171.84/44.03 YES 171.84/44.08 171.84/44.08 Problem: 171.84/44.08 a(x1) -> x1 171.84/44.08 a(a(b(x1))) -> b(b(b(a(a(x1))))) 171.84/44.08 b(x1) -> c(a(x1)) 171.84/44.08 171.84/44.08 Proof: 171.84/44.08 String Reversal Processor: 171.84/44.08 a(x1) -> x1 171.84/44.08 b(a(a(x1))) -> a(a(b(b(b(x1))))) 171.84/44.08 b(x1) -> a(c(x1)) 171.84/44.08 DP Processor: 171.84/44.08 DPs: 171.84/44.08 b#(a(a(x1))) -> b#(x1) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) 171.84/44.08 b#(a(a(x1))) -> a#(b(b(b(x1)))) 171.84/44.08 b#(a(a(x1))) -> a#(a(b(b(b(x1))))) 171.84/44.08 b#(x1) -> a#(c(x1)) 171.84/44.08 TRS: 171.84/44.08 a(x1) -> x1 171.84/44.08 b(a(a(x1))) -> a(a(b(b(b(x1))))) 171.84/44.08 b(x1) -> a(c(x1)) 171.84/44.08 TDG Processor: 171.84/44.08 DPs: 171.84/44.08 b#(a(a(x1))) -> b#(x1) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) 171.84/44.08 b#(a(a(x1))) -> a#(b(b(b(x1)))) 171.84/44.08 b#(a(a(x1))) -> a#(a(b(b(b(x1))))) 171.84/44.08 b#(x1) -> a#(c(x1)) 171.84/44.08 TRS: 171.84/44.08 a(x1) -> x1 171.84/44.08 b(a(a(x1))) -> a(a(b(b(b(x1))))) 171.84/44.08 b(x1) -> a(c(x1)) 171.84/44.08 graph: 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) -> b#(x1) -> a#(c(x1)) 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) -> a#(a(b(b(b(x1))))) 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) -> a#(b(b(b(x1)))) 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(b(x1))) 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) -> b#(b(x1)) 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) -> b#(a(a(x1))) -> b#(x1) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) -> b#(x1) -> a#(c(x1)) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(b(b(b(x1))))) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(b(b(b(x1)))) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(b(x1))) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1)) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(x1) 171.84/44.08 b#(a(a(x1))) -> b#(x1) -> b#(x1) -> a#(c(x1)) 171.84/44.08 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(b(b(x1))))) 171.84/44.08 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(b(b(x1)))) 171.84/44.08 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(b(x1))) 171.84/44.08 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(x1)) 171.84/44.08 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1) 171.84/44.08 SCC Processor: 171.84/44.08 #sccs: 1 171.84/44.08 #rules: 3 171.84/44.08 #arcs: 18/36 171.84/44.08 DPs: 171.84/44.08 b#(a(a(x1))) -> b#(b(b(x1))) 171.84/44.08 b#(a(a(x1))) -> b#(x1) 171.84/44.08 b#(a(a(x1))) -> b#(b(x1)) 171.84/44.08 TRS: 171.84/44.08 a(x1) -> x1 171.84/44.08 b(a(a(x1))) -> a(a(b(b(b(x1))))) 171.84/44.08 b(x1) -> a(c(x1)) 171.84/44.08 Arctic Interpretation Processor: 171.84/44.08 dimension: 2 171.84/44.08 usable rules: 171.84/44.08 a(x1) -> x1 171.84/44.08 b(a(a(x1))) -> a(a(b(b(b(x1))))) 171.84/44.08 b(x1) -> a(c(x1)) 171.84/44.08 interpretation: 171.84/44.08 [b#](x0) = [0 0]x0 + [0], 171.84/44.08 171.84/44.08 [0 0 ] [0 ] 171.84/44.08 [c](x0) = [-& -&]x0 + [-&], 171.84/44.08 171.84/44.08 [0 0] [0] 171.84/44.08 [b](x0) = [0 0]x0 + [0], 171.84/44.08 171.84/44.08 [0 1] [0] 171.84/44.08 [a](x0) = [0 0]x0 + [0] 171.84/44.08 orientation: 171.84/44.08 b#(a(a(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(b(b(x1))) 171.84/44.08 171.84/44.08 b#(a(a(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(x1) 171.84/44.08 171.84/44.08 b#(a(a(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(b(x1)) 171.84/44.08 171.84/44.08 [0 1] [0] 171.84/44.08 a(x1) = [0 0]x1 + [0] >= x1 = x1 171.84/44.08 171.84/44.08 [1 1] [1] [1 1] [1] 171.84/44.08 b(a(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(a(b(b(b(x1))))) 171.84/44.08 171.84/44.08 [0 0] [0] [0 0] [0] 171.84/44.08 b(x1) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(c(x1)) 171.84/44.08 problem: 171.84/44.08 DPs: 171.84/44.08 171.84/44.08 TRS: 171.84/44.08 a(x1) -> x1 171.84/44.08 b(a(a(x1))) -> a(a(b(b(b(x1))))) 171.84/44.08 b(x1) -> a(c(x1)) 171.84/44.08 Qed 171.84/44.08 EOF