169.36/43.27 YES 169.36/43.28 169.36/43.28 Problem: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 169.36/43.28 Proof: 169.36/43.28 DP Processor: 169.36/43.28 DPs: 169.36/43.28 a#(b(b(x1))) -> c#(x1) 169.36/43.28 c#(c(x1)) -> a#(x1) 169.36/43.28 c#(c(x1)) -> c#(a(x1)) 169.36/43.28 c#(c(x1)) -> a#(b(c(a(x1)))) 169.36/43.28 TRS: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 TDG Processor: 169.36/43.28 DPs: 169.36/43.28 a#(b(b(x1))) -> c#(x1) 169.36/43.28 c#(c(x1)) -> a#(x1) 169.36/43.28 c#(c(x1)) -> c#(a(x1)) 169.36/43.28 c#(c(x1)) -> a#(b(c(a(x1)))) 169.36/43.28 TRS: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 graph: 169.36/43.28 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(b(c(a(x1)))) 169.36/43.28 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) 169.36/43.28 c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1) 169.36/43.28 c#(c(x1)) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> c#(x1) 169.36/43.28 c#(c(x1)) -> a#(x1) -> a#(b(b(x1))) -> c#(x1) 169.36/43.28 a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(c(a(x1)))) 169.36/43.28 a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> c#(a(x1)) 169.36/43.28 a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(x1) 169.36/43.28 Arctic Interpretation Processor: 169.36/43.28 dimension: 1 169.36/43.28 usable rules: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 interpretation: 169.36/43.28 [c#](x0) = 2x0 + 0, 169.36/43.28 169.36/43.28 [a#](x0) = x0 + 0, 169.36/43.28 169.36/43.28 [c](x0) = 3x0 + 14, 169.36/43.28 169.36/43.28 [b](x0) = 1x0 + 12, 169.36/43.28 169.36/43.28 [a](x0) = 1x0 + 12 169.36/43.28 orientation: 169.36/43.28 a#(b(b(x1))) = 2x1 + 13 >= 2x1 + 0 = c#(x1) 169.36/43.28 169.36/43.28 c#(c(x1)) = 5x1 + 16 >= x1 + 0 = a#(x1) 169.36/43.28 169.36/43.28 c#(c(x1)) = 5x1 + 16 >= 3x1 + 14 = c#(a(x1)) 169.36/43.28 169.36/43.28 c#(c(x1)) = 5x1 + 16 >= 5x1 + 16 = a#(b(c(a(x1)))) 169.36/43.28 169.36/43.28 a(x1) = 1x1 + 12 >= 1x1 + 12 = b(x1) 169.36/43.28 169.36/43.28 a(b(b(x1))) = 3x1 + 14 >= 3x1 + 14 = c(x1) 169.36/43.28 169.36/43.28 c(c(x1)) = 6x1 + 17 >= 6x1 + 17 = a(b(c(a(x1)))) 169.36/43.28 problem: 169.36/43.28 DPs: 169.36/43.28 a#(b(b(x1))) -> c#(x1) 169.36/43.28 c#(c(x1)) -> a#(b(c(a(x1)))) 169.36/43.28 TRS: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 Restore Modifier: 169.36/43.28 DPs: 169.36/43.28 a#(b(b(x1))) -> c#(x1) 169.36/43.28 c#(c(x1)) -> a#(b(c(a(x1)))) 169.36/43.28 TRS: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 EDG Processor: 169.36/43.28 DPs: 169.36/43.28 a#(b(b(x1))) -> c#(x1) 169.36/43.28 c#(c(x1)) -> a#(b(c(a(x1)))) 169.36/43.28 TRS: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 graph: 169.36/43.28 c#(c(x1)) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> c#(x1) 169.36/43.28 a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(c(a(x1)))) 169.36/43.28 Matrix Interpretation Processor: dim=4 169.36/43.28 169.36/43.28 interpretation: 169.36/43.28 [c#](x0) = [0 0 1 0]x0, 169.36/43.28 169.36/43.28 [a#](x0) = [0 1 0 0]x0, 169.36/43.28 169.36/43.28 [0 0 0 0] [0] 169.36/43.28 [0 0 1 0] [0] 169.36/43.28 [c](x0) = [0 0 0 0]x0 + [1] 169.36/43.28 [0 0 0 0] [0], 169.36/43.28 169.36/43.28 [0 0 0 0] 169.36/43.28 [0 0 0 1] 169.36/43.28 [b](x0) = [0 0 0 0]x0 169.36/43.28 [0 0 1 0] , 169.36/43.28 169.36/43.28 [0 1 1 0] [0] 169.36/43.28 [0 1 0 1] [0] 169.36/43.28 [a](x0) = [0 0 0 0]x0 + [1] 169.36/43.28 [0 0 1 0] [0] 169.36/43.28 orientation: 169.36/43.28 a#(b(b(x1))) = [0 0 1 0]x1 >= [0 0 1 0]x1 = c#(x1) 169.36/43.28 169.36/43.28 c#(c(x1)) = [1] >= [0] = a#(b(c(a(x1)))) 169.36/43.28 169.36/43.28 [0 1 1 0] [0] [0 0 0 0] 169.36/43.28 [0 1 0 1] [0] [0 0 0 1] 169.36/43.28 a(x1) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 = b(x1) 169.36/43.28 [0 0 1 0] [0] [0 0 1 0] 169.36/43.28 169.36/43.28 [0 0 1 0] [0] [0 0 0 0] [0] 169.36/43.28 [0 0 1 0] [0] [0 0 1 0] [0] 169.36/43.28 a(b(b(x1))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = c(x1) 169.36/43.28 [0 0 0 0] [0] [0 0 0 0] [0] 169.36/43.28 169.36/43.28 [0] [0] 169.36/43.28 [1] [1] 169.36/43.28 c(c(x1)) = [1] >= [1] = a(b(c(a(x1)))) 169.36/43.28 [0] [0] 169.36/43.28 problem: 169.36/43.28 DPs: 169.36/43.28 a#(b(b(x1))) -> c#(x1) 169.36/43.28 TRS: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 Restore Modifier: 169.36/43.28 DPs: 169.36/43.28 a#(b(b(x1))) -> c#(x1) 169.36/43.28 TRS: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 EDG Processor: 169.36/43.28 DPs: 169.36/43.28 a#(b(b(x1))) -> c#(x1) 169.36/43.28 TRS: 169.36/43.28 a(x1) -> b(x1) 169.36/43.28 a(b(b(x1))) -> c(x1) 169.36/43.28 c(c(x1)) -> a(b(c(a(x1)))) 169.36/43.28 graph: 169.36/43.28 169.36/43.28 SCC Processor: 169.36/43.28 #sccs: 0 169.36/43.28 #rules: 0 169.36/43.28 #arcs: 0/1 169.36/43.28 169.36/43.28 EOF