191.73/48.66 YES 191.73/48.67 191.73/48.67 Problem: 191.73/48.67 a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) 191.73/48.67 b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) 191.73/48.67 c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) 191.73/48.67 b(b(x1)) -> d(d(d(d(x1)))) 191.73/48.67 c(c(d(d(d(d(x1)))))) -> a(a(x1)) 191.73/48.67 191.73/48.67 Proof: 191.73/48.67 DP Processor: 191.73/48.67 DPs: 191.73/48.67 a#(a(a(a(x1)))) -> b#(x1) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(x1)) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(x1))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) 191.73/48.67 b#(b(b(b(x1)))) -> c#(x1) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(x1)) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(x1))) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) 191.73/48.67 TRS: 191.73/48.67 a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) 191.73/48.67 b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) 191.73/48.67 c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) 191.73/48.67 b(b(x1)) -> d(d(d(d(x1)))) 191.73/48.67 c(c(d(d(d(d(x1)))))) -> a(a(x1)) 191.73/48.67 TDG Processor: 191.73/48.67 DPs: 191.73/48.67 a#(a(a(a(x1)))) -> b#(x1) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(x1)) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(x1))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) 191.73/48.67 b#(b(b(b(x1)))) -> c#(x1) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(x1)) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(x1))) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) 191.73/48.67 TRS: 191.73/48.67 a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) 191.73/48.67 b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) 191.73/48.67 c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) 191.73/48.67 b(b(x1)) -> d(d(d(d(x1)))) 191.73/48.67 c(c(d(d(d(d(x1)))))) -> a(a(x1)) 191.73/48.67 graph: 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(x1))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(x1)) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(x1) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(x1))) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(x1)) 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) -> 191.73/48.67 a#(a(a(a(x1)))) -> b#(x1) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) -> 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) -> 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) -> 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) -> 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) -> 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) -> 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(x1))) -> 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(x1))) -> c#(c(d(d(d(d(x1)))))) -> a#(x1) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(x1)) -> c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(x1)) -> c#(c(d(d(d(d(x1)))))) -> a#(x1) 191.73/48.67 b#(b(b(b(x1)))) -> c#(x1) -> c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) 191.73/48.67 b#(b(b(b(x1)))) -> c#(x1) -> 191.73/48.67 c#(c(d(d(d(d(x1)))))) -> a#(x1) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(c(x1))) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> 191.73/48.67 b#(b(b(b(x1)))) -> c#(c(x1)) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> 191.73/48.67 b#(b(b(b(x1)))) -> c#(x1) 191.73/48.67 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(x1))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(x1)) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(x1) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(x1))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(x1)) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(b(b(x1)))) -> c#(x1) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(x1))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(x1))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(x1))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(x1))) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(x1))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> c#(c(x1)) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> c#(x1) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(x1)) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(x1)) -> 