191.48/48.91 YES 191.54/48.92 191.54/48.92 Problem: 191.54/48.92 a(b(x1)) -> b(c(a(x1))) 191.54/48.92 b(c(x1)) -> c(b(b(x1))) 191.54/48.92 a(c(x1)) -> c(a(b(x1))) 191.54/48.92 a(a(x1)) -> a(d(d(d(x1)))) 191.54/48.92 d(a(x1)) -> d(d(c(x1))) 191.54/48.92 a(d(d(c(x1)))) -> a(a(a(d(x1)))) 191.54/48.92 e(e(f(f(x1)))) -> f(f(f(e(e(x1))))) 191.54/48.92 e(x1) -> a(x1) 191.54/48.92 b(d(x1)) -> d(d(x1)) 191.54/48.92 191.54/48.92 Proof: 191.54/48.92 String Reversal Processor: 191.54/48.92 b(a(x1)) -> a(c(b(x1))) 191.54/48.92 c(b(x1)) -> b(b(c(x1))) 191.54/48.92 c(a(x1)) -> b(a(c(x1))) 191.54/48.92 a(a(x1)) -> d(d(d(a(x1)))) 191.54/48.92 a(d(x1)) -> c(d(d(x1))) 191.54/48.92 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.54/48.92 f(f(e(e(x1)))) -> e(e(f(f(f(x1))))) 191.54/48.92 e(x1) -> a(x1) 191.54/48.92 d(b(x1)) -> d(d(x1)) 191.54/48.92 Matrix Interpretation Processor: dim=1 191.54/48.92 191.54/48.92 interpretation: 191.54/48.92 [e](x0) = 2x0 + 1, 191.54/48.92 191.54/48.92 [f](x0) = x0, 191.54/48.92 191.54/48.92 [d](x0) = x0, 191.54/48.92 191.54/48.92 [c](x0) = x0, 191.54/48.92 191.54/48.92 [a](x0) = x0, 191.54/48.92 191.54/48.92 [b](x0) = x0 191.54/48.92 orientation: 191.54/48.92 b(a(x1)) = x1 >= x1 = a(c(b(x1))) 191.54/48.92 191.54/48.92 c(b(x1)) = x1 >= x1 = b(b(c(x1))) 191.54/48.92 191.54/48.92 c(a(x1)) = x1 >= x1 = b(a(c(x1))) 191.54/48.92 191.54/48.92 a(a(x1)) = x1 >= x1 = d(d(d(a(x1)))) 191.54/48.92 191.54/48.92 a(d(x1)) = x1 >= x1 = c(d(d(x1))) 191.54/48.92 191.54/48.92 c(d(d(a(x1)))) = x1 >= x1 = d(a(a(a(x1)))) 191.54/48.92 191.54/48.92 f(f(e(e(x1)))) = 4x1 + 3 >= 4x1 + 3 = e(e(f(f(f(x1))))) 191.54/48.92 191.54/48.92 e(x1) = 2x1 + 1 >= x1 = a(x1) 191.54/48.92 191.54/48.92 d(b(x1)) = x1 >= x1 = d(d(x1)) 191.54/48.92 problem: 191.54/48.92 b(a(x1)) -> a(c(b(x1))) 191.54/48.92 c(b(x1)) -> b(b(c(x1))) 191.54/48.92 c(a(x1)) -> b(a(c(x1))) 191.54/48.92 a(a(x1)) -> d(d(d(a(x1)))) 191.54/48.92 a(d(x1)) -> c(d(d(x1))) 191.54/48.92 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.54/48.92 f(f(e(e(x1)))) -> e(e(f(f(f(x1))))) 191.54/48.92 d(b(x1)) -> d(d(x1)) 191.54/48.92 String Reversal Processor: 191.54/48.92 a(b(x1)) -> b(c(a(x1))) 191.54/48.92 b(c(x1)) -> c(b(b(x1))) 191.54/48.92 a(c(x1)) -> c(a(b(x1))) 191.54/48.92 a(a(x1)) -> a(d(d(d(x1)))) 191.54/48.92 d(a(x1)) -> d(d(c(x1))) 191.54/48.92 a(d(d(c(x1)))) -> a(a(a(d(x1)))) 191.54/48.92 e(e(f(f(x1)))) -> f(f(f(e(e(x1))))) 191.54/48.92 b(d(x1)) -> d(d(x1)) 191.54/48.92 Matrix Interpretation Processor: dim=1 191.54/48.92 191.54/48.92 interpretation: 191.54/48.92 [e](x0) = 2x0 + 4, 191.54/48.92 191.54/48.92 [f](x0) = x0 + 1, 191.54/48.92 191.54/48.92 [d](x0) = x0, 191.54/48.92 191.54/48.92 [c](x0) = x0, 191.54/48.92 191.54/48.92 [a](x0) = x0, 191.54/48.92 191.54/48.92 [b](x0) = x0 191.54/48.92 orientation: 191.54/48.92 a(b(x1)) = x1 >= x1 = b(c(a(x1))) 191.54/48.92 191.54/48.92 b(c(x1)) = x1 >= x1 = c(b(b(x1))) 191.54/48.92 191.54/48.92 a(c(x1)) = x1 >= x1 = c(a(b(x1))) 191.54/48.92 191.54/48.92 a(a(x1)) = x1 >= x1 = a(d(d(d(x1)))) 191.54/48.92 191.54/48.92 d(a(x1)) = x1 >= x1 = d(d(c(x1))) 191.54/48.92 191.54/48.92 a(d(d(c(x1)))) = x1 >= x1 = a(a(a(d(x1)))) 191.54/48.92 191.54/48.92 e(e(f(f(x1)))) = 4x1 + 20 >= 4x1 + 15 = f(f(f(e(e(x1))))) 191.54/48.92 191.54/48.92 b(d(x1)) = x1 >= x1 = d(d(x1)) 191.54/48.92 problem: 191.54/48.92 a(b(x1)) -> b(c(a(x1))) 191.54/48.92 b(c(x1)) -> c(b(b(x1))) 191.54/48.92 a(c(x1)) -> c(a(b(x1))) 191.54/48.92 a(a(x1)) -> a(d(d(d(x1)))) 191.54/48.92 d(a(x1)) -> d(d(c(x1))) 191.54/48.92 a(d(d(c(x1)))) -> a(a(a(d(x1)))) 191.54/48.92 b(d(x1)) -> d(d(x1)) 191.54/48.92 Matrix Interpretation Processor: dim=3 191.54/48.92 191.54/48.92 interpretation: 191.54/48.92 [1 0 0] [0] 191.54/48.92 [d](x0) = [0 0 0]x0 + [1] 191.54/48.92 [0 0 0] [0], 191.54/48.92 191.54/48.92 [1 0 1] 191.54/48.92 [c](x0) = [0 1 1]x0 191.54/48.92 [0 1 1] , 191.54/48.92 191.54/48.92 [1 0 1] 191.54/48.92 [a](x0) = [0 0 0]x0 191.54/48.92 [0 0 0] , 191.54/48.92 191.54/48.92 [1 1 1] 191.54/48.92 [b](x0) = [0 1 0]x0 191.54/48.92 [0 0 1] 191.54/48.92 orientation: 191.54/48.92 [1 1 2] [1 0 1] 191.54/48.92 a(b(x1)) = [0 0 0]x1 >= [0 0 0]x1 = b(c(a(x1))) 191.54/48.92 [0 0 0] [0 0 0] 191.54/48.92 191.54/48.92 [1 2 3] [1 2 3] 191.54/48.92 b(c(x1)) = [0 1 1]x1 >= [0 1 1]x1 = c(b(b(x1))) 191.54/48.92 [0 1 1] [0 1 1] 191.54/48.92 191.54/48.92 [1 1 2] [1 1 2] 191.54/48.92 a(c(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(a(b(x1))) 191.54/48.92 [0 0 0] [0 0 0] 191.54/48.92 191.54/48.92 [1 0 1] [1 0 0] 191.54/48.92 a(a(x1)) = [0 0 0]x1 >= [0 0 0]x1 = a(d(d(d(x1)))) 191.54/48.92 [0 0 0] [0 0 0] 191.54/48.92 191.54/48.92 [1 0 1] [0] [1 0 1] [0] 191.54/48.92 d(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = d(d(c(x1))) 191.54/48.92 [0 0 0] [0] [0 0 0] [0] 191.54/48.92 191.54/48.92 [1 0 1] [1 0 0] 191.54/48.92 a(d(d(c(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a(a(d(x1)))) 191.54/48.92 [0 0 0] [0 0 0] 191.55/48.93 191.55/48.93 [1 0 0] [1] [1 0 0] [0] 191.55/48.93 b(d(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = d(d(x1)) 191.55/48.93 [0 0 0] [0] [0 0 0] [0] 191.55/48.93 problem: 191.55/48.93 a(b(x1)) -> b(c(a(x1))) 191.55/48.93 b(c(x1)) -> c(b(b(x1))) 191.55/48.93 a(c(x1)) -> c(a(b(x1))) 191.55/48.93 a(a(x1)) -> a(d(d(d(x1)))) 191.55/48.93 d(a(x1)) -> d(d(c(x1))) 191.55/48.93 a(d(d(c(x1)))) -> a(a(a(d(x1)))) 191.55/48.93 String Reversal Processor: 191.55/48.93 b(a(x1)) -> a(c(b(x1))) 191.55/48.93 c(b(x1)) -> b(b(c(x1))) 191.55/48.93 c(a(x1)) -> b(a(c(x1))) 191.55/48.93 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.93 a(d(x1)) -> c(d(d(x1))) 191.55/48.93 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.93 DP Processor: 191.55/48.93 DPs: 191.55/48.93 b#(a(x1)) -> b#(x1) 191.55/48.93 b#(a(x1)) -> c#(b(x1)) 191.55/48.93 b#(a(x1)) -> a#(c(b(x1))) 191.55/48.93 c#(b(x1)) -> c#(x1) 191.55/48.93 c#(b(x1)) -> b#(c(x1)) 191.55/48.93 c#(b(x1)) -> b#(b(c(x1))) 191.55/48.93 c#(a(x1)) -> c#(x1) 191.55/48.93 c#(a(x1)) -> a#(c(x1)) 191.55/48.93 