178.65/45.67 YES 178.65/45.67 178.65/45.67 Problem: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 178.65/45.67 Proof: 178.65/45.67 DP Processor: 178.65/45.67 DPs: 178.65/45.67 a#(a(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> a#(b(c(x1))) 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(c(x1)) 178.65/45.67 c#(b(x1)) -> a#(a(c(x1))) 178.65/45.67 TRS: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 TDG Processor: 178.65/45.67 DPs: 178.65/45.67 a#(a(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> a#(b(c(x1))) 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(c(x1)) 178.65/45.67 c#(b(x1)) -> a#(a(c(x1))) 178.65/45.67 TRS: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 graph: 178.65/45.67 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1))) 178.65/45.67 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 178.65/45.67 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(x1))) 178.65/45.67 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) 178.65/45.67 c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1))) 178.65/45.67 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 178.65/45.67 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) 178.65/45.67 a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1) 178.65/45.67 EDG Processor: 178.65/45.67 DPs: 178.65/45.67 a#(a(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> a#(b(c(x1))) 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(c(x1)) 178.65/45.67 c#(b(x1)) -> a#(a(c(x1))) 178.65/45.67 TRS: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 graph: 178.65/45.67 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 178.65/45.67 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1))) 178.65/45.67 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(x1))) 178.65/45.67 c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(a(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) 178.65/45.67 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 178.65/45.67 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(x1))) 178.65/45.67 SCC Processor: 178.65/45.67 #sccs: 1 178.65/45.67 #rules: 4 178.65/45.67 #arcs: 10/25 178.65/45.67 DPs: 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(a(c(x1))) 178.65/45.67 a#(a(x1)) -> c#(x1) 178.65/45.67 c#(b(x1)) -> a#(c(x1)) 178.65/45.67 TRS: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 Arctic Interpretation Processor: 178.65/45.67 dimension: 2 178.65/45.67 usable rules: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 interpretation: 178.65/45.67 [c#](x0) = [0 1]x0 + [2], 178.65/45.67 178.65/45.67 [a#](x0) = [-& 0 ]x0 + [0], 178.65/45.67 178.65/45.67 [2 1] [3] 178.65/45.67 [b](x0) = [1 0]x0 + [2], 178.65/45.67 178.65/45.67 [-& 0 ] [0] 178.65/45.67 [c](x0) = [0 -&]x0 + [1], 178.65/45.67 178.65/45.67 [-& 0 ] [0] 178.65/45.67 [a](x0) = [0 1 ]x0 + [2] 178.65/45.67 orientation: 178.65/45.67 c#(b(x1)) = [2 1]x1 + [3] >= [0 1]x1 + [2] = c#(x1) 178.65/45.67 178.65/45.67 c#(b(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = a#(a(c(x1))) 178.65/45.67 178.65/45.67 a#(a(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = c#(x1) 178.65/45.67 178.65/45.67 c#(b(x1)) = [2 1]x1 + [3] >= [0 -&]x1 + [1] = a#(c(x1)) 178.65/45.67 178.65/45.67 [0 1] [2] [0 1] [2] 178.65/45.67 a(a(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = a(b(c(x1))) 178.65/45.67 178.65/45.67 [0 1 ] [2] 178.65/45.67 c(a(x1)) = [-& 0 ]x1 + [1] >= x1 = x1 178.65/45.67 178.65/45.67 [1 0] [2] [1 0] [2] 178.65/45.67 c(b(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = a(a(c(x1))) 178.65/45.67 problem: 178.65/45.67 DPs: 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> c#(x1) 178.65/45.67 TRS: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 Restore Modifier: 178.65/45.67 DPs: 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> c#(x1) 178.65/45.67 TRS: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 EDG Processor: 178.65/45.67 DPs: 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> c#(x1) 178.65/45.67 TRS: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 graph: 178.65/45.67 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 178.65/45.67 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 178.65/45.67 SCC Processor: 178.65/45.67 #sccs: 1 178.65/45.67 #rules: 1 178.65/45.67 #arcs: 2/4 178.65/45.67 DPs: 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 TRS: 178.65/45.67 a(a(x1)) -> a(b(c(x1))) 178.65/45.67 c(a(x1)) -> x1 178.65/45.67 c(b(x1)) -> a(a(c(x1))) 178.65/45.67 Usable Rule Processor: 178.65/45.67 DPs: 178.65/45.67 c#(b(x1)) -> c#(x1) 178.65/45.67 TRS: 178.65/45.67 178.65/45.67 Arctic Interpretation Processor: 178.65/45.67 dimension: 4 178.65/45.67 usable rules: 178.65/45.67 178.65/45.67 interpretation: 178.65/45.67 [c#](x0) = [0 -& -& -&]x0, 178.65/45.67 178.65/45.67 [1 0 0 0] [0] 178.65/45.67 [0 0 0 0] [0] 178.65/45.67 [b](x0) = [1 0 0 0]x0 + [0] 178.65/45.67 [0 0 0 0] [0] 178.65/45.67 orientation: 178.65/45.67 c#(b(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = c#(x1) 178.65/45.67 problem: 178.65/45.67 DPs: 178.65/45.67 178.65/45.67 TRS: 178.65/45.67 178.65/45.67 Qed 178.65/45.68 EOF