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(c(c(x1))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(c(x1)) 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(x1) 191.73/48.69 a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(c(x1))) 191.73/48.69 a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(x1)) 191.73/48.69 a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(x1) 191.73/48.69 Matrix Interpretation Processor: dim=1 191.73/48.69 191.73/48.69 interpretation: 191.73/48.69 [c#](x0) = x0 + 1, 191.73/48.69 191.73/48.69 [b#](x0) = x0 + 4, 191.73/48.69 191.73/48.69 [a#](x0) = x0 + 7, 191.73/48.69 191.73/48.69 [d](x0) = x0 + 4, 191.73/48.69 191.73/48.69 [c](x0) = x0 + 6, 191.73/48.69 191.73/48.69 [b](x0) = x0 + 9, 191.73/48.69 191.73/48.69 [a](x0) = x0 + 14 191.73/48.69 orientation: 191.73/48.69 a#(a(a(a(x1)))) = x1 + 49 >= x1 + 4 = b#(x1) 191.73/48.69 191.73/48.69 a#(a(a(a(x1)))) = x1 + 49 >= x1 + 13 = b#(b(x1)) 191.73/48.69 191.73/48.69 a#(a(a(a(x1)))) = x1 + 49 >= x1 + 22 = b#(b(b(x1))) 191.73/48.69 191.73/48.69 a#(a(a(a(x1)))) = x1 + 49 >= x1 + 31 = b#(b(b(b(x1)))) 191.73/48.69 191.73/48.69 a#(a(a(a(x1)))) = x1 + 49 >= x1 + 40 = b#(b(b(b(b(x1))))) 191.73/48.69 191.73/48.69 a#(a(a(a(x1)))) = x1 + 49 >= x1 + 49 = b#(b(b(b(b(b(x1)))))) 191.73/48.69 191.73/48.69 b#(b(b(b(x1)))) = x1 + 31 >= x1 + 1 = c#(x1) 191.73/48.69 191.73/48.69 b#(b(b(b(x1)))) = x1 + 31 >= x1 + 7 = c#(c(x1)) 191.73/48.69 191.73/48.69 b#(b(b(b(x1)))) = x1 + 31 >= x1 + 13 = c#(c(c(x1))) 191.73/48.69 191.73/48.69 b#(b(b(b(x1)))) = x1 + 31 >= x1 + 19 = c#(c(c(c(x1)))) 191.73/48.69 191.73/48.69 b#(b(b(b(x1)))) = x1 + 31 >= x1 + 25 = c#(c(c(c(c(x1))))) 191.73/48.69 191.73/48.69 b#(b(b(b(x1)))) = x1 + 31 >= x1 + 31 = c#(c(c(c(c(c(x1)))))) 191.73/48.69 191.73/48.69 c#(c(d(d(d(d(x1)))))) = x1 + 23 >= x1 + 7 = a#(x1) 191.73/48.69 191.73/48.69 c#(c(d(d(d(d(x1)))))) = x1 + 23 >= x1 + 21 = a#(a(x1)) 191.73/48.69 191.73/48.69 a(a(a(a(x1)))) = x1 + 56 >= x1 + 54 = b(b(b(b(b(b(x1)))))) 191.73/48.69 191.73/48.69 b(b(b(b(x1)))) = x1 + 36 >= x1 + 36 = c(c(c(c(c(c(x1)))))) 191.73/48.69 191.73/48.69 c(c(c(c(x1)))) = x1 + 24 >= x1 + 24 = d(d(d(d(d(d(x1)))))) 191.73/48.69 191.73/48.69 b(b(x1)) = x1 + 18 >= x1 + 16 = d(d(d(d(x1)))) 191.73/48.69 191.73/48.69 c(c(d(d(d(d(x1)))))) = x1 + 28 >= x1 + 28 = a(a(x1)) 191.73/48.69 problem: 191.73/48.69 DPs: 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 TRS: 191.73/48.69 a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) 191.73/48.69 b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) 191.73/48.69 c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) 191.73/48.69 b(b(x1)) -> d(d(d(d(x1)))) 191.73/48.69 c(c(d(d(d(d(x1)))))) -> a(a(x1)) 191.73/48.69 Restore Modifier: 191.73/48.69 DPs: 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 TRS: 191.73/48.69 a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) 191.73/48.69 b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) 191.73/48.69 c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) 191.73/48.69 b(b(x1)) -> d(d(d(d(x1)))) 191.73/48.69 c(c(d(d(d(d(x1)))))) -> a(a(x1)) 191.73/48.69 EDG Processor: 191.73/48.69 DPs: 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) 191.73/48.69 b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 TRS: 191.73/48.69 a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) 191.73/48.69 b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) 191.73/48.69 c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) 191.73/48.69 b(b(x1)) -> d(d(d(d(x1)))) 191.73/48.69 c(c(d(d(d(d(x1)))))) -> a(a(x1)) 191.73/48.69 graph: 191.73/48.69 a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) 191.73/48.69 SCC Processor: 191.73/48.69 #sccs: 0 191.73/48.69 #rules: 0 191.73/48.69 #arcs: 1/4 191.73/48.69 191.73/48.69 EOF