c#(a(x1)) -> b#(a(c(x1))) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) 191.55/48.93 c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.93 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.93 TRS: 191.55/48.93 b(a(x1)) -> a(c(b(x1))) 191.55/48.93 c(b(x1)) -> b(b(c(x1))) 191.55/48.93 c(a(x1)) -> b(a(c(x1))) 191.55/48.93 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.93 a(d(x1)) -> c(d(d(x1))) 191.55/48.93 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.93 TDG Processor: 191.55/48.93 DPs: 191.55/48.93 b#(a(x1)) -> b#(x1) 191.55/48.93 b#(a(x1)) -> c#(b(x1)) 191.55/48.93 b#(a(x1)) -> a#(c(b(x1))) 191.55/48.93 c#(b(x1)) -> c#(x1) 191.55/48.93 c#(b(x1)) -> b#(c(x1)) 191.55/48.93 c#(b(x1)) -> b#(b(c(x1))) 191.55/48.93 c#(a(x1)) -> c#(x1) 191.55/48.93 c#(a(x1)) -> a#(c(x1)) 191.55/48.93 c#(a(x1)) -> b#(a(c(x1))) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) 191.55/48.93 c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.93 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.93 TRS: 191.55/48.93 b(a(x1)) -> a(c(b(x1))) 191.55/48.93 c(b(x1)) -> b(b(c(x1))) 191.55/48.93 c(a(x1)) -> b(a(c(x1))) 191.55/48.93 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.93 a(d(x1)) -> c(d(d(x1))) 191.55/48.93 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.93 graph: 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) -> c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) -> c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) -> c#(a(x1)) -> b#(a(c(x1))) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) -> c#(a(x1)) -> a#(c(x1)) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) -> c#(a(x1)) -> c#(x1) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) -> c#(b(x1)) -> b#(b(c(x1))) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) -> c#(b(x1)) -> b#(c(x1)) 191.55/48.93 a#(d(x1)) -> c#(d(d(x1))) -> c#(b(x1)) -> c#(x1) 191.55/48.93 c#(d(d(a(x1)))) -> a#(a(a(x1))) -> a#(d(x1)) -> c#(d(d(x1))) 191.55/48.93 c#(d(d(a(x1)))) -> a#(a(x1)) -> a#(d(x1)) -> c#(d(d(x1))) 191.55/48.93 c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> c#(d(d(x1))) 191.55/48.93 c#(a(x1)) -> c#(x1) -> c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.93 c#(a(x1)) -> c#(x1) -> c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.93 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(c(x1))) 191.55/48.93 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 191.55/48.93 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 191.55/48.93 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(b(c(x1))) 191.55/48.93 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1)) 191.55/48.93 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 191.55/48.93 c#(a(x1)) -> b#(a(c(x1))) -> b#(a(x1)) -> a#(c(b(x1))) 191.55/48.93 c#(a(x1)) -> b#(a(c(x1))) -> b#(a(x1)) -> c#(b(x1)) 191.55/48.93 c#(a(x1)) -> b#(a(c(x1))) -> b#(a(x1)) -> b#(x1) 191.55/48.93 c#(b(x1)) -> c#(x1) -> c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.93 