169.61/43.46 YES 170.15/43.47 170.15/43.47 Problem: 170.15/43.47 a(x1) -> x1 170.15/43.47 a(b(c(x1))) -> c(c(b(b(a(x1))))) 170.15/43.47 b(x1) -> a(x1) 170.15/43.47 170.15/43.47 Proof: 170.15/43.47 String Reversal Processor: 170.15/43.47 a(x1) -> x1 170.15/43.47 c(b(a(x1))) -> a(b(b(c(c(x1))))) 170.15/43.47 b(x1) -> a(x1) 170.15/43.47 DP Processor: 170.15/43.47 DPs: 170.15/43.47 c#(b(a(x1))) -> c#(x1) 170.15/43.47 c#(b(a(x1))) -> c#(c(x1)) 170.15/43.47 c#(b(a(x1))) -> b#(c(c(x1))) 170.15/43.47 c#(b(a(x1))) -> b#(b(c(c(x1)))) 170.15/43.47 c#(b(a(x1))) -> a#(b(b(c(c(x1))))) 170.15/43.47 b#(x1) -> a#(x1) 170.15/43.47 TRS: 170.15/43.47 a(x1) -> x1 170.15/43.47 c(b(a(x1))) -> a(b(b(c(c(x1))))) 170.15/43.47 b(x1) -> a(x1) 170.15/43.47 TDG Processor: 170.15/43.47 DPs: 170.15/43.47 c#(b(a(x1))) -> c#(x1) 170.15/43.47 c#(b(a(x1))) -> c#(c(x1)) 170.15/43.47 c#(b(a(x1))) -> b#(c(c(x1))) 170.15/43.47 c#(b(a(x1))) -> b#(b(c(c(x1)))) 170.15/43.47 c#(b(a(x1))) -> a#(b(b(c(c(x1))))) 170.15/43.47 b#(x1) -> a#(x1) 170.15/43.47 TRS: 170.15/43.47 a(x1) -> x1 170.15/43.47 c(b(a(x1))) -> a(b(b(c(c(x1))))) 170.15/43.47 b(x1) -> a(x1) 170.15/43.47 graph: 170.15/43.47 c#(b(a(x1))) -> b#(b(c(c(x1)))) -> b#(x1) -> a#(x1) 170.15/43.47 c#(b(a(x1))) -> b#(c(c(x1))) -> b#(x1) -> a#(x1) 170.15/43.47 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(b(b(c(c(x1))))) 170.15/43.47 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(b(c(c(x1)))) 170.15/43.47 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(c(c(x1))) 170.15/43.47 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) 170.15/43.47 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(x1) 170.15/43.47 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(b(b(c(c(x1))))) 170.15/43.47 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(b(c(c(x1)))) 170.15/43.47 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(c(c(x1))) 170.15/43.47 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(x1)) 170.15/43.47 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(x1) 170.15/43.47 SCC Processor: 170.15/43.47 #sccs: 1 170.15/43.47 #rules: 2 170.15/43.47 #arcs: 12/36 170.15/43.47 DPs: 170.15/43.47 c#(b(a(x1))) -> c#(c(x1)) 170.15/43.47 c#(b(a(x1))) -> c#(x1) 170.15/43.47 TRS: 170.15/43.47 a(x1) -> x1 170.15/43.47 c(b(a(x1))) -> a(b(b(c(c(x1))))) 170.15/43.47 b(x1) -> a(x1) 170.15/43.47 Arctic Interpretation Processor: 170.15/43.47 dimension: 2 170.15/43.47 usable rules: 170.15/43.47 a(x1) -> x1 170.15/43.47 c(b(a(x1))) -> a(b(b(c(c(x1))))) 170.15/43.47 b(x1) -> a(x1) 170.15/43.47 interpretation: 170.15/43.47 [c#](x0) = [2 0]x0, 170.15/43.47 170.15/43.47 [0 0] 170.15/43.47 [b](x0) = [1 0]x0, 170.15/43.47 170.15/43.47 [0 -&] 170.15/43.47 [c](x0) = [1 0 ]x0, 170.15/43.47 170.15/43.47 [0 -&] 170.15/43.47 [a](x0) = [1 0 ]x0 170.15/43.47 orientation: 170.15/43.47 c#(b(a(x1))) = [3 2]x1 >= [2 0]x1 = c#(c(x1)) 170.15/43.47 170.15/43.47 c#(b(a(x1))) = [3 2]x1 >= [2 0]x1 = c#(x1) 170.15/43.47 170.15/43.47 [0 -&] 170.15/43.47 a(x1) = [1 0 ]x1 >= x1 = x1 170.15/43.47 170.15/43.47 [1 0] [1 0] 170.15/43.47 c(b(a(x1))) = [2 1]x1 >= [2 1]x1 = a(b(b(c(c(x1))))) 170.15/43.47 170.15/43.47 [0 0] [0 -&] 170.15/43.47 b(x1) = [1 0]x1 >= [1 0 ]x1 = a(x1) 170.15/43.47 problem: 170.15/43.47 DPs: 170.15/43.47 170.15/43.47 TRS: 170.15/43.47 a(x1) -> x1 170.15/43.47 c(b(a(x1))) -> a(b(b(c(c(x1))))) 170.15/43.47 b(x1) -> a(x1) 170.15/43.47 Qed 170.15/43.47 EOF