] = c(b(c(a(a(x1))))) 186.63/47.58 186.63/47.58 [0 1] [1] 186.63/47.58 c(c(x1)) = [1 2]x1 + [2] >= x1 = x1 186.63/47.58 problem: 186.63/47.58 DPs: 186.63/47.58 b#(b(c(x1))) -> a#(x1) 186.63/47.58 a#(x1) -> b#(x1) 186.63/47.58 TRS: 186.63/47.58 a(x1) -> b(x1) 186.63/47.58 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.58 c(c(x1)) -> x1 186.63/47.58 Restore Modifier: 186.63/47.58 DPs: 186.63/47.58 b#(b(c(x1))) -> a#(x1) 186.63/47.58 a#(x1) -> b#(x1) 186.63/47.58 TRS: 186.63/47.58 a(x1) -> b(x1) 186.63/47.58 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.58 c(c(x1)) -> x1 186.63/47.58 EDG Processor: 186.63/47.58 DPs: 186.63/47.58 b#(b(c(x1))) -> a#(x1) 186.63/47.58 a#(x1) -> b#(x1) 186.63/47.58 TRS: 186.63/47.58 a(x1) -> b(x1) 186.63/47.58 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.58 c(c(x1)) -> x1 186.63/47.58 graph: 186.63/47.58 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 186.63/47.58 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 186.63/47.58 Usable Rule Processor: 186.63/47.58 DPs: 186.63/47.58 b#(b(c(x1))) -> a#(x1) 186.63/47.58 a#(x1) -> b#(x1) 186.63/47.58 TRS: 186.63/47.58 186.63/47.58 Arctic Interpretation Processor: 186.63/47.58 dimension: 1 186.63/47.58 usable rules: 186.63/47.58 186.63/47.58 interpretation: 186.63/47.58 [b#](x0) = x0, 186.63/47.58 186.63/47.58 [a#](x0) = x0, 186.63/47.58 186.63/47.58 [c](x0) = 1x0, 186.63/47.58 186.63/47.58 [b](x0) = x0 186.63/47.58 orientation: 186.63/47.58 b#(b(c(x1))) = 1x1 >= x1 = a#(x1) 186.63/47.58 186.63/47.58 a#(x1) = x1 >= x1 = b#(x1) 186.63/47.58 problem: 186.63/47.58 DPs: 186.63/47.58 a#(x1) -> b#(x1) 186.63/47.58 TRS: 186.63/47.58 186.63/47.58 Restore Modifier: 186.63/47.58 DPs: 186.63/47.58 a#(x1) -> b#(x1) 186.63/47.58 TRS: 186.63/47.58 a(x1) -> b(x1) 186.63/47.58 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.58 c(c(x1)) -> x1 186.63/47.58 EDG Processor: 186.63/47.58 DPs: 186.63/47.58 a#(x1) -> b#(x1) 186.63/47.58 TRS: 186.63/47.58 a(x1) -> b(x1) 186.63/47.58 b(b(c(x1))) -> c(b(c(a(a(x1))))) 186.63/47.58 c(c(x1)) -> x1 186.63/47.58 graph: 186.63/47.58 186.63/47.58 SCC Processor: 186.63/47.58 #sccs: 0 186.63/47.58 #rules: 0 186.63/47.58 #arcs: 0/1 186.63/47.58 186.63/47.58 EOF