c#(b(x1)) -> c#(x1) -> c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.93 c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(c(x1))) 191.55/48.93 c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 191.55/48.93 c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 191.55/48.93 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(b(c(x1))) 191.55/48.93 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1)) 191.55/48.93 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 191.55/48.93 c#(b(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(b(x1))) 191.55/48.93 c#(b(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(x1)) 191.55/48.93 c#(b(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(x1) 191.55/48.93 c#(b(x1)) -> b#(b(c(x1))) -> b#(a(x1)) -> a#(c(b(x1))) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) -> b#(a(x1)) -> c#(b(x1)) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) -> b#(a(x1)) -> b#(x1) 191.55/48.94 b#(a(x1)) -> a#(c(b(x1))) -> a#(d(x1)) -> c#(d(d(x1))) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> a#(c(x1)) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(x1) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> b#(c(x1)) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> c#(x1) 191.55/48.94 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 191.55/48.94 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 191.55/48.94 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 191.55/48.94 EDG Processor: 191.55/48.94 DPs: 191.55/48.94 b#(a(x1)) -> b#(x1) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) 191.55/48.94 b#(a(x1)) -> a#(c(b(x1))) 191.55/48.94 c#(b(x1)) -> c#(x1) 191.55/48.94 c#(b(x1)) -> b#(c(x1)) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 c#(a(x1)) -> c#(x1) 191.55/48.94 c#(a(x1)) -> a#(c(x1)) 191.55/48.94 c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 a#(d(x1)) -> c#(d(d(x1))) 191.55/48.94 c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.94 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.94 TRS: 191.55/48.94 b(a(x1)) -> a(c(b(x1))) 191.55/48.94 c(b(x1)) -> b(b(c(x1))) 191.55/48.94 c(a(x1)) -> b(a(c(x1))) 191.55/48.94 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.94 a(d(x1)) -> c(d(d(x1))) 191.55/48.94 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.94 graph: 191.55/48.94 a#(d(x1)) -> c#(d(d(x1))) -> c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.94 a#(d(x1)) -> c#(d(d(x1))) -> 191.55/48.94 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.94 c#(d(d(a(x1)))) -> a#(a(a(x1))) -> a#(d(x1)) -> c#(d(d(x1))) 191.55/48.94 c#(d(d(a(x1)))) -> a#(a(x1)) -> a#(d(x1)) -> c#(d(d(x1))) 191.55/48.94 c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> c#(d(d(x1))) 191.55/48.94 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 191.55/48.94 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1)) 191.55/48.94 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 191.55/48.94 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 191.55/48.94 