183.89/46.92 YES 183.95/46.93 183.95/46.93 Problem: 183.95/46.93 a(x1) -> x1 183.95/46.93 a(a(b(x1))) -> b(b(a(a(x1)))) 183.95/46.93 b(b(x1)) -> c(a(x1)) 183.95/46.93 183.95/46.93 Proof: 183.95/46.93 String Reversal Processor: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 DP Processor: 183.95/46.93 DPs: 183.95/46.93 b#(a(a(x1))) -> b#(x1) 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 b#(a(a(x1))) -> a#(b(b(x1))) 183.95/46.93 b#(a(a(x1))) -> a#(a(b(b(x1)))) 183.95/46.93 b#(b(x1)) -> a#(c(x1)) 183.95/46.93 TRS: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 TDG Processor: 183.95/46.93 DPs: 183.95/46.93 b#(a(a(x1))) -> b#(x1) 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 b#(a(a(x1))) -> a#(b(b(x1))) 183.95/46.93 b#(a(a(x1))) -> a#(a(b(b(x1)))) 183.95/46.93 b#(b(x1)) -> a#(c(x1)) 183.95/46.93 TRS: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 graph: 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) -> b#(b(x1)) -> a#(c(x1)) 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(b(b(x1)))) 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(b(b(x1))) 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(x1) 183.95/46.93 b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(c(x1)) 183.95/46.93 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(b(x1)))) 183.95/46.93 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(b(x1))) 183.95/46.93 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1) 183.95/46.93 SCC Processor: 183.95/46.93 #sccs: 1 183.95/46.93 #rules: 2 183.95/46.93 #arcs: 10/25 183.95/46.93 DPs: 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 b#(a(a(x1))) -> b#(x1) 183.95/46.93 TRS: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 Arctic Interpretation Processor: 183.95/46.93 dimension: 2 183.95/46.93 usable rules: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 interpretation: 183.95/46.93 [b#](x0) = [0 0]x0 + [0], 183.95/46.93 183.95/46.93 [-& 0 ] [0] 183.95/46.93 [c](x0) = [-& 0 ]x0 + [0], 183.95/46.93 183.95/46.93 [0 1 ] [1] 183.95/46.93 [b](x0) = [-& 0 ]x0 + [0], 183.95/46.93 183.95/46.93 [0 1] [1] 183.95/46.93 [a](x0) = [0 0]x0 + [0] 183.95/46.93 orientation: 183.95/46.93 b#(a(a(x1))) = [1 1]x1 + [1] >= [0 1]x1 + [1] = b#(b(x1)) 183.95/46.93 183.95/46.93 b#(a(a(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(x1) 183.95/46.93 183.95/46.93 [0 1] [1] 183.95/46.93 a(x1) = [0 0]x1 + [0] >= x1 = x1 183.95/46.93 183.95/46.93 [1 2] [2] [1 2] [2] 183.95/46.93 b(a(a(x1))) = [0 1]x1 + [1] >= [0 1]x1 + [1] = a(a(b(b(x1)))) 183.95/46.93 183.95/46.93 [0 1 ] [1] [-& 1 ] [1] 183.95/46.93 b(b(x1)) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = a(c(x1)) 183.95/46.93 problem: 183.95/46.93 DPs: 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 TRS: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 Restore Modifier: 183.95/46.93 DPs: 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 TRS: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 EDG Processor: 183.95/46.93 DPs: 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 TRS: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 graph: 183.95/46.93 b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1)) 183.95/46.93 Arctic Interpretation Processor: 183.95/46.93 dimension: 2 183.95/46.93 usable rules: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 interpretation: 183.95/46.93 [b#](x0) = [2 0]x0 + [1], 183.95/46.93 183.95/46.93 [0 -&] 183.95/46.93 [c](x0) = [0 -&]x0, 183.95/46.93 183.95/46.93 [0 -&] [-&] 183.95/46.93 [b](x0) = [1 0 ]x0 + [0 ], 183.95/46.93 183.95/46.93 [0 0] [-&] 183.95/46.93 [a](x0) = [1 0]x0 + [0 ] 183.95/46.93 orientation: 183.95/46.93 b#(a(a(x1))) = [3 2]x1 + [2] >= [2 0]x1 + [1] = b#(b(x1)) 183.95/46.93 183.95/46.93 [0 0] [-&] 183.95/46.93 a(x1) = [1 0]x1 + [0 ] >= x1 = x1 183.95/46.93 183.95/46.93 [1 0] [0] [1 0] [0] 183.95/46.93 b(a(a(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = a(a(b(b(x1)))) 183.95/46.93 183.95/46.93 [0 -&] [-&] [0 -&] [-&] 183.95/46.93 b(b(x1)) = [1 0 ]x1 + [0 ] >= [1 -&]x1 + [0 ] = a(c(x1)) 183.95/46.93 problem: 183.95/46.93 DPs: 183.95/46.93 183.95/46.93 TRS: 183.95/46.93 a(x1) -> x1 183.95/46.93 b(a(a(x1))) -> a(a(b(b(x1)))) 183.95/46.93 b(b(x1)) -> a(c(x1)) 183.95/46.93 Qed 183.95/46.94 EOF