176.09/45.04 YES 176.09/45.05 176.09/45.05 Problem: 176.09/45.05 b(a(a(x1))) -> a(b(c(x1))) 176.09/45.05 c(a(x1)) -> a(c(x1)) 176.09/45.05 c(b(x1)) -> b(a(x1)) 176.09/45.05 a(a(b(x1))) -> d(b(a(x1))) 176.09/45.05 a(d(x1)) -> d(a(x1)) 176.09/45.05 b(d(x1)) -> a(b(x1)) 176.09/45.05 a(a(x1)) -> a(b(a(x1))) 176.09/45.05 176.09/45.05 Proof: 176.09/45.05 String Reversal Processor: 176.09/45.05 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.05 a(c(x1)) -> c(a(x1)) 176.09/45.05 b(c(x1)) -> a(b(x1)) 176.09/45.05 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.05 d(a(x1)) -> a(d(x1)) 176.09/45.05 d(b(x1)) -> b(a(x1)) 176.09/45.05 a(a(x1)) -> a(b(a(x1))) 176.09/45.05 DP Processor: 176.09/45.05 DPs: 176.09/45.05 a#(a(b(x1))) -> a#(x1) 176.09/45.05 a#(a(b(x1))) -> b#(a(x1)) 176.09/45.05 a#(c(x1)) -> a#(x1) 176.09/45.05 b#(c(x1)) -> b#(x1) 176.09/45.05 b#(c(x1)) -> a#(b(x1)) 176.09/45.05 b#(a(a(x1))) -> d#(x1) 176.09/45.05 b#(a(a(x1))) -> b#(d(x1)) 176.09/45.05 b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.05 d#(a(x1)) -> d#(x1) 176.09/45.05 d#(a(x1)) -> a#(d(x1)) 176.09/45.05 d#(b(x1)) -> a#(x1) 176.09/45.05 d#(b(x1)) -> b#(a(x1)) 176.09/45.05 a#(a(x1)) -> b#(a(x1)) 176.09/45.05 a#(a(x1)) -> a#(b(a(x1))) 176.09/45.05 TRS: 176.09/45.05 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.05 a(c(x1)) -> c(a(x1)) 176.09/45.05 b(c(x1)) -> a(b(x1)) 176.09/45.05 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.05 d(a(x1)) -> a(d(x1)) 176.09/45.05 d(b(x1)) -> b(a(x1)) 176.09/45.05 a(a(x1)) -> a(b(a(x1))) 176.09/45.05 TDG Processor: 176.09/45.05 DPs: 176.09/45.05 a#(a(b(x1))) -> a#(x1) 176.09/45.05 a#(a(b(x1))) -> b#(a(x1)) 176.09/45.05 a#(c(x1)) -> a#(x1) 176.09/45.05 b#(c(x1)) -> b#(x1) 176.09/45.05 b#(c(x1)) -> a#(b(x1)) 176.09/45.05 b#(a(a(x1))) -> d#(x1) 176.09/45.05 b#(a(a(x1))) -> b#(d(x1)) 176.09/45.05 b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.05 d#(a(x1)) -> d#(x1) 176.09/45.05 d#(a(x1)) -> a#(d(x1)) 176.09/45.05 d#(b(x1)) -> a#(x1) 176.09/45.05 d#(b(x1)) -> b#(a(x1)) 176.09/45.05 a#(a(x1)) -> b#(a(x1)) 176.09/45.05 a#(a(x1)) -> a#(b(a(x1))) 176.09/45.05 TRS: 176.09/45.05 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.05 a(c(x1)) -> c(a(x1)) 176.09/45.05 b(c(x1)) -> a(b(x1)) 176.09/45.05 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.05 d(a(x1)) -> a(d(x1)) 176.09/45.05 d(b(x1)) -> b(a(x1)) 176.09/45.05 a(a(x1)) -> a(b(a(x1))) 176.09/45.05 graph: 176.09/45.05 d#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.05 d#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(d(x1)) 176.09/45.05 d#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> d#(x1) 176.09/45.05 d#(b(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(x1)) 176.09/45.05 d#(b(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(x1) 176.09/45.05 d#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.05 d#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 176.09/45.05 d#(b(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1) 176.09/45.05 d#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1)) 176.09/45.05 d#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) 176.09/45.05 d#(a(x1)) -> d#(x1) -> d#(b(x1)) -> b#(a(x1)) 176.09/45.05 d#(a(x1)) -> d#(x1) -> d#(b(x1)) -> a#(x1) 176.09/45.05 d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> a#(d(x1)) 176.09/45.05 