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 c#(a(x1)) -> c#(x1) -> c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.94 c#(a(x1)) -> c#(x1) -> c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.94 c#(a(x1)) -> b#(a(c(x1))) -> b#(a(x1)) -> b#(x1) 191.55/48.94 c#(a(x1)) -> b#(a(c(x1))) -> b#(a(x1)) -> c#(b(x1)) 191.55/48.94 c#(a(x1)) -> b#(a(c(x1))) -> b#(a(x1)) -> a#(c(b(x1))) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1)) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.94 c#(b(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(x1) 191.55/48.94 c#(b(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(x1)) 191.55/48.94 c#(b(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(b(x1))) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) -> b#(a(x1)) -> b#(x1) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) -> b#(a(x1)) -> c#(b(x1)) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) -> b#(a(x1)) -> a#(c(b(x1))) 191.55/48.94 b#(a(x1)) -> a#(c(b(x1))) -> a#(d(x1)) -> c#(d(d(x1))) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> c#(x1) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> b#(c(x1)) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(x1) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> a#(c(x1)) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) -> c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.94 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 191.55/48.94 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1)) 191.55/48.94 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1))) 191.55/48.94 SCC Processor: 191.55/48.94 #sccs: 2 191.55/48.94 #rules: 10 191.55/48.94 #arcs: 42/144 191.55/48.94 DPs: 191.55/48.94 c#(a(x1)) -> c#(x1) 191.55/48.94 c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 b#(a(x1)) -> c#(b(x1)) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 b#(a(x1)) -> b#(x1) 191.55/48.94 c#(b(x1)) -> b#(c(x1)) 191.55/48.94 c#(b(x1)) -> c#(x1) 191.55/48.94 TRS: 191.55/48.94 b(a(x1)) -> a(c(b(x1))) 191.55/48.94 c(b(x1)) -> b(b(c(x1))) 191.55/48.94 c(a(x1)) -> b(a(c(x1))) 191.55/48.94 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.94 a(d(x1)) -> c(d(d(x1))) 191.55/48.94 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.94 KBO Processor: 191.55/48.94 argument filtering: 191.55/48.94 pi(b) = 0 191.55/48.94 pi(a) = [0] 191.55/48.94 pi(c) = 0 191.55/48.94 pi(d) = [] 191.55/48.94 pi(b#) = 0 191.55/48.94 pi(c#) = 0 191.55/48.94 usable rules: 191.55/48.94 b(a(x1)) -> a(c(b(x1))) 191.55/48.94 c(b(x1)) -> b(b(c(x1))) 191.55/48.94 c(a(x1)) -> b(a(c(x1))) 191.55/48.94 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.94 a(d(x1)) -> c(d(d(x1))) 191.55/48.94 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.94 weight function: 191.55/48.94 w0 = 1 191.55/48.94 w(d) = w(a) = 1 191.55/48.94 w(c#) = w(b#) = w(c) = w(b) = 0 191.55/48.94 precedence: 191.55/48.94 c# ~ b# ~ d ~ c ~ a ~ b 191.55/48.94 problem: 191.55/48.94 DPs: 191.55/48.94 