169.69/43.31 YES 169.78/43.31 169.78/43.31 Problem: 169.78/43.31 a(x1) -> x1 169.78/43.31 a(b(c(x1))) -> c(c(a(b(b(x1))))) 169.78/43.31 b(x1) -> a(x1) 169.78/43.31 169.78/43.31 Proof: 169.78/43.31 String Reversal Processor: 169.78/43.31 a(x1) -> x1 169.78/43.31 c(b(a(x1))) -> b(b(a(c(c(x1))))) 169.78/43.31 b(x1) -> a(x1) 169.78/43.31 DP Processor: 169.78/43.31 DPs: 169.78/43.31 c#(b(a(x1))) -> c#(x1) 169.78/43.31 c#(b(a(x1))) -> c#(c(x1)) 169.78/43.31 c#(b(a(x1))) -> a#(c(c(x1))) 169.78/43.31 c#(b(a(x1))) -> b#(a(c(c(x1)))) 169.78/43.31 c#(b(a(x1))) -> b#(b(a(c(c(x1))))) 169.78/43.31 b#(x1) -> a#(x1) 169.78/43.31 TRS: 169.78/43.31 a(x1) -> x1 169.78/43.31 c(b(a(x1))) -> b(b(a(c(c(x1))))) 169.78/43.31 b(x1) -> a(x1) 169.78/43.31 TDG Processor: 169.78/43.31 DPs: 169.78/43.31 c#(b(a(x1))) -> c#(x1) 169.78/43.31 c#(b(a(x1))) -> c#(c(x1)) 169.78/43.31 c#(b(a(x1))) -> a#(c(c(x1))) 169.78/43.31 c#(b(a(x1))) -> b#(a(c(c(x1)))) 169.78/43.31 c#(b(a(x1))) -> b#(b(a(c(c(x1))))) 169.78/43.31 b#(x1) -> a#(x1) 169.78/43.31 TRS: 169.78/43.31 a(x1) -> x1 169.78/43.31 c(b(a(x1))) -> b(b(a(c(c(x1))))) 169.78/43.31 b(x1) -> a(x1) 169.78/43.31 graph: 169.78/43.31 c#(b(a(x1))) -> b#(b(a(c(c(x1))))) -> b#(x1) -> a#(x1) 169.78/43.31 c#(b(a(x1))) -> b#(a(c(c(x1)))) -> b#(x1) -> a#(x1) 169.78/43.31 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(b(a(c(c(x1))))) 169.78/43.31 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(a(c(c(x1)))) 169.78/43.31 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(c(c(x1))) 169.78/43.31 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) 169.78/43.31 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(x1) 169.78/43.31 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(b(a(c(c(x1))))) 169.78/43.31 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(a(c(c(x1)))) 169.78/43.31 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(c(c(x1))) 169.78/43.31 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(x1)) 169.78/43.31 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(x1) 169.78/43.31 SCC Processor: 169.78/43.31 #sccs: 1 169.78/43.31 #rules: 2 169.78/43.31 #arcs: 12/36 169.78/43.31 DPs: 169.78/43.31 c#(b(a(x1))) -> c#(c(x1)) 169.78/43.31 c#(b(a(x1))) -> c#(x1) 169.78/43.31 TRS: 169.78/43.31 a(x1) -> x1 169.78/43.31 c(b(a(x1))) -> b(b(a(c(c(x1))))) 169.78/43.31 b(x1) -> a(x1) 169.78/43.31 Arctic Interpretation Processor: 169.78/43.31 dimension: 2 169.78/43.31 usable rules: 169.78/43.31 a(x1) -> x1 169.78/43.31 c(b(a(x1))) -> b(b(a(c(c(x1))))) 169.78/43.31 b(x1) -> a(x1) 169.78/43.31 interpretation: 169.78/43.31 [c#](x0) = [0 -&]x0 + [0], 169.78/43.31 169.78/43.31 [0 0] [3] 169.78/43.31 [b](x0) = [1 0]x0 + [0], 169.78/43.31 169.78/43.31 [0 -&] [0] 169.78/43.31 [c](x0) = [1 0 ]x0 + [0], 169.78/43.31 169.78/43.31 [0 -&] [1] 169.78/43.31 [a](x0) = [1 0 ]x0 + [0] 169.78/43.31 orientation: 169.78/43.31 c#(b(a(x1))) = [1 0]x1 + [3] >= [0 -&]x1 + [0] = c#(c(x1)) 169.78/43.31 169.78/43.31 c#(b(a(x1))) = [1 0]x1 + [3] >= [0 -&]x1 + [0] = c#(x1) 169.78/43.31 169.78/43.31 [0 -&] [1] 169.78/43.31 a(x1) = [1 0 ]x1 + [0] >= x1 = x1 169.78/43.31 169.78/43.31 [1 0] [3] [1 0] [3] 169.78/43.31 c(b(a(x1))) = [2 1]x1 + [4] >= [2 1]x1 + [4] = b(b(a(c(c(x1))))) 169.78/43.31 169.78/43.31 [0 0] [3] [0 -&] [1] 169.78/43.31 b(x1) = [1 0]x1 + [0] >= [1 0 ]x1 + [0] = a(x1) 169.78/43.31 problem: 169.78/43.31 DPs: 169.78/43.31 169.78/43.31 TRS: 169.78/43.31 a(x1) -> x1 169.78/43.31 c(b(a(x1))) -> b(b(a(c(c(x1))))) 169.78/43.31 b(x1) -> a(x1) 169.78/43.31 Qed 169.78/43.32 EOF