d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(x1) 176.09/45.05 d#(a(x1)) -> a#(d(x1)) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.05 d#(a(x1)) -> a#(d(x1)) -> a#(a(x1)) -> b#(a(x1)) 176.09/45.05 d#(a(x1)) -> a#(d(x1)) -> a#(c(x1)) -> a#(x1) 176.09/45.05 d#(a(x1)) -> a#(d(x1)) -> a#(a(b(x1))) -> b#(a(x1)) 176.09/45.05 d#(a(x1)) -> a#(d(x1)) -> a#(a(b(x1))) -> a#(x1) 176.09/45.05 b#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.05 b#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> b#(d(x1)) 176.09/45.05 b#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> d#(x1) 176.09/45.05 b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(x1)) 176.09/45.05 b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) 176.09/45.05 b#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.05 b#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(a(x1)) 176.09/45.05 b#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(x1) 176.09/45.05 b#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> b#(a(x1)) 176.09/45.05 b#(c(x1)) -> a#(b(x1)) -> a#(a(b(x1))) -> a#(x1) 176.09/45.05 b#(a(a(x1))) -> d#(x1) -> d#(b(x1)) -> b#(a(x1)) 176.09/45.05 b#(a(a(x1))) -> d#(x1) -> d#(b(x1)) -> a#(x1) 176.09/45.05 b#(a(a(x1))) -> d#(x1) -> d#(a(x1)) -> a#(d(x1)) 176.09/45.05 b#(a(a(x1))) -> d#(x1) -> d#(a(x1)) -> d#(x1) 176.09/45.05 b#(a(a(x1))) -> b#(d(x1)) -> b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.05 b#(a(a(x1))) -> b#(d(x1)) -> b#(a(a(x1))) -> b#(d(x1)) 176.09/45.05 b#(a(a(x1))) -> b#(d(x1)) -> b#(a(a(x1))) -> d#(x1) 176.09/45.05 b#(a(a(x1))) -> b#(d(x1)) -> b#(c(x1)) -> a#(b(x1)) 176.09/45.05 b#(a(a(x1))) -> b#(d(x1)) -> b#(c(x1)) -> b#(x1) 176.09/45.05 b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.05 b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(x1)) -> b#(a(x1)) 176.09/45.05 b#(a(a(x1))) -> a#(b(d(x1))) -> a#(c(x1)) -> a#(x1) 176.09/45.05 b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(b(x1))) -> b#(a(x1)) 176.09/45.05 b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(b(x1))) -> a#(x1) 176.09/45.05 a#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.05 a#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 176.09/45.05 a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1) 176.09/45.06 a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1)) 176.09/45.06 a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) 176.09/45.06 a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.06 a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(d(x1)) 176.09/45.06 a#(a(b(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> d#(x1) 176.09/45.06 a#(a(b(x1))) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(x1)) 176.09/45.06 a#(a(b(x1))) -> b#(a(x1)) -> b#(c(x1)) -> b#(x1) 176.09/45.06 a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 a#(a(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 176.09/45.06 a#(a(b(x1))) -> a#(x1) -> a#(c(x1)) -> a#(x1) 176.09/45.06 a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(x1)) 176.09/45.06 a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1) 176.09/45.06 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.06 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(d(x1)) 176.09/45.06 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> d#(x1) 176.09/45.06 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(x1)) 176.09/45.06 