182.48/46.63 YES 182.48/46.64 182.48/46.64 Problem: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 182.48/46.64 Proof: 182.48/46.64 DP Processor: 182.48/46.64 DPs: 182.48/46.64 a#(a(x1)) -> c#(x1) 182.48/46.64 a#(a(x1)) -> a#(b(b(c(x1)))) 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) 182.48/46.64 TRS: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 TDG Processor: 182.48/46.64 DPs: 182.48/46.64 a#(a(x1)) -> c#(x1) 182.48/46.64 a#(a(x1)) -> a#(b(b(c(x1)))) 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) 182.48/46.64 TRS: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 graph: 182.48/46.64 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 182.48/46.64 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1)))) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) 182.48/46.64 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 182.48/46.64 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 182.48/46.64 a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1)))) 182.48/46.64 a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> c#(x1) 182.48/46.64 EDG Processor: 182.48/46.64 DPs: 182.48/46.64 a#(a(x1)) -> c#(x1) 182.48/46.64 a#(a(x1)) -> a#(b(b(c(x1)))) 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) 182.48/46.64 TRS: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 graph: 182.48/46.64 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1)))) 182.48/46.64 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 182.48/46.64 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 182.48/46.64 SCC Processor: 182.48/46.64 #sccs: 1 182.48/46.64 #rules: 3 182.48/46.64 #arcs: 6/16 182.48/46.64 DPs: 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) 182.48/46.64 a#(a(x1)) -> c#(x1) 182.48/46.64 TRS: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 Arctic Interpretation Processor: 182.48/46.64 dimension: 2 182.48/46.64 usable rules: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 interpretation: 182.48/46.64 [c#](x0) = [0 1]x0 + [0], 182.48/46.64 182.48/46.64 [a#](x0) = [1 1]x0 + [2], 182.48/46.64 182.48/46.64 [1 0] [2] 182.48/46.64 [b](x0) = [0 0]x0 + [1], 182.48/46.64 182.48/46.64 [-& 0 ] [0 ] 182.48/46.64 [c](x0) = [0 -&]x0 + [-&], 182.48/46.64 182.48/46.64 [-& 0 ] [0] 182.48/46.64 [a](x0) = [0 1 ]x0 + [2] 182.48/46.64 orientation: 182.48/46.64 c#(b(x1)) = [1 1]x1 + [2] >= [0 1]x1 + [0] = c#(x1) 182.48/46.64 182.48/46.64 c#(b(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a#(c(x1)) 182.48/46.64 182.48/46.64 a#(a(x1)) = [1 2]x1 + [3] >= [0 1]x1 + [0] = c#(x1) 182.48/46.64 182.48/46.64 [0 1] [2] [0 1] [2] 182.48/46.64 a(a(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = a(b(b(c(x1)))) 182.48/46.64 182.48/46.64 [0 0] [1] 182.48/46.64 a(b(x1)) = [1 1]x1 + [2] >= x1 = x1 182.48/46.64 182.48/46.64 [0 0] [1] [0 -&] [0] 182.48/46.64 c(b(x1)) = [1 0]x1 + [2] >= [1 0 ]x1 + [2] = a(c(x1)) 182.48/46.64 problem: 182.48/46.64 DPs: 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) 182.48/46.64 TRS: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 Restore Modifier: 182.48/46.64 DPs: 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) 182.48/46.64 TRS: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 EDG Processor: 182.48/46.64 DPs: 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 c#(b(x1)) -> a#(c(x1)) 182.48/46.64 TRS: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 graph: 182.48/46.64 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 182.48/46.64 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 182.48/46.64 SCC Processor: 182.48/46.64 #sccs: 1 182.48/46.64 #rules: 1 182.48/46.64 #arcs: 2/4 182.48/46.64 DPs: 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 TRS: 182.48/46.64 a(a(x1)) -> a(b(b(c(x1)))) 182.48/46.64 a(b(x1)) -> x1 182.48/46.64 c(b(x1)) -> a(c(x1)) 182.48/46.64 Usable Rule Processor: 182.48/46.64 DPs: 182.48/46.64 c#(b(x1)) -> c#(x1) 182.48/46.64 TRS: 182.48/46.64 182.48/46.64 Arctic Interpretation Processor: 182.48/46.64 dimension: 4 182.48/46.64 usable rules: 182.48/46.64 182.48/46.64 interpretation: 182.48/46.64 [c#](x0) = [0 -& -& -&]x0, 182.48/46.64 182.48/46.64 [1 0 0 0] [0] 182.48/46.64 [0 0 0 0] [0] 182.48/46.64 [b](x0) = [1 0 0 0]x0 + [0] 182.48/46.64 [0 0 0 0] [0] 182.48/46.64 orientation: 182.48/46.64 c#(b(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = c#(x1) 182.48/46.64 problem: 182.48/46.64 DPs: 182.48/46.64 182.48/46.64 TRS: 182.48/46.64 182.48/46.64 Qed 182.48/46.64 EOF