178.04/45.53 YES 178.04/45.54 178.04/45.54 Problem: 178.04/45.54 a(a(a(a(x1)))) -> b(a(b(b(x1)))) 178.04/45.54 b(b(a(b(x1)))) -> a(b(b(b(x1)))) 178.04/45.54 a(a(b(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.54 178.04/45.54 Proof: 178.04/45.54 String Reversal Processor: 178.04/45.54 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.54 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.54 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.54 DP Processor: 178.04/45.54 DPs: 178.04/45.54 a#(a(a(a(x1)))) -> b#(x1) 178.04/45.54 a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.54 a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.54 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.54 b#(a(b(b(x1)))) -> a#(x1) 178.04/45.54 b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.54 TRS: 178.04/45.54 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.54 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.54 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.54 TDG Processor: 178.04/45.54 DPs: 178.04/45.54 a#(a(a(a(x1)))) -> b#(x1) 178.04/45.54 a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.54 a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.54 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.54 b#(a(b(b(x1)))) -> a#(x1) 178.04/45.54 b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.54 TRS: 178.04/45.54 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.54 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.54 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.54 graph: 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.54 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.54 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.54 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.54 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.54 b#(a(b(b(x1)))) -> a#(x1) -> a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.54 b#(a(b(b(x1)))) -> a#(x1) -> a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.54 b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.54 b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.54 b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.54 b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.54 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.54 a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.54 a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> a#(a(a(a(x1)))) -> b#(x1) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.54 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.54 a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.54 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(x1) 178.04/45.54 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.54 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.54 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.54 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.54 a#(a(a(a(x1)))) -> b#(a(b(x1))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.54 a#(a(a(a(x1)))) -> b#(a(b(x1))) -> 178.04/45.54 b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.54 a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.54 a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.54 a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(a(a(a(x1)))) -> b#(x1) 178.04/45.55 EDG Processor: 178.04/45.55 DPs: 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.55 a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.55 b#(a(b(b(x1)))) -> a#(x1) 178.04/45.55 b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.55 b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.55 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.55 TRS: 178.04/45.55 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.55 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.55 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.55 graph: 178.04/45.55 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.55 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.55 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.55 b#(a(b(b(x1)))) -> b#(a(x1)) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.55 b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) 178.04/45.55 b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.55 b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.55 b#(a(b(b(x1)))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.55 b#(a(b(b(x1)))) -> a#(x1) -> a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.55 b#(a(b(b(x1)))) -> a#(x1) -> 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.55 a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.55 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(x1) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.55 