179.27/45.80 YES 179.27/45.81 179.27/45.81 Problem: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(b(a(b(c(a(x1)))))) 179.27/45.81 c(b(x1)) -> a(x1) 179.27/45.81 179.27/45.81 Proof: 179.27/45.81 String Reversal Processor: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 DP Processor: 179.27/45.81 DPs: 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) 179.27/45.81 b#(c(x1)) -> a#(x1) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 TDG Processor: 179.27/45.81 DPs: 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) 179.27/45.81 b#(c(x1)) -> a#(x1) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 graph: 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) -> b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 179.27/45.81 a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) -> 179.27/45.81 a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) 179.27/45.81 a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) -> 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) -> 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) -> a#(a(x1)) -> b#(a(x1)) 179.27/45.81 EDG Processor: 179.27/45.81 DPs: 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) 179.27/45.81 b#(c(x1)) -> a#(x1) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 graph: 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) -> b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) 179.27/45.81 SCC Processor: 179.27/45.81 #sccs: 1 179.27/45.81 #rules: 4 179.27/45.81 #arcs: 10/25 179.27/45.81 DPs: 179.27/45.81 b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> a#(b(a(x1))) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 Arctic Interpretation Processor: 179.27/45.81 dimension: 2 179.27/45.81 usable rules: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 interpretation: 179.27/45.81 [b#](x0) = [-& 3 ]x0 + [0], 179.27/45.81 179.27/45.81 [a#](x0) = [0 3]x0 + [0], 179.27/45.81 179.27/45.81 [0 -&] 179.27/45.81 [b](x0) = [0 -&]x0, 179.27/45.81 179.27/45.81 [1 1] [1] 179.27/45.81 [c](x0) = [0 0]x0 + [0], 179.27/45.81 179.27/45.81 [0 0] [-&] 179.27/45.81 [a](x0) = [1 1]x0 + [1 ] 179.27/45.81 orientation: 179.27/45.81 b#(c(x1)) = [3 3]x1 + [3] >= [0 3]x1 + [0] = a#(x1) 179.27/45.81 179.27/45.81 a#(a(x1)) = [4 4]x1 + [4] >= [4 4]x1 + [4] = b#(a(b(a(x1)))) 179.27/45.81 179.27/45.81 a#(a(x1)) = [4 4]x1 + [4] >= [3 3]x1 + [0] = a#(b(a(x1))) 179.27/45.81 179.27/45.81 a#(a(x1)) = [4 4]x1 + [4] >= [4 4]x1 + [4] = b#(a(x1)) 179.27/45.81 179.27/45.81 [0 0] [-&] 179.27/45.81 a(x1) = [1 1]x1 + [1 ] >= x1 = x1 179.27/45.81 179.27/45.81 [1 1] [1] [1 1] [1] 179.27/45.81 a(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = a(c(b(a(b(a(x1)))))) 179.27/45.81 179.27/45.81 [1 1] [1] [0 0] [-&] 179.27/45.81 b(c(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1 ] = a(x1) 179.27/45.81 problem: 179.27/45.81 DPs: 179.27/45.81 b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 Restore Modifier: 179.27/45.81 DPs: 179.27/45.81 b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 EDG Processor: 179.27/45.81 DPs: 179.27/45.81 b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 graph: 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) -> b#(c(x1)) -> a#(x1) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) 179.27/45.81 Arctic Interpretation Processor: 179.27/45.81 dimension: 2 179.27/45.81 usable rules: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 interpretation: 179.27/45.81 [b#](x0) = [0 2]x0 + [0], 179.27/45.81 179.27/45.81 [a#](x0) = [0 2]x0, 179.27/45.81 179.27/45.81 [-& 0 ] [0] 179.27/45.81 [b](x0) = [-& 0 ]x0 + [0], 179.27/45.81 179.27/45.81 [0 0] [1] 179.27/45.81 [c](x0) = [2 2]x0 + [2], 179.27/45.81 179.27/45.81 [2 2] [2 ] 179.27/45.81 [a](x0) = [0 0]x0 + [-&] 179.27/45.81 orientation: 179.27/45.81 b#(c(x1)) = [4 4]x1 + [4] >= [0 2]x1 = a#(x1) 179.27/45.81 179.27/45.81 a#(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = b#(a(b(a(x1)))) 179.27/45.81 179.27/45.81 a#(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = b#(a(x1)) 179.27/45.81 179.27/45.81 [2 2] [2 ] 179.27/45.81 a(x1) = [0 0]x1 + [-&] >= x1 = x1 179.27/45.81 179.27/45.81 [4 4] [4] [4 4] [4] 179.27/45.81 a(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = a(c(b(a(b(a(x1)))))) 179.27/45.81 179.27/45.81 [2 2] [2] [2 2] [2 ] 179.27/45.81 b(c(x1)) = [2 2]x1 + [2] >= [0 0]x1 + [-&] = a(x1) 179.27/45.81 problem: 179.27/45.81 DPs: 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 Restore Modifier: 179.27/45.81 DPs: 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 EDG Processor: 179.27/45.81 DPs: 179.27/45.81 a#(a(x1)) -> b#(a(b(a(x1)))) 179.27/45.81 a#(a(x1)) -> b#(a(x1)) 179.27/45.81 TRS: 179.27/45.81 a(x1) -> x1 179.27/45.81 a(a(x1)) -> a(c(b(a(b(a(x1)))))) 179.27/45.81 b(c(x1)) -> a(x1) 179.27/45.81 graph: 179.27/45.81 179.27/45.81 SCC Processor: 179.27/45.81 #sccs: 0 179.27/45.81 #rules: 0 179.27/45.81 #arcs: 0/4 179.27/45.81 179.27/45.82 EOF