178.37/45.57 YES 178.37/45.57 178.37/45.57 Problem: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 178.37/45.57 Proof: 178.37/45.57 DP Processor: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(a(x1)) 178.37/45.57 b#(a(c(x1))) -> c#(a(a(x1))) 178.37/45.57 b#(a(c(x1))) -> a#(c(a(a(x1)))) 178.37/45.57 b#(a(c(x1))) -> c#(a(c(a(a(x1))))) 178.37/45.57 TRS: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 TDG Processor: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(a(x1)) 178.37/45.57 b#(a(c(x1))) -> c#(a(a(x1))) 178.37/45.57 b#(a(c(x1))) -> a#(c(a(a(x1)))) 178.37/45.57 b#(a(c(x1))) -> c#(a(c(a(a(x1))))) 178.37/45.57 TRS: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 graph: 178.37/45.57 b#(a(c(x1))) -> a#(c(a(a(x1)))) -> a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 178.37/45.57 a#(x1) -> b#(x1) -> b#(a(c(x1))) -> c#(a(c(a(a(x1))))) 178.37/45.57 a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(c(a(a(x1)))) 178.37/45.57 a#(x1) -> b#(x1) -> b#(a(c(x1))) -> c#(a(a(x1))) 178.37/45.57 a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(a(x1)) 178.37/45.57 a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(x1) 178.37/45.57 SCC Processor: 178.37/45.57 #sccs: 1 178.37/45.57 #rules: 4 178.37/45.57 #arcs: 8/36 178.37/45.57 DPs: 178.37/45.57 b#(a(c(x1))) -> a#(c(a(a(x1)))) 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(a(x1)) 178.37/45.57 TRS: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 Arctic Interpretation Processor: 178.37/45.57 dimension: 2 178.37/45.57 usable rules: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 interpretation: 178.37/45.57 [b#](x0) = [2 0]x0 + [0], 178.37/45.57 178.37/45.57 [a#](x0) = [2 0]x0 + [3], 178.37/45.57 178.37/45.57 [-& 0 ] [0] 178.37/45.57 [c](x0) = [0 1 ]x0 + [2], 178.37/45.57 178.37/45.57 [-& 0 ] [0 ] 178.37/45.57 [b](x0) = [0 -&]x0 + [-&], 178.37/45.57 178.37/45.57 [-& 0 ] [0] 178.37/45.57 [a](x0) = [0 -&]x0 + [0] 178.37/45.57 orientation: 178.37/45.57 b#(a(c(x1))) = [2 3]x1 + [4] >= [0 2]x1 + [3] = a#(c(a(a(x1)))) 178.37/45.57 178.37/45.57 a#(x1) = [2 0]x1 + [3] >= [2 0]x1 + [0] = b#(x1) 178.37/45.57 178.37/45.57 b#(a(c(x1))) = [2 3]x1 + [4] >= [2 0]x1 + [3] = a#(x1) 178.37/45.57 178.37/45.57 b#(a(c(x1))) = [2 3]x1 + [4] >= [0 2]x1 + [3] = a#(a(x1)) 178.37/45.57 178.37/45.57 [-& 0 ] [0] [-& 0 ] [0 ] 178.37/45.57 a(x1) = [0 -&]x1 + [0] >= [0 -&]x1 + [-&] = b(x1) 178.37/45.57 178.37/45.57 [-& 0 ] [0] [-& 0 ] [0] 178.37/45.57 b(a(c(x1))) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = c(a(c(a(a(x1))))) 178.37/45.57 178.37/45.57 [0 1] [2] 178.37/45.57 c(c(x1)) = [1 2]x1 + [3] >= x1 = x1 178.37/45.57 problem: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(x1) 178.37/45.57 TRS: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 Restore Modifier: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(x1) 178.37/45.57 TRS: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 EDG Processor: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(x1) 178.37/45.57 TRS: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 graph: 178.37/45.57 b#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 178.37/45.57 a#(x1) -> b#(x1) -> b#(a(c(x1))) -> a#(x1) 178.37/45.57 Usable Rule Processor: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 b#(a(c(x1))) -> a#(x1) 178.37/45.57 TRS: 178.37/45.57 178.37/45.57 Arctic Interpretation Processor: 178.37/45.57 dimension: 1 178.37/45.57 usable rules: 178.37/45.57 178.37/45.57 interpretation: 178.37/45.57 [b#](x0) = x0, 178.37/45.57 178.37/45.57 [a#](x0) = x0, 178.37/45.57 178.37/45.57 [c](x0) = 5x0 + 14, 178.37/45.57 178.37/45.57 [a](x0) = x0 + 0 178.37/45.57 orientation: 178.37/45.57 a#(x1) = x1 >= x1 = b#(x1) 178.37/45.57 178.37/45.57 b#(a(c(x1))) = 5x1 + 14 >= x1 = a#(x1) 178.37/45.57 problem: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 TRS: 178.37/45.57 178.37/45.57 Restore Modifier: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 TRS: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 EDG Processor: 178.37/45.57 DPs: 178.37/45.57 a#(x1) -> b#(x1) 178.37/45.57 TRS: 178.37/45.57 a(x1) -> b(x1) 178.37/45.57 b(a(c(x1))) -> c(a(c(a(a(x1))))) 178.37/45.57 c(c(x1)) -> x1 178.37/45.57 graph: 178.37/45.57 178.37/45.57 SCC Processor: 178.37/45.57 #sccs: 0 178.37/45.57 #rules: 0 178.37/45.57 #arcs: 0/1 178.37/45.57 178.37/45.58 EOF