c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 c#(b(x1)) -> b#(c(x1)) 191.55/48.94 c#(b(x1)) -> c#(x1) 191.55/48.94 TRS: 191.55/48.94 b(a(x1)) -> a(c(b(x1))) 191.55/48.94 c(b(x1)) -> b(b(c(x1))) 191.55/48.94 c(a(x1)) -> b(a(c(x1))) 191.55/48.94 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.94 a(d(x1)) -> c(d(d(x1))) 191.55/48.94 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.94 Restore Modifier: 191.55/48.94 DPs: 191.55/48.94 c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 c#(b(x1)) -> b#(c(x1)) 191.55/48.94 c#(b(x1)) -> c#(x1) 191.55/48.94 TRS: 191.55/48.94 b(a(x1)) -> a(c(b(x1))) 191.55/48.94 c(b(x1)) -> b(b(c(x1))) 191.55/48.94 c(a(x1)) -> b(a(c(x1))) 191.55/48.94 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.94 a(d(x1)) -> c(d(d(x1))) 191.55/48.94 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.94 EDG Processor: 191.55/48.94 DPs: 191.55/48.94 c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 c#(b(x1)) -> b#(c(x1)) 191.55/48.94 c#(b(x1)) -> c#(x1) 191.55/48.94 TRS: 191.55/48.94 b(a(x1)) -> a(c(b(x1))) 191.55/48.94 c(b(x1)) -> b(b(c(x1))) 191.55/48.94 c(a(x1)) -> b(a(c(x1))) 191.55/48.94 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.94 a(d(x1)) -> c(d(d(x1))) 191.55/48.94 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.94 graph: 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(c(x1))) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(b(c(x1))) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1)) 191.55/48.94 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 191.55/48.94 SCC Processor: 191.55/48.94 #sccs: 1 191.55/48.94 #rules: 1 191.55/48.94 #arcs: 4/16 191.55/48.94 DPs: 191.55/48.94 c#(b(x1)) -> c#(x1) 191.55/48.94 TRS: 191.55/48.94 b(a(x1)) -> a(c(b(x1))) 191.55/48.94 c(b(x1)) -> b(b(c(x1))) 191.55/48.94 c(a(x1)) -> b(a(c(x1))) 191.55/48.94 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.94 a(d(x1)) -> c(d(d(x1))) 191.55/48.94 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.94 Usable Rule Processor: 191.55/48.94 DPs: 191.55/48.94 c#(b(x1)) -> c#(x1) 191.55/48.94 TRS: 191.55/48.94 191.55/48.94 Arctic Interpretation Processor: 191.55/48.94 dimension: 4 191.55/48.94 usable rules: 191.55/48.94 191.55/48.94 interpretation: 191.55/48.94 [c#](x0) = [0 -& -& -&]x0, 191.55/48.94 191.55/48.94 [1 0 0 0] [0] 191.55/48.94 [0 0 0 0] [0] 191.55/48.94 [b](x0) = [1 0 0 0]x0 + [0] 191.55/48.94 [0 0 0 0] [0] 191.55/48.94 orientation: 191.55/48.94 c#(b(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = c#(x1) 191.55/48.94 problem: 191.55/48.94 DPs: 191.55/48.94 191.55/48.94 TRS: 191.55/48.95 191.55/48.95 Qed 191.55/48.95 191.55/48.95 DPs: 191.55/48.95 a#(d(x1)) -> c#(d(d(x1))) 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.95 TRS: 191.55/48.95 b(a(x1)) -> a(c(b(x1))) 191.55/48.95 c(b(x1)) -> b(b(c(x1))) 191.55/48.95 c(a(x1)) -> b(a(c(x1))) 191.55/48.95 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.95 a(d(x1)) -> c(d(d(x1))) 191.55/48.95 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.95 