a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(x1) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) -> a#(c(x1)) -> a#(x1) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(b(x1))) -> b#(a(x1)) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(b(x1))) -> a#(x1) 176.09/45.06 Arctic Interpretation Processor: 176.09/45.06 dimension: 1 176.09/45.06 usable rules: 176.09/45.06 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.06 a(c(x1)) -> c(a(x1)) 176.09/45.06 b(c(x1)) -> a(b(x1)) 176.09/45.06 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.06 d(a(x1)) -> a(d(x1)) 176.09/45.06 d(b(x1)) -> b(a(x1)) 176.09/45.06 a(a(x1)) -> a(b(a(x1))) 176.09/45.06 interpretation: 176.09/45.06 [d#](x0) = 8x0, 176.09/45.06 176.09/45.06 [b#](x0) = 6x0 + 0, 176.09/45.06 176.09/45.06 [a#](x0) = 8x0 + 0, 176.09/45.06 176.09/45.06 [d](x0) = 2x0 + 1, 176.09/45.06 176.09/45.06 [c](x0) = 2x0 + 3, 176.09/45.06 176.09/45.06 [b](x0) = x0 + 0, 176.09/45.06 176.09/45.06 [a](x0) = 2x0 + 1 176.09/45.06 orientation: 176.09/45.06 a#(a(b(x1))) = 10x1 + 10 >= 8x1 + 0 = a#(x1) 176.09/45.06 176.09/45.06 a#(a(b(x1))) = 10x1 + 10 >= 8x1 + 7 = b#(a(x1)) 176.09/45.06 176.09/45.06 a#(c(x1)) = 10x1 + 11 >= 8x1 + 0 = a#(x1) 176.09/45.06 176.09/45.06 b#(c(x1)) = 8x1 + 9 >= 6x1 + 0 = b#(x1) 176.09/45.06 176.09/45.06 b#(c(x1)) = 8x1 + 9 >= 8x1 + 8 = a#(b(x1)) 176.09/45.06 176.09/45.06 b#(a(a(x1))) = 10x1 + 9 >= 8x1 = d#(x1) 176.09/45.06 176.09/45.06 b#(a(a(x1))) = 10x1 + 9 >= 8x1 + 7 = b#(d(x1)) 176.09/45.06 176.09/45.06 b#(a(a(x1))) = 10x1 + 9 >= 10x1 + 9 = a#(b(d(x1))) 176.09/45.06 176.09/45.06 d#(a(x1)) = 10x1 + 9 >= 8x1 = d#(x1) 176.09/45.06 176.09/45.06 d#(a(x1)) = 10x1 + 9 >= 10x1 + 9 = a#(d(x1)) 176.09/45.06 176.09/45.06 d#(b(x1)) = 8x1 + 8 >= 8x1 + 0 = a#(x1) 176.09/45.06 176.09/45.06 d#(b(x1)) = 8x1 + 8 >= 8x1 + 7 = b#(a(x1)) 176.09/45.06 176.09/45.06 a#(a(x1)) = 10x1 + 9 >= 8x1 + 7 = b#(a(x1)) 176.09/45.06 176.09/45.06 a#(a(x1)) = 10x1 + 9 >= 10x1 + 9 = a#(b(a(x1))) 176.09/45.06 176.09/45.06 a(a(b(x1))) = 4x1 + 4 >= 4x1 + 3 = c(b(a(x1))) 176.09/45.06 176.09/45.06 a(c(x1)) = 4x1 + 5 >= 4x1 + 3 = c(a(x1)) 176.09/45.06 176.09/45.06 b(c(x1)) = 2x1 + 3 >= 2x1 + 2 = a(b(x1)) 176.09/45.06 176.09/45.06 b(a(a(x1))) = 4x1 + 3 >= 4x1 + 3 = a(b(d(x1))) 176.09/45.06 176.09/45.06 d(a(x1)) = 4x1 + 3 >= 4x1 + 3 = a(d(x1)) 176.09/45.06 176.09/45.06 d(b(x1)) = 2x1 + 2 >= 2x1 + 1 = b(a(x1)) 176.09/45.06 176.09/45.06 a(a(x1)) = 4x1 + 3 >= 4x1 + 3 = a(b(a(x1))) 176.09/45.06 problem: 176.09/45.06 DPs: 176.09/45.06 b#(c(x1)) -> a#(b(x1)) 176.09/45.06 b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.06 d#(a(x1)) -> a#(d(x1)) 176.09/45.06 d#(b(x1)) -> a#(x1) 176.09/45.06 d#(b(x1)) -> b#(a(x1)) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 TRS: 176.09/45.06 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.06 a(c(x1)) -> c(a(x1)) 176.09/45.06 b(c(x1)) -> a(b(x1)) 176.09/45.06 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.06 d(a(x1)) -> a(d(x1)) 176.09/45.06 d(b(x1)) -> b(a(x1)) 176.09/45.06 a(a(x1)) -> a(b(a(x1))) 176.09/45.06 Restore Modifier: 176.09/45.06 DPs: 176.09/45.06 b#(c(x1)) -> a#(b(x1)) 176.09/45.06 b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.06 d#(a(x1)) -> a#(d(x1)) 176.09/45.06 d#(b(x1)) -> a#(x1) 176.09/45.06 d#(b(x1)) -> b#(a(x1)) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 TRS: 