178.97/45.59 YES 178.97/45.60 178.97/45.60 Problem: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 178.97/45.60 Proof: 178.97/45.60 DP Processor: 178.97/45.60 DPs: 178.97/45.60 a#(x1) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> b#(b(x1)) 178.97/45.60 b#(b(c(x1))) -> c#(b(b(x1))) 178.97/45.60 b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 b#(b(c(x1))) -> c#(a(c(b(b(x1))))) 178.97/45.60 TRS: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 TDG Processor: 178.97/45.60 DPs: 178.97/45.60 a#(x1) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> b#(b(x1)) 178.97/45.60 b#(b(c(x1))) -> c#(b(b(x1))) 178.97/45.60 b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 b#(b(c(x1))) -> c#(a(c(b(b(x1))))) 178.97/45.60 TRS: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 graph: 178.97/45.60 b#(b(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(a(c(b(b(x1))))) 178.97/45.60 b#(b(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 b#(b(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(b(b(x1))) 178.97/45.60 b#(b(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> b#(b(x1)) 178.97/45.60 b#(b(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(b(b(x1))))) 178.97/45.60 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(b(b(x1))) 178.97/45.60 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(b(x1)) 178.97/45.60 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> a#(c(b(b(x1)))) -> a#(x1) -> b#(x1) 178.97/45.60 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(b(b(x1))))) 178.97/45.60 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(b(b(x1))) 178.97/45.60 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(b(x1)) 178.97/45.60 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 178.97/45.60 SCC Processor: 178.97/45.60 #sccs: 1 178.97/45.60 #rules: 4 178.97/45.60 #arcs: 16/36 178.97/45.60 DPs: 178.97/45.60 b#(b(c(x1))) -> b#(b(x1)) 178.97/45.60 b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 a#(x1) -> b#(x1) 178.97/45.60 TRS: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 Arctic Interpretation Processor: 178.97/45.60 dimension: 2 178.97/45.60 usable rules: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 interpretation: 178.97/45.60 [b#](x0) = [1 0]x0 + [0], 178.97/45.60 178.97/45.60 [a#](x0) = [3 1]x0 + [2], 178.97/45.60 178.97/45.60 [-& 0 ] [0] 178.97/45.60 [c](x0) = [0 2 ]x0 + [3], 178.97/45.60 178.97/45.60 [-& 0 ] [0] 178.97/45.60 [b](x0) = [0 -&]x0 + [1], 178.97/45.60 178.97/45.60 [0 0 ] [0] 178.97/45.60 [a](x0) = [0 -&]x0 + [1] 178.97/45.60 orientation: 178.97/45.60 b#(b(c(x1))) = [1 3]x1 + [4] >= [0 1]x1 + [1] = b#(b(x1)) 178.97/45.60 178.97/45.60 b#(b(c(x1))) = [1 3]x1 + [4] >= [1 0]x1 + [0] = b#(x1) 178.97/45.60 178.97/45.60 b#(b(c(x1))) = [1 3]x1 + [4] >= [1 3]x1 + [4] = a#(c(b(b(x1)))) 178.97/45.60 178.97/45.60 a#(x1) = [3 1]x1 + [2] >= [1 0]x1 + [0] = b#(x1) 178.97/45.60 178.97/45.60 [0 0 ] [0] [-& 0 ] [0] 178.97/45.60 a(x1) = [0 -&]x1 + [1] >= [0 -&]x1 + [1] = b(x1) 178.97/45.60 178.97/45.60 [-& 0 ] [1] [-& 0 ] [1] 178.97/45.60 b(b(c(x1))) = [0 2 ]x1 + [3] >= [0 2 ]x1 + [3] = c(a(c(b(b(x1))))) 178.97/45.60 178.97/45.60 [0 2] [3] 178.97/45.60 c(c(x1)) = [2 4]x1 + [5] >= x1 = x1 178.97/45.60 problem: 178.97/45.60 DPs: 178.97/45.60 b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 TRS: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 Restore Modifier: 178.97/45.60 DPs: 178.97/45.60 b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 TRS: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 EDG Processor: 178.97/45.60 DPs: 178.97/45.60 b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 TRS: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 graph: 178.97/45.60 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 178.97/45.60 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(c(b(b(x1)))) 178.97/45.60 SCC Processor: 178.97/45.60 #sccs: 1 178.97/45.60 #rules: 1 178.97/45.60 #arcs: 2/4 178.97/45.60 DPs: 178.97/45.60 b#(b(c(x1))) -> b#(x1) 178.97/45.60 TRS: 178.97/45.60 a(x1) -> b(x1) 178.97/45.60 b(b(c(x1))) -> c(a(c(b(b(x1))))) 178.97/45.60 c(c(x1)) -> x1 178.97/45.60 Usable Rule Processor: 178.97/45.60 DPs: 178.97/45.60 b#(b(c(x1))) -> b#(x1) 178.97/45.60 TRS: 178.97/45.60 178.97/45.60 Arctic Interpretation Processor: 178.97/45.60 dimension: 1 178.97/45.60 usable rules: 178.97/45.60 178.97/45.60 interpretation: 178.97/45.60 [b#](x0) = 6x0, 178.97/45.60 178.97/45.60 [c](x0) = x0 + 9, 178.97/45.60 178.97/45.60 [b](x0) = 1x0 + 12 178.97/45.60 orientation: 178.97/45.60 b#(b(c(x1))) = 7x1 + 18 >= 6x1 = b#(x1) 178.97/45.60 problem: 178.97/45.60 DPs: 178.97/45.60 178.97/45.60 TRS: 178.97/45.60 178.97/45.60 Qed 178.97/45.61 EOF