184.99/47.26 YES 184.99/47.27 184.99/47.27 Problem: 184.99/47.27 a(x1) -> x1 184.99/47.27 a(b(x1)) -> b(c(a(x1))) 184.99/47.27 c(c(a(x1))) -> a(b(a(x1))) 184.99/47.27 184.99/47.27 Proof: 184.99/47.27 String Reversal Processor: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 DP Processor: 184.99/47.27 DPs: 184.99/47.27 b#(a(x1)) -> b#(x1) 184.99/47.27 b#(a(x1)) -> a#(c(b(x1))) 184.99/47.27 a#(c(c(x1))) -> a#(x1) 184.99/47.27 a#(c(c(x1))) -> b#(a(x1)) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 TRS: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 TDG Processor: 184.99/47.27 DPs: 184.99/47.27 b#(a(x1)) -> b#(x1) 184.99/47.27 b#(a(x1)) -> a#(c(b(x1))) 184.99/47.27 a#(c(c(x1))) -> a#(x1) 184.99/47.27 a#(c(c(x1))) -> b#(a(x1)) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 TRS: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 graph: 184.99/47.27 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 184.99/47.27 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 184.99/47.27 b#(a(x1)) -> a#(c(b(x1))) -> a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 b#(a(x1)) -> a#(c(b(x1))) -> a#(c(c(x1))) -> b#(a(x1)) 184.99/47.27 b#(a(x1)) -> a#(c(b(x1))) -> a#(c(c(x1))) -> a#(x1) 184.99/47.27 a#(c(c(x1))) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(b(x1))) 184.99/47.27 a#(c(c(x1))) -> b#(a(x1)) -> b#(a(x1)) -> b#(x1) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) -> a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) -> a#(c(c(x1))) -> b#(a(x1)) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) -> a#(c(c(x1))) -> a#(x1) 184.99/47.27 a#(c(c(x1))) -> a#(x1) -> a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 a#(c(c(x1))) -> a#(x1) -> a#(c(c(x1))) -> b#(a(x1)) 184.99/47.27 a#(c(c(x1))) -> a#(x1) -> a#(c(c(x1))) -> a#(x1) 184.99/47.27 Arctic Interpretation Processor: 184.99/47.27 dimension: 2 184.99/47.27 usable rules: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 interpretation: 184.99/47.27 [b#](x0) = [-& 0 ]x0 + [3], 184.99/47.27 184.99/47.27 [a#](x0) = [-& 1 ]x0 + [0], 184.99/47.27 184.99/47.27 [3 3] [3] 184.99/47.27 [c](x0) = [0 0]x0 + [0], 184.99/47.27 184.99/47.27 [-& 0 ] [0] 184.99/47.27 [b](x0) = [-& 0 ]x0 + [0], 184.99/47.27 184.99/47.27 [0 1 ] [3] 184.99/47.27 [a](x0) = [-& 3 ]x0 + [3] 184.99/47.27 orientation: 184.99/47.27 b#(a(x1)) = [-& 3 ]x1 + [3] >= [-& 0 ]x1 + [3] = b#(x1) 184.99/47.27 184.99/47.27 b#(a(x1)) = [-& 3 ]x1 + [3] >= [-& 1 ]x1 + [1] = a#(c(b(x1))) 184.99/47.27 184.99/47.27 a#(c(c(x1))) = [4 4]x1 + [4] >= [-& 1 ]x1 + [0] = a#(x1) 184.99/47.27 184.99/47.27 a#(c(c(x1))) = [4 4]x1 + [4] >= [-& 3 ]x1 + [3] = b#(a(x1)) 184.99/47.27 184.99/47.27 a#(c(c(x1))) = [4 4]x1 + [4] >= [-& 4 ]x1 + [4] = a#(b(a(x1))) 184.99/47.27 184.99/47.27 [0 1 ] [3] 184.99/47.27 a(x1) = [-& 3 ]x1 + [3] >= x1 = x1 184.99/47.27 184.99/47.27 [-& 3 ] [3] [-& 3 ] [3] 184.99/47.27 