185.75/47.42 YES 185.75/47.43 185.75/47.43 Problem: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 185.75/47.43 Proof: 185.75/47.43 DP Processor: 185.75/47.43 DPs: 185.75/47.43 a#(a(x1)) -> c#(x1) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) 185.75/47.43 a#(a(x1)) -> a#(b(c(c(x1)))) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 TDG Processor: 185.75/47.43 DPs: 185.75/47.43 a#(a(x1)) -> c#(x1) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) 185.75/47.43 a#(a(x1)) -> a#(b(c(c(x1)))) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 graph: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(c(c(x1)))) 185.75/47.43 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(x1) 185.75/47.43 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(c(c(x1)))) 185.75/47.43 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1)) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 185.75/47.43 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(x1)) 185.75/47.43 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 185.75/47.43 a#(a(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> a#(b(c(c(x1)))) 185.75/47.43 a#(a(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> c#(c(x1)) 185.75/47.43 a#(a(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> c#(x1) 185.75/47.43 EDG Processor: 185.75/47.43 DPs: 185.75/47.43 a#(a(x1)) -> c#(x1) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) 185.75/47.43 a#(a(x1)) -> a#(b(c(c(x1)))) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 graph: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(x1) 185.75/47.43 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(c(c(x1)))) 185.75/47.43 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 185.75/47.43 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(c(c(x1)))) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1)) 185.75/47.43 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 185.75/47.43 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(x1)) 185.75/47.43 SCC Processor: 185.75/47.43 #sccs: 1 185.75/47.43 #rules: 4 185.75/47.43 #arcs: 10/25 185.75/47.43 DPs: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 a#(a(x1)) -> c#(x1) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 Arctic Interpretation Processor: 185.75/47.43 dimension: 2 185.75/47.43 usable rules: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 interpretation: 185.75/47.43 [c#](x0) = [0 1]x0, 185.75/47.43 185.75/47.43 [a#](x0) = [1 1]x0 + [0], 185.75/47.43 185.75/47.43 [1 2] [2] 185.75/47.43 [b](x0) = [0 1]x0 + [1], 185.75/47.43 185.75/47.43 [-& 0 ] [0 ] 185.75/47.43 [c](x0) = [0 -&]x0 + [-&], 185.75/47.43 185.75/47.43 [-& 0 ] [0] 185.75/47.43 [a](x0) = [0 1 ]x0 + [1] 185.75/47.43 orientation: 185.75/47.43 c#(b(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = a#(a(x1)) 185.75/47.43 185.75/47.43 a#(a(x1)) = [1 2]x1 + [2] >= [1 0]x1 + [0] = c#(c(x1)) 185.75/47.43 185.75/47.43 c#(b(x1)) = [1 2]x1 + [2] >= [1 1]x1 + [0] = a#(x1) 185.75/47.43 185.75/47.43 a#(a(x1)) = [1 2]x1 + [2] >= [0 1]x1 = c#(x1) 185.75/47.43 185.75/47.43 [0 1] [1] [0 1] [1] 185.75/47.43 a(a(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = a(b(c(c(x1)))) 185.75/47.43 185.75/47.43 [0 1 ] [1] 185.75/47.43 c(a(x1)) = [-& 0 ]x1 + [0] >= x1 = x1 185.75/47.43 185.75/47.43 [0 1] [1] [0 1] [1] 185.75/47.43 c(b(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = a(a(x1)) 185.75/47.43 problem: 185.75/47.43 DPs: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 Restore Modifier: 185.75/47.43 DPs: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 EDG Processor: 185.75/47.43 DPs: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 graph: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(c(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(x1)) 185.75/47.43 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 185.75/47.43 Arctic Interpretation Processor: 185.75/47.43 dimension: 2 185.75/47.43 usable rules: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 interpretation: 185.75/47.43 [c#](x0) = [-1 -&]x0 + [0], 185.75/47.43 185.75/47.43 [a#](x0) = [-& 0 ]x0 + [1], 185.75/47.43 185.75/47.43 [0 2 ] [2 ] 185.75/47.43 [b](x0) = [-2 0 ]x0 + [-&], 185.75/47.43 185.75/47.43 [-& 1 ] [0 ] 185.75/47.43 [c](x0) = [0 -&]x0 + [-&], 185.75/47.43 185.75/47.43 [-& 0 ] [0] 185.75/47.43 [a](x0) = [-1 1 ]x0 + [0] 185.75/47.43 orientation: 185.75/47.43 c#(b(x1)) = [-1 1 ]x1 + [1] >= [-1 1 ]x1 + [1] = a#(a(x1)) 185.75/47.43 185.75/47.43 a#(a(x1)) = [-1 1 ]x1 + [1] >= [-& 0 ]x1 + [0] = c#(c(x1)) 185.75/47.43 185.75/47.43 c#(b(x1)) = [-1 1 ]x1 + [1] >= [-& 0 ]x1 + [1] = a#(x1) 185.75/47.43 185.75/47.43 [-1 1 ] [0] [-1 1 ] [0] 185.75/47.43 a(a(x1)) = [0 2 ]x1 + [1] >= [0 2 ]x1 + [1] = a(b(c(c(x1)))) 185.75/47.43 185.75/47.43 [0 2 ] [1] 185.75/47.43 c(a(x1)) = [-& 0 ]x1 + [0] >= x1 = x1 185.75/47.43 185.75/47.43 [-1 1 ] [0] [-1 1 ] [0] 185.75/47.43 c(b(x1)) = [0 2 ]x1 + [2] >= [0 2 ]x1 + [1] = a(a(x1)) 185.75/47.43 problem: 185.75/47.43 DPs: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 Restore Modifier: 185.75/47.43 DPs: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 EDG Processor: 185.75/47.43 DPs: 185.75/47.43 c#(b(x1)) -> a#(a(x1)) 185.75/47.43 c#(b(x1)) -> a#(x1) 185.75/47.43 TRS: 185.75/47.43 a(a(x1)) -> a(b(c(c(x1)))) 185.75/47.43 c(a(x1)) -> x1 185.75/47.43 c(b(x1)) -> a(a(x1)) 185.75/47.43 graph: 185.75/47.43 185.75/47.43 SCC Processor: 185.75/47.43 #sccs: 0 185.75/47.43 #rules: 0 185.75/47.43 #arcs: 0/4 185.75/47.43 185.75/47.43 EOF