Usable Rule Processor: 191.55/48.95 DPs: 191.55/48.95 a#(d(x1)) -> c#(d(d(x1))) 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.95 TRS: 191.55/48.95 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.95 a(d(x1)) -> c(d(d(x1))) 191.55/48.95 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.95 Matrix Interpretation Processor: dim=4 191.55/48.95 191.55/48.95 interpretation: 191.55/48.95 [a#](x0) = [0 0 0 1]x0 + [1], 191.55/48.95 191.55/48.95 [c#](x0) = [0 1 0 0]x0, 191.55/48.95 191.55/48.95 [0 0 1 0] 191.55/48.95 [0 0 0 1] 191.55/48.95 [d](x0) = [0 0 1 0]x0 191.55/48.95 [1 0 0 0] , 191.55/48.95 191.55/48.95 [0 1 0 0] 191.55/48.95 [1 0 0 0] 191.55/48.95 [c](x0) = [0 1 0 0]x0 191.55/48.95 [0 1 0 0] , 191.55/48.95 191.55/48.95 [0 0 0 1] [1] 191.55/48.95 [0 0 1 0] [0] 191.55/48.95 [a](x0) = [0 0 0 1]x0 + [0] 191.55/48.95 [0 0 0 1] [0] 191.55/48.95 orientation: 191.55/48.95 a#(d(x1)) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = c#(d(d(x1))) 191.55/48.95 191.55/48.95 c#(d(d(a(x1)))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [1] = a#(a(a(x1))) 191.55/48.95 191.55/48.95 c#(d(d(a(x1)))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [1] = a#(a(x1)) 191.55/48.95 191.55/48.95 [0 0 0 1] [1] [0 0 0 1] 191.55/48.95 [0 0 0 1] [0] [0 0 0 1] 191.55/48.95 a(a(x1)) = [0 0 0 1]x1 + [0] >= [0 0 0 1]x1 = d(d(d(a(x1)))) 191.55/48.95 [0 0 0 1] [0] [0 0 0 1] 191.55/48.95 191.55/48.95 [1 0 0 0] [1] [1 0 0 0] 191.55/48.95 [0 0 1 0] [0] [0 0 1 0] 191.55/48.95 a(d(x1)) = [1 0 0 0]x1 + [0] >= [1 0 0 0]x1 = c(d(d(x1))) 191.55/48.95 [1 0 0 0] [0] [1 0 0 0] 191.55/48.95 191.55/48.95 [0 0 0 1] [1] [0 0 0 1] [0] 191.55/48.95 [0 0 0 1] [0] [0 0 0 1] [0] 191.55/48.95 c(d(d(a(x1)))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [0] = d(a(a(a(x1)))) 191.55/48.95 [0 0 0 1] [1] [0 0 0 1] [1] 191.55/48.95 problem: 191.55/48.95 DPs: 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.95 TRS: 191.55/48.95 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.95 a(d(x1)) -> c(d(d(x1))) 191.55/48.95 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.95 Restore Modifier: 191.55/48.95 DPs: 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.95 TRS: 191.55/48.95 b(a(x1)) -> a(c(b(x1))) 191.55/48.95 c(b(x1)) -> b(b(c(x1))) 191.55/48.95 c(a(x1)) -> b(a(c(x1))) 191.55/48.95 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.95 a(d(x1)) -> c(d(d(x1))) 191.55/48.95 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.95 EDG Processor: 191.55/48.95 DPs: 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(a(x1))) 191.55/48.95 c#(d(d(a(x1)))) -> a#(a(x1)) 191.55/48.95 TRS: 191.55/48.95 b(a(x1)) -> a(c(b(x1))) 191.55/48.95 c(b(x1)) -> b(b(c(x1))) 191.55/48.95 c(a(x1)) -> b(a(c(x1))) 191.55/48.95 a(a(x1)) -> d(d(d(a(x1)))) 191.55/48.95 a(d(x1)) -> c(d(d(x1))) 191.55/48.95 c(d(d(a(x1)))) -> d(a(a(a(x1)))) 191.55/48.95 graph: 191.55/48.95 191.55/48.95 SCC Processor: 191.55/48.95 #sccs: 0 191.55/48.95 #rules: 0 191.55/48.95 #arcs: 0/4 191.55/48.95 191.55/48.96 EOF