b(a(x1)) = [-& 3 ]x1 + [3] >= [-& 3 ]x1 + [3] = a(c(b(x1))) 184.99/47.27 184.99/47.27 [6 6] [6] [-& 4 ] [4] 184.99/47.27 a(c(c(x1))) = [6 6]x1 + [6] >= [-& 6 ]x1 + [6] = a(b(a(x1))) 184.99/47.27 problem: 184.99/47.27 DPs: 184.99/47.27 b#(a(x1)) -> b#(x1) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 TRS: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 Restore Modifier: 184.99/47.27 DPs: 184.99/47.27 b#(a(x1)) -> b#(x1) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 TRS: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 EDG Processor: 184.99/47.27 DPs: 184.99/47.27 b#(a(x1)) -> b#(x1) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 TRS: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 graph: 184.99/47.27 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) -> a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 SCC Processor: 184.99/47.27 #sccs: 2 184.99/47.27 #rules: 2 184.99/47.27 #arcs: 2/4 184.99/47.27 DPs: 184.99/47.27 a#(c(c(x1))) -> a#(b(a(x1))) 184.99/47.27 TRS: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 Arctic Interpretation Processor: 184.99/47.27 dimension: 2 184.99/47.27 usable rules: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 interpretation: 184.99/47.27 [a#](x0) = [1 -&]x0 + [0], 184.99/47.27 184.99/47.27 [1 1 ] [3] 184.99/47.27 [c](x0) = [-& 0 ]x0 + [0], 184.99/47.27 184.99/47.27 [-& 0 ] [0] 184.99/47.27 [b](x0) = [-& 0 ]x0 + [1], 184.99/47.27 184.99/47.27 [0 0] [0] 184.99/47.27 [a](x0) = [0 1]x0 + [3] 184.99/47.27 orientation: 184.99/47.27 a#(c(c(x1))) = [3 3]x1 + [5] >= [1 2]x1 + [4] = a#(b(a(x1))) 184.99/47.27 184.99/47.27 [0 0] [0] 184.99/47.27 a(x1) = [0 1]x1 + [3] >= x1 = x1 184.99/47.27 184.99/47.27 [0 1] [3] [-& 1 ] [3] 184.99/47.27 b(a(x1)) = [0 1]x1 + [3] >= [-& 1 ]x1 + [3] = a(c(b(x1))) 184.99/47.27 184.99/47.27 [2 2] [4] [0 1] [3] 184.99/47.27 a(c(c(x1))) = [2 2]x1 + [4] >= [1 2]x1 + [4] = a(b(a(x1))) 184.99/47.27 problem: 184.99/47.27 DPs: 184.99/47.27 184.99/47.27 TRS: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 Qed 184.99/47.27 184.99/47.27 DPs: 184.99/47.27 b#(a(x1)) -> b#(x1) 184.99/47.27 TRS: 184.99/47.27 a(x1) -> x1 184.99/47.27 b(a(x1)) -> a(c(b(x1))) 184.99/47.27 a(c(c(x1))) -> a(b(a(x1))) 184.99/47.27 Usable Rule Processor: 184.99/47.27 DPs: 184.99/47.27 b#(a(x1)) -> b#(x1) 184.99/47.27 TRS: 184.99/47.27 184.99/47.27 Arctic Interpretation Processor: 184.99/47.27 dimension: 4 184.99/47.27 usable rules: 184.99/47.27 184.99/47.27 interpretation: 184.99/47.27 [b#](x0) = [0 -& -& -&]x0, 184.99/47.27 184.99/47.27 [1 0 0 0] [0] 184.99/47.27 [0 0 0 0] [0] 184.99/47.27 [a](x0) = [1 0 0 0]x0 + [0] 184.99/47.27 [0 0 0 0] [0] 184.99/47.27 orientation: 184.99/47.27 b#(a(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = b#(x1) 184.99/47.27 problem: 184.99/47.27 DPs: 184.99/47.27 184.99/47.27 TRS: 184.99/47.27 184.99/47.27 Qed 184.99/47.28 EOF