a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.55 a#(a(a(a(x1)))) -> b#(b(a(b(x1)))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) -> 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.55 a#(a(a(a(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.55 a#(a(a(a(x1)))) -> b#(a(b(x1))) -> 178.04/45.55 b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.55 a#(a(a(a(x1)))) -> b#(a(b(x1))) -> 178.04/45.55 b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> b#(a(b(x1))) -> 178.04/45.55 b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> a#(x1) 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) -> b#(a(b(b(x1)))) -> b#(b(b(a(x1)))) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) -> a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.55 SCC Processor: 178.04/45.55 #sccs: 1 178.04/45.55 #rules: 7 178.04/45.55 #arcs: 32/100 178.04/45.55 DPs: 178.04/45.55 b#(a(b(b(x1)))) -> b#(a(x1)) 178.04/45.55 b#(a(b(b(x1)))) -> a#(x1) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.55 a#(b(a(a(x1)))) -> a#(a(a(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> b#(a(b(x1))) 178.04/45.55 a#(a(a(a(x1)))) -> a#(b(x1)) 178.04/45.55 a#(a(a(a(x1)))) -> b#(x1) 178.04/45.55 TRS: 178.04/45.55 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.55 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.55 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.55 Arctic Interpretation Processor: 178.04/45.55 dimension: 1 178.04/45.55 usable rules: 178.04/45.55 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.56 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.56 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.56 interpretation: 178.04/45.56 [b#](x0) = 1x0 + 0, 178.04/45.56 178.04/45.56 [a#](x0) = 8x0 + 0, 178.04/45.56 178.04/45.56 [b](x0) = 4x0 + 2, 178.04/45.56 178.04/45.56 [a](x0) = 4x0 + 2 178.04/45.56 orientation: 178.04/45.56 b#(a(b(b(x1)))) = 13x1 + 11 >= 5x1 + 3 = b#(a(x1)) 178.04/45.56 178.04/45.56 b#(a(b(b(x1)))) = 13x1 + 11 >= 8x1 + 0 = a#(x1) 178.04/45.56 178.04/45.56 a#(b(a(a(x1)))) = 20x1 + 18 >= 20x1 + 18 = a#(a(a(a(x1)))) 178.04/45.56 178.04/45.56 a#(b(a(a(x1)))) = 20x1 + 18 >= 16x1 + 14 = a#(a(a(x1))) 178.04/45.56 178.04/45.56 a#(a(a(a(x1)))) = 20x1 + 18 >= 9x1 + 7 = b#(a(b(x1))) 178.04/45.56 178.04/45.56 a#(a(a(a(x1)))) = 20x1 + 18 >= 12x1 + 10 = a#(b(x1)) 178.04/45.56 178.04/45.56 a#(a(a(a(x1)))) = 20x1 + 18 >= 1x1 + 0 = b#(x1) 178.04/45.56 178.04/45.56 a(a(a(a(x1)))) = 16x1 + 14 >= 16x1 + 14 = b(b(a(b(x1)))) 178.04/45.56 178.04/45.56 b(a(b(b(x1)))) = 16x1 + 14 >= 16x1 + 14 = b(b(b(a(x1)))) 178.04/45.56 178.04/45.56 a(b(a(a(x1)))) = 16x1 + 14 >= 16x1 + 14 = a(a(a(a(x1)))) 178.04/45.56 problem: 178.04/45.56 DPs: 178.04/45.56 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.56 TRS: 178.04/45.56 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.56 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.56 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.56 Restore Modifier: 178.04/45.56 DPs: 178.04/45.56 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.56 TRS: 178.04/45.56 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.56 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.56 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.56 EDG Processor: 178.04/45.56 DPs: 178.04/45.56 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.56 TRS: 178.04/45.56 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.56 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.56 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.56 graph: 178.04/45.56 a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) -> a#(b(a(a(x1)))) -> a#(a(a(a(x1)))) 178.04/45.56 Matrix Interpretation Processor: dim=4 178.04/45.56 178.04/45.56 interpretation: 178.04/45.56 [a#](x0) = [0 0 1 0]x0, 178.04/45.56 178.04/45.56 [0 0 0 0] 178.04/45.56 [0 0 0 0] 178.04/45.56 [b](x0) = [1 0 0 0]x0 178.04/45.56 [0 0 0 0] , 178.04/45.56 178.04/45.56 [0 1 1 0] [0] 178.04/45.56 [0 0 0 0] [1] 178.04/45.56 [a](x0) = [0 0 0 0]x0 + [0] 178.04/45.56 [0 0 0 0] [0] 178.04/45.56 orientation: 178.04/45.56 a#(b(a(a(x1)))) = [1] >= [0] = a#(a(a(a(x1)))) 178.04/45.56 178.04/45.56 [1] [0] 178.04/45.56 [1] [0] 178.04/45.56 a(a(a(a(x1)))) = [0] >= [0] = b(b(a(b(x1)))) 178.04/45.56 [0] [0] 178.04/45.56 178.04/45.56 [0] [0] 178.04/45.56 [0] [0] 178.04/45.56 b(a(b(b(x1)))) = [0] >= [0] = b(b(b(a(x1)))) 178.04/45.56 [0] [0] 178.04/45.56 178.04/45.56 [1] [1] 178.04/45.56 [1] [1] 178.04/45.56 a(b(a(a(x1)))) = [0] >= [0] = a(a(a(a(x1)))) 178.04/45.56 [0] [0] 178.04/45.56 problem: 178.04/45.56 DPs: 178.04/45.56 178.04/45.56 TRS: 178.04/45.56 a(a(a(a(x1)))) -> b(b(a(b(x1)))) 178.04/45.56 b(a(b(b(x1)))) -> b(b(b(a(x1)))) 178.04/45.56 a(b(a(a(x1)))) -> a(a(a(a(x1)))) 178.04/45.56 Qed 178.18/45.57 EOF