167.39/42.80 YES 167.39/42.81 167.39/42.81 Problem: 167.39/42.81 a(x1) -> x1 167.39/42.81 a(x1) -> b(x1) 167.39/42.81 a(b(c(x1))) -> c(c(a(b(a(x1))))) 167.39/42.81 b(x1) -> x1 167.39/42.81 167.39/42.81 Proof: 167.39/42.81 String Reversal Processor: 167.39/42.81 a(x1) -> x1 167.39/42.81 a(x1) -> b(x1) 167.39/42.81 c(b(a(x1))) -> a(b(a(c(c(x1))))) 167.39/42.81 b(x1) -> x1 167.39/42.81 DP Processor: 167.39/42.81 DPs: 167.39/42.81 a#(x1) -> b#(x1) 167.39/42.81 c#(b(a(x1))) -> c#(x1) 167.39/42.81 c#(b(a(x1))) -> c#(c(x1)) 167.39/42.81 c#(b(a(x1))) -> a#(c(c(x1))) 167.39/42.81 c#(b(a(x1))) -> b#(a(c(c(x1)))) 167.39/42.81 c#(b(a(x1))) -> a#(b(a(c(c(x1))))) 167.39/42.81 TRS: 167.39/42.81 a(x1) -> x1 167.39/42.81 a(x1) -> b(x1) 167.39/42.81 c(b(a(x1))) -> a(b(a(c(c(x1))))) 167.39/42.81 b(x1) -> x1 167.39/42.81 TDG Processor: 167.39/42.81 DPs: 167.39/42.81 a#(x1) -> b#(x1) 167.39/42.81 c#(b(a(x1))) -> c#(x1) 167.39/42.81 c#(b(a(x1))) -> c#(c(x1)) 167.39/42.81 c#(b(a(x1))) -> a#(c(c(x1))) 167.39/42.81 c#(b(a(x1))) -> b#(a(c(c(x1)))) 167.39/42.81 c#(b(a(x1))) -> a#(b(a(c(c(x1))))) 167.39/42.81 TRS: 167.39/42.81 a(x1) -> x1 167.39/42.81 a(x1) -> b(x1) 167.39/42.81 c(b(a(x1))) -> a(b(a(c(c(x1))))) 167.39/42.81 b(x1) -> x1 167.39/42.81 graph: 167.39/42.81 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(b(a(c(c(x1))))) 167.39/42.81 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(a(c(c(x1)))) 167.39/42.81 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(c(c(x1))) 167.39/42.81 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1)) 167.39/42.81 c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(x1) 167.39/42.81 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(b(a(c(c(x1))))) 167.39/42.81 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(a(c(c(x1)))) 167.39/42.81 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(c(c(x1))) 167.39/42.81 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(x1)) 167.39/42.81 c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(x1) 167.39/42.81 c#(b(a(x1))) -> a#(c(c(x1))) -> a#(x1) -> b#(x1) 167.39/42.81 c#(b(a(x1))) -> a#(b(a(c(c(x1))))) -> a#(x1) -> b#(x1) 167.39/42.81 SCC Processor: 167.39/42.81 #sccs: 1 167.39/42.81 #rules: 2 167.39/42.81 #arcs: 12/36 167.39/42.81 DPs: 167.39/42.81 c#(b(a(x1))) -> c#(c(x1)) 167.39/42.81 c#(b(a(x1))) -> c#(x1) 167.39/42.81 TRS: 167.39/42.81 a(x1) -> x1 167.39/42.81 a(x1) -> b(x1) 167.39/42.81 c(b(a(x1))) -> a(b(a(c(c(x1))))) 167.39/42.81 b(x1) -> x1 167.39/42.81 Arctic Interpretation Processor: 167.39/42.81 dimension: 2 167.39/42.81 usable rules: 167.39/42.81 a(x1) -> x1 167.39/42.81 a(x1) -> b(x1) 167.39/42.81 c(b(a(x1))) -> a(b(a(c(c(x1))))) 167.39/42.81 b(x1) -> x1 167.39/42.81 interpretation: 167.39/42.81 [c#](x0) = [0 0]x0 + [0], 167.39/42.81 167.39/42.81 [-& 0 ] [0 ] 167.39/42.81 [c](x0) = [-& 0 ]x0 + [-&], 167.39/42.81 167.39/42.81 [0 -&] [0] 167.39/42.81 [b](x0) = [2 0 ]x0 + [0], 167.39/42.81 167.39/42.81 [0 0] [0] 167.39/42.81 [a](x0) = [2 0]x0 + [0] 167.39/42.81 orientation: 167.39/42.81 c#(b(a(x1))) = [2 2]x1 + [2] >= [-& 0 ]x1 + [0] = c#(c(x1)) 167.39/42.81 167.39/42.81 c#(b(a(x1))) = [2 2]x1 + [2] >= [0 0]x1 + [0] = c#(x1) 167.39/42.81 167.39/42.81 [0 0] [0] 167.39/42.81 a(x1) = [2 0]x1 + [0] >= x1 = x1 167.39/42.81 167.39/42.81 [0 0] [0] [0 -&] [0] 167.39/42.81 a(x1) = [2 0]x1 + [0] >= [2 0 ]x1 + [0] = b(x1) 167.39/42.81 167.39/42.81 [2 2] [2] [-& 2 ] [2] 167.39/42.81 c(b(a(x1))) = [2 2]x1 + [2] >= [-& 2 ]x1 + [2] = a(b(a(c(c(x1))))) 167.39/42.81 167.39/42.81 [0 -&] [0] 167.39/42.81 b(x1) = [2 0 ]x1 + [0] >= x1 = x1 167.39/42.81 problem: 167.39/42.81 DPs: 167.39/42.81 167.39/42.81 TRS: 167.39/42.81 a(x1) -> x1 167.39/42.81 a(x1) -> b(x1) 167.39/42.81 c(b(a(x1))) -> a(b(a(c(c(x1))))) 167.39/42.81 b(x1) -> x1 167.39/42.81 Qed 167.39/42.82 EOF