169.97/43.48 YES 169.97/43.49 169.97/43.49 Problem: 169.97/43.49 a(x1) -> x1 169.97/43.49 a(x1) -> b(x1) 169.97/43.49 b(x1) -> x1 169.97/43.49 b(a(c(x1))) -> c(c(a(a(b(x1))))) 169.97/43.49 169.97/43.49 Proof: 169.97/43.49 String Reversal Processor: 169.97/43.49 a(x1) -> x1 169.97/43.49 a(x1) -> b(x1) 169.97/43.49 b(x1) -> x1 169.97/43.49 c(a(b(x1))) -> b(a(a(c(c(x1))))) 169.97/43.49 DP Processor: 169.97/43.49 DPs: 169.97/43.49 a#(x1) -> b#(x1) 169.97/43.49 c#(a(b(x1))) -> c#(x1) 169.97/43.49 c#(a(b(x1))) -> c#(c(x1)) 169.97/43.49 c#(a(b(x1))) -> a#(c(c(x1))) 169.97/43.49 c#(a(b(x1))) -> a#(a(c(c(x1)))) 169.97/43.49 c#(a(b(x1))) -> b#(a(a(c(c(x1))))) 169.97/43.49 TRS: 169.97/43.49 a(x1) -> x1 169.97/43.49 a(x1) -> b(x1) 169.97/43.49 b(x1) -> x1 169.97/43.49 c(a(b(x1))) -> b(a(a(c(c(x1))))) 169.97/43.49 TDG Processor: 169.97/43.49 DPs: 169.97/43.49 a#(x1) -> b#(x1) 169.97/43.49 c#(a(b(x1))) -> c#(x1) 169.97/43.49 c#(a(b(x1))) -> c#(c(x1)) 169.97/43.49 c#(a(b(x1))) -> a#(c(c(x1))) 169.97/43.49 c#(a(b(x1))) -> a#(a(c(c(x1)))) 169.97/43.49 c#(a(b(x1))) -> b#(a(a(c(c(x1))))) 169.97/43.49 TRS: 169.97/43.49 a(x1) -> x1 169.97/43.49 a(x1) -> b(x1) 169.97/43.49 b(x1) -> x1 169.97/43.49 c(a(b(x1))) -> b(a(a(c(c(x1))))) 169.97/43.49 graph: 169.97/43.49 c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> b#(a(a(c(c(x1))))) 169.97/43.49 c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(a(c(c(x1)))) 169.97/43.49 c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(c(c(x1))) 169.97/43.49 c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1)) 169.97/43.49 c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(x1) 169.97/43.49 c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> b#(a(a(c(c(x1))))) 169.97/43.49 c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(a(c(c(x1)))) 169.97/43.49 c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(c(c(x1))) 169.97/43.49 c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(c(x1)) 169.97/43.49 c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(x1) 169.97/43.49 c#(a(b(x1))) -> a#(c(c(x1))) -> a#(x1) -> b#(x1) 169.97/43.49 c#(a(b(x1))) -> a#(a(c(c(x1)))) -> a#(x1) -> b#(x1) 169.97/43.49 SCC Processor: 169.97/43.49 #sccs: 1 169.97/43.49 #rules: 2 169.97/43.49 #arcs: 12/36 169.97/43.49 DPs: 169.97/43.49 c#(a(b(x1))) -> c#(c(x1)) 169.97/43.49 c#(a(b(x1))) -> c#(x1) 169.97/43.49 TRS: 169.97/43.49 a(x1) -> x1 169.97/43.49 a(x1) -> b(x1) 169.97/43.49 b(x1) -> x1 169.97/43.49 c(a(b(x1))) -> b(a(a(c(c(x1))))) 169.97/43.49 Arctic Interpretation Processor: 169.97/43.49 dimension: 2 169.97/43.49 usable rules: 169.97/43.49 a(x1) -> x1 169.97/43.49 a(x1) -> b(x1) 169.97/43.49 b(x1) -> x1 169.97/43.49 c(a(b(x1))) -> b(a(a(c(c(x1))))) 169.97/43.49 interpretation: 169.97/43.49 [c#](x0) = [2 0]x0 + [3], 169.97/43.49 169.97/43.49 [0 -&] [0] 169.97/43.49 [c](x0) = [1 0 ]x0 + [2], 169.97/43.49 169.97/43.49 [0 -&] [0] 169.97/43.49 [b](x0) = [1 0 ]x0 + [2], 169.97/43.49 169.97/43.49 [0 0] [0] 169.97/43.49 [a](x0) = [1 0]x0 + [2] 169.97/43.49 orientation: 169.97/43.49 c#(a(b(x1))) = [3 2]x1 + [4] >= [2 0]x1 + [3] = c#(c(x1)) 169.97/43.49 169.97/43.49 c#(a(b(x1))) = [3 2]x1 + [4] >= [2 0]x1 + [3] = c#(x1) 169.97/43.49 169.97/43.49 [0 0] [0] 169.97/43.49 a(x1) = [1 0]x1 + [2] >= x1 = x1 169.97/43.49 169.97/43.49 [0 0] [0] [0 -&] [0] 169.97/43.49 a(x1) = [1 0]x1 + [2] >= [1 0 ]x1 + [2] = b(x1) 169.97/43.49 169.97/43.49 [0 -&] [0] 169.97/43.49 b(x1) = [1 0 ]x1 + [2] >= x1 = x1 169.97/43.49 169.97/43.49 [1 0] [2] [1 0] [2] 169.97/43.49 c(a(b(x1))) = [2 1]x1 + [3] >= [2 1]x1 + [3] = b(a(a(c(c(x1))))) 169.97/43.49 problem: 169.97/43.49 DPs: 169.97/43.49 169.97/43.49 TRS: 169.97/43.49 a(x1) -> x1 169.97/43.49 a(x1) -> b(x1) 169.97/43.49 b(x1) -> x1 169.97/43.49 c(a(b(x1))) -> b(a(a(c(c(x1))))) 169.97/43.49 Qed 169.97/43.49 EOF