186.81/47.63 YES 186.81/47.64 186.81/47.64 Problem: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 186.81/47.64 Proof: 186.81/47.64 DP Processor: 186.81/47.64 DPs: 186.81/47.64 a#(a(b(x1))) -> c#(x1) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 a#(a(b(x1))) -> a#(b(a(a(c(x1))))) 186.81/47.64 TRS: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 TDG Processor: 186.81/47.64 DPs: 186.81/47.64 a#(a(b(x1))) -> c#(x1) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 a#(a(b(x1))) -> a#(b(a(a(c(x1))))) 186.81/47.64 TRS: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 graph: 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(b(a(a(c(x1))))) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> c#(x1) 186.81/47.64 a#(a(b(x1))) -> a#(b(a(a(c(x1))))) -> 186.81/47.64 a#(a(b(x1))) -> a#(b(a(a(c(x1))))) 186.81/47.64 a#(a(b(x1))) -> a#(b(a(a(c(x1))))) -> 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 a#(a(b(x1))) -> a#(b(a(a(c(x1))))) -> 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(b(a(a(c(x1))))) -> a#(a(b(x1))) -> c#(x1) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(b(a(a(c(x1))))) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> c#(x1) 186.81/47.64 EDG Processor: 186.81/47.64 DPs: 186.81/47.64 a#(a(b(x1))) -> c#(x1) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 a#(a(b(x1))) -> a#(b(a(a(c(x1))))) 186.81/47.64 TRS: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 graph: 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> c#(x1) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(b(a(a(c(x1))))) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> c#(x1) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(b(a(a(c(x1))))) 186.81/47.64 SCC Processor: 186.81/47.64 #sccs: 1 186.81/47.64 #rules: 2 186.81/47.64 #arcs: 8/16 186.81/47.64 DPs: 186.81/47.64 a#(a(b(x1))) -> a#(c(x1)) 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 TRS: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 Arctic Interpretation Processor: 186.81/47.64 dimension: 2 186.81/47.64 usable rules: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 interpretation: 186.81/47.64 [a#](x0) = [0 2]x0 + [0], 186.81/47.64 186.81/47.64 [0 0 ] [0 ] 186.81/47.64 [c](x0) = [0 -&]x0 + [-&], 186.81/47.64 186.81/47.64 [-& 0 ] [2 ] 186.81/47.64 [b](x0) = [0 -&]x0 + [-&], 186.81/47.64 186.81/47.64 [-& 0 ] [2] 186.81/47.64 [a](x0) = [0 2 ]x0 + [1] 186.81/47.64 orientation: 186.81/47.64 a#(a(b(x1))) = [4 2]x1 + [4] >= [2 0]x1 + [0] = a#(c(x1)) 186.81/47.64 186.81/47.64 a#(a(b(x1))) = [4 2]x1 + [4] >= [4 2]x1 + [3] = a#(a(c(x1))) 186.81/47.64 186.81/47.64 [-& 0 ] [2] [-& 0 ] [2 ] 186.81/47.64 a(x1) = [0 2 ]x1 + [1] >= [0 -&]x1 + [-&] = b(x1) 186.81/47.64 186.81/47.64 [2 0] [2] [2 0] [2] 186.81/47.64 a(a(b(x1))) = [4 2]x1 + [4] >= [4 2]x1 + [4] = a(b(a(a(c(x1))))) 186.81/47.64 186.81/47.64 [0 0 ] [2] 186.81/47.64 c(b(x1)) = [-& 0 ]x1 + [2] >= x1 = x1 186.81/47.64 problem: 186.81/47.64 DPs: 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 TRS: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 Restore Modifier: 186.81/47.64 DPs: 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 TRS: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 EDG Processor: 186.81/47.64 DPs: 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 TRS: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 graph: 186.81/47.64 a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(a(c(x1))) 186.81/47.64 Arctic Interpretation Processor: 186.81/47.64 dimension: 2 186.81/47.64 usable rules: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 interpretation: 186.81/47.64 [a#](x0) = [-& 0 ]x0 + [0], 186.81/47.64 186.81/47.64 [-& 0 ] [0] 186.81/47.64 [c](x0) = [-& 0 ]x0 + [0], 186.81/47.64 186.81/47.64 [-& 1 ] [1] 186.81/47.64 [b](x0) = [0 0 ]x0 + [0], 186.81/47.64 186.81/47.64 [1 1] [1] 186.81/47.64 [a](x0) = [0 0]x0 + [0] 186.81/47.64 orientation: 186.81/47.64 a#(a(b(x1))) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a#(a(c(x1))) 186.81/47.64 186.81/47.64 [1 1] [1] [-& 1 ] [1] 186.81/47.64 a(x1) = [0 0]x1 + [0] >= [0 0 ]x1 + [0] = b(x1) 186.81/47.64 186.81/47.64 [2 3] [3] [-& 3 ] [3] 186.81/47.64 a(a(b(x1))) = [1 2]x1 + [2] >= [-& 2 ]x1 + [2] = a(b(a(a(c(x1))))) 186.81/47.64 186.81/47.64 [0 0] [0] 186.81/47.64 c(b(x1)) = [0 0]x1 + [0] >= x1 = x1 186.81/47.64 problem: 186.81/47.64 DPs: 186.81/47.64 186.81/47.64 TRS: 186.81/47.64 a(x1) -> b(x1) 186.81/47.64 a(a(b(x1))) -> a(b(a(a(c(x1))))) 186.81/47.64 c(b(x1)) -> x1 186.81/47.64 Qed 186.94/47.65 EOF