179.03/45.76 YES 179.03/45.77 179.03/45.77 Problem: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 179.03/45.77 Proof: 179.03/45.77 DP Processor: 179.03/45.77 DPs: 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 b#(b(c(x1))) -> a#(x1) 179.03/45.77 b#(b(c(x1))) -> b#(a(x1)) 179.03/45.77 b#(b(c(x1))) -> c#(b(a(x1))) 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) 179.03/45.77 b#(b(c(x1))) -> c#(b(c(b(a(x1))))) 179.03/45.77 TRS: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 TDG Processor: 179.03/45.77 DPs: 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 b#(b(c(x1))) -> a#(x1) 179.03/45.77 b#(b(c(x1))) -> b#(a(x1)) 179.03/45.77 b#(b(c(x1))) -> c#(b(a(x1))) 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) 179.03/45.77 b#(b(c(x1))) -> c#(b(c(b(a(x1))))) 179.03/45.77 TRS: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 graph: 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) -> 179.03/45.77 b#(b(c(x1))) -> c#(b(c(b(a(x1))))) 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) -> 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) -> b#(b(c(x1))) -> c#(b(a(x1))) 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) -> b#(b(c(x1))) -> b#(a(x1)) 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) -> b#(b(c(x1))) -> a#(x1) 179.03/45.77 b#(b(c(x1))) -> b#(a(x1)) -> b#(b(c(x1))) -> c#(b(c(b(a(x1))))) 179.03/45.77 b#(b(c(x1))) -> b#(a(x1)) -> b#(b(c(x1))) -> b#(c(b(a(x1)))) 179.03/45.77 b#(b(c(x1))) -> b#(a(x1)) -> b#(b(c(x1))) -> c#(b(a(x1))) 179.03/45.77 b#(b(c(x1))) -> b#(a(x1)) -> b#(b(c(x1))) -> b#(a(x1)) 179.03/45.77 b#(b(c(x1))) -> b#(a(x1)) -> b#(b(c(x1))) -> a#(x1) 179.03/45.77 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 179.03/45.77 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(b(c(b(a(x1))))) 179.03/45.77 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(c(b(a(x1)))) 179.03/45.77 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(b(a(x1))) 179.03/45.77 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(a(x1)) 179.03/45.77 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 179.03/45.77 SCC Processor: 179.03/45.77 #sccs: 1 179.03/45.77 #rules: 4 179.03/45.77 #arcs: 16/36 179.03/45.77 DPs: 179.03/45.77 b#(b(c(x1))) -> b#(c(b(a(x1)))) 179.03/45.77 b#(b(c(x1))) -> a#(x1) 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 b#(b(c(x1))) -> b#(a(x1)) 179.03/45.77 TRS: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 Arctic Interpretation Processor: 179.03/45.77 dimension: 2 179.03/45.77 usable rules: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 interpretation: 179.03/45.77 [b#](x0) = [3 2]x0 + [0], 179.03/45.77 179.03/45.77 [a#](x0) = [3 2]x0 + [0], 179.03/45.77 179.03/45.77 [-& 0 ] [0] 179.03/45.77 [c](x0) = [0 2 ]x0 + [3], 179.03/45.77 179.03/45.77 [-& 0 ] [0 ] 179.03/45.77 [b](x0) = [0 -&]x0 + [-&], 179.03/45.77 179.03/45.77 [-& 0 ] [0] 179.03/45.77 [a](x0) = [0 0 ]x0 + [0] 179.03/45.77 orientation: 179.03/45.77 b#(b(c(x1))) = [3 5]x1 + [6] >= [2 4]x1 + [5] = b#(c(b(a(x1)))) 179.03/45.77 179.03/45.77 b#(b(c(x1))) = [3 5]x1 + [6] >= [3 2]x1 + [0] = a#(x1) 179.03/45.77 179.03/45.77 a#(x1) = [3 2]x1 + [0] >= [3 2]x1 + [0] = b#(x1) 179.03/45.77 179.03/45.77 b#(b(c(x1))) = [3 5]x1 + [6] >= [2 3]x1 + [3] = b#(a(x1)) 179.03/45.77 179.03/45.77 [-& 0 ] [0] [-& 0 ] [0 ] 179.03/45.77 a(x1) = [0 0 ]x1 + [0] >= [0 -&]x1 + [-&] = b(x1) 179.03/45.77 179.03/45.77 [-& 0 ] [0] [-& 0 ] [0] 179.03/45.77 b(b(c(x1))) = [0 2 ]x1 + [3] >= [0 2 ]x1 + [3] = c(b(c(b(a(x1))))) 179.03/45.77 179.03/45.77 [0 2] [3] 179.03/45.77 c(c(x1)) = [2 4]x1 + [5] >= x1 = x1 179.03/45.77 problem: 179.03/45.77 DPs: 179.03/45.77 b#(b(c(x1))) -> a#(x1) 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 TRS: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 Restore Modifier: 179.03/45.77 DPs: 179.03/45.77 b#(b(c(x1))) -> a#(x1) 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 TRS: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 EDG Processor: 179.03/45.77 DPs: 179.03/45.77 b#(b(c(x1))) -> a#(x1) 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 TRS: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 graph: 179.03/45.77 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 179.03/45.77 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 179.03/45.77 Usable Rule Processor: 179.03/45.77 DPs: 179.03/45.77 b#(b(c(x1))) -> a#(x1) 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 TRS: 179.03/45.77 179.03/45.77 Arctic Interpretation Processor: 179.03/45.77 dimension: 1 179.03/45.77 usable rules: 179.03/45.77 179.03/45.77 interpretation: 179.03/45.77 [b#](x0) = x0, 179.03/45.77 179.03/45.77 [a#](x0) = x0, 179.03/45.77 179.03/45.77 [c](x0) = 1x0, 179.03/45.77 179.03/45.77 [b](x0) = x0 179.03/45.77 orientation: 179.03/45.77 b#(b(c(x1))) = 1x1 >= x1 = a#(x1) 179.03/45.77 179.03/45.77 a#(x1) = x1 >= x1 = b#(x1) 179.03/45.77 problem: 179.03/45.77 DPs: 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 TRS: 179.03/45.77 179.03/45.77 Restore Modifier: 179.03/45.77 DPs: 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 TRS: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 EDG Processor: 179.03/45.77 DPs: 179.03/45.77 a#(x1) -> b#(x1) 179.03/45.77 TRS: 179.03/45.77 a(x1) -> b(x1) 179.03/45.77 b(b(c(x1))) -> c(b(c(b(a(x1))))) 179.03/45.77 c(c(x1)) -> x1 179.03/45.77 graph: 179.03/45.77 179.03/45.77 SCC Processor: 179.03/45.77 #sccs: 0 179.03/45.77 #rules: 0 179.03/45.77 #arcs: 0/1 179.03/45.77 179.03/45.77 EOF