176.09/45.06 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.06 a(c(x1)) -> c(a(x1)) 176.09/45.06 b(c(x1)) -> a(b(x1)) 176.09/45.06 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.06 d(a(x1)) -> a(d(x1)) 176.09/45.06 d(b(x1)) -> b(a(x1)) 176.09/45.06 a(a(x1)) -> a(b(a(x1))) 176.09/45.06 EDG Processor: 176.09/45.06 DPs: 176.09/45.06 b#(c(x1)) -> a#(b(x1)) 176.09/45.06 b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.06 d#(a(x1)) -> a#(d(x1)) 176.09/45.06 d#(b(x1)) -> a#(x1) 176.09/45.06 d#(b(x1)) -> b#(a(x1)) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 TRS: 176.09/45.06 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.06 a(c(x1)) -> c(a(x1)) 176.09/45.06 b(c(x1)) -> a(b(x1)) 176.09/45.06 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.06 d(a(x1)) -> a(d(x1)) 176.09/45.06 d(b(x1)) -> b(a(x1)) 176.09/45.06 a(a(x1)) -> a(b(a(x1))) 176.09/45.06 graph: 176.09/45.06 d#(b(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(x1)) 176.09/45.06 d#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(d(x1))) 176.09/45.06 d#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 d#(a(x1)) -> a#(d(x1)) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 b#(c(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 b#(a(a(x1))) -> a#(b(d(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 SCC Processor: 176.09/45.06 #sccs: 1 176.09/45.06 #rules: 1 176.09/45.06 #arcs: 7/36 176.09/45.06 DPs: 176.09/45.06 a#(a(x1)) -> a#(b(a(x1))) 176.09/45.06 TRS: 176.09/45.06 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.06 a(c(x1)) -> c(a(x1)) 176.09/45.06 b(c(x1)) -> a(b(x1)) 176.09/45.06 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.06 d(a(x1)) -> a(d(x1)) 176.09/45.06 d(b(x1)) -> b(a(x1)) 176.09/45.06 a(a(x1)) -> a(b(a(x1))) 176.09/45.06 Arctic Interpretation Processor: 176.09/45.06 dimension: 1 176.09/45.06 usable rules: 176.09/45.06 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.06 a(c(x1)) -> c(a(x1)) 176.09/45.06 b(c(x1)) -> a(b(x1)) 176.09/45.06 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.06 d(a(x1)) -> a(d(x1)) 176.09/45.06 d(b(x1)) -> b(a(x1)) 176.09/45.06 a(a(x1)) -> a(b(a(x1))) 176.09/45.06 interpretation: 176.09/45.06 [a#](x0) = x0 + 0, 176.09/45.06 176.09/45.06 [d](x0) = 12x0 + 1, 176.09/45.06 176.09/45.06 [c](x0) = 12x0 + 15, 176.09/45.06 176.09/45.06 [b](x0) = -1x0 + 0, 176.09/45.06 176.09/45.06 [a](x0) = 12x0 + 1 176.09/45.06 orientation: 176.09/45.06 a#(a(x1)) = 12x1 + 1 >= 11x1 + 0 = a#(b(a(x1))) 176.09/45.06 176.09/45.06 a(a(b(x1))) = 23x1 + 24 >= 23x1 + 15 = c(b(a(x1))) 176.09/45.06 176.09/45.06 a(c(x1)) = 24x1 + 27 >= 24x1 + 15 = c(a(x1)) 176.09/45.06 176.09/45.06 b(c(x1)) = 11x1 + 14 >= 11x1 + 12 = a(b(x1)) 176.09/45.06 176.09/45.06 b(a(a(x1))) = 23x1 + 12 >= 23x1 + 12 = a(b(d(x1))) 176.09/45.06 176.09/45.06 d(a(x1)) = 24x1 + 13 >= 24x1 + 13 = a(d(x1)) 176.09/45.06 176.09/45.06 d(b(x1)) = 11x1 + 12 >= 11x1 + 0 = b(a(x1)) 176.09/45.06 176.09/45.06 a(a(x1)) = 24x1 + 13 >= 23x1 + 12 = a(b(a(x1))) 176.09/45.06 problem: 176.09/45.06 DPs: 176.09/45.06 176.09/45.06 TRS: 176.09/45.06 a(a(b(x1))) -> c(b(a(x1))) 176.09/45.06 a(c(x1)) -> c(a(x1)) 176.09/45.06 b(c(x1)) -> a(b(x1)) 176.09/45.06 b(a(a(x1))) -> a(b(d(x1))) 176.09/45.06 d(a(x1)) -> a(d(x1)) 176.09/45.06 d(b(x1)) -> b(a(x1)) 176.09/45.06 a(a(x1)) -> a(b(a(x1))) 176.09/45.06 Qed 176.09/45.07 EOF