5.63/1.93 YES 5.63/1.93 5.63/1.93 Problem: 5.63/1.93 a(a(x1)) -> b(c(x1)) 5.63/1.93 b(b(x1)) -> c(d(x1)) 5.63/1.93 b(x1) -> a(x1) 5.63/1.93 c(c(x1)) -> d(f(x1)) 5.63/1.93 d(d(x1)) -> f(f(f(x1))) 5.63/1.93 d(x1) -> b(x1) 5.63/1.93 f(f(x1)) -> g(a(x1)) 5.63/1.93 g(g(x1)) -> a(x1) 5.63/1.93 5.63/1.93 Proof: 5.63/1.93 String Reversal Processor: 5.63/1.93 a(a(x1)) -> c(b(x1)) 5.63/1.93 b(b(x1)) -> d(c(x1)) 5.63/1.93 b(x1) -> a(x1) 5.63/1.93 c(c(x1)) -> f(d(x1)) 5.63/1.93 d(d(x1)) -> f(f(f(x1))) 5.63/1.93 d(x1) -> b(x1) 5.63/1.93 f(f(x1)) -> a(g(x1)) 5.63/1.93 g(g(x1)) -> a(x1) 5.63/1.93 Matrix Interpretation Processor: dim=3 5.63/1.93 5.63/1.93 interpretation: 5.63/1.93 [1 1 0] [0] 5.63/1.93 [g](x0) = [0 0 1]x0 + [1] 5.63/1.93 [0 0 0] [0], 5.63/1.93 5.63/1.93 [1 1 0] 5.63/1.93 [f](x0) = [0 0 0]x0 5.63/1.93 [0 0 0] , 5.63/1.93 5.63/1.93 [1 0 1] 5.63/1.93 [d](x0) = [0 0 0]x0 5.63/1.93 [0 1 0] , 5.63/1.93 5.63/1.93 [1 0 1] 5.63/1.93 [b](x0) = [0 0 0]x0 5.63/1.93 [0 0 0] , 5.63/1.93 5.63/1.93 [1 0 1] 5.63/1.93 [c](x0) = [0 0 0]x0 5.63/1.93 [0 0 0] , 5.63/1.93 5.63/1.93 [1 0 1] 5.63/1.93 [a](x0) = [0 0 0]x0 5.63/1.93 [0 0 0] 5.63/1.93 orientation: 5.63/1.93 [1 0 1] [1 0 1] 5.63/1.93 a(a(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(b(x1)) 5.63/1.93 [0 0 0] [0 0 0] 5.63/1.93 5.63/1.93 [1 0 1] [1 0 1] 5.63/1.93 b(b(x1)) = [0 0 0]x1 >= [0 0 0]x1 = d(c(x1)) 5.63/1.93 [0 0 0] [0 0 0] 5.63/1.93 5.63/1.93 [1 0 1] [1 0 1] 5.63/1.93 b(x1) = [0 0 0]x1 >= [0 0 0]x1 = a(x1) 5.63/1.93 [0 0 0] [0 0 0] 5.63/1.93 5.63/1.93 [1 0 1] [1 0 1] 5.63/1.93 c(c(x1)) = [0 0 0]x1 >= [0 0 0]x1 = f(d(x1)) 5.63/1.93 [0 0 0] [0 0 0] 5.63/1.93 5.63/1.93 [1 1 1] [1 1 0] 5.63/1.93 d(d(x1)) = [0 0 0]x1 >= [0 0 0]x1 = f(f(f(x1))) 5.63/1.93 [0 0 0] [0 0 0] 5.63/1.93 5.63/1.93 [1 0 1] [1 0 1] 5.63/1.93 d(x1) = [0 0 0]x1 >= [0 0 0]x1 = b(x1) 5.63/1.93 [0 1 0] [0 0 0] 5.63/1.93 5.63/1.93 [1 1 0] [1 1 0] 5.63/1.93 f(f(x1)) = [0 0 0]x1 >= [0 0 0]x1 = a(g(x1)) 5.63/1.93 [0 0 0] [0 0 0] 5.63/1.93 5.63/1.93 [1 1 1] [1] [1 0 1] 5.63/1.93 g(g(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(x1) 5.63/1.93 [0 0 0] [0] [0 0 0] 5.63/1.93 problem: 5.63/1.93 a(a(x1)) -> c(b(x1)) 5.63/1.93 b(b(x1)) -> d(c(x1)) 5.63/1.93 b(x1) -> a(x1) 5.63/1.93 c(c(x1)) -> f(d(x1)) 5.63/1.93 d(d(x1)) -> f(f(f(x1))) 5.63/1.93 d(x1) -> b(x1) 5.63/1.93 f(f(x1)) -> a(g(x1)) 5.63/1.93 String Reversal Processor: 5.63/1.93 a(a(x1)) -> b(c(x1)) 5.63/1.93 b(b(x1)) -> c(d(x1)) 5.63/1.93 b(x1) -> a(x1) 5.63/1.93 c(c(x1)) -> d(f(x1)) 5.63/1.93 d(d(x1)) -> f(f(f(x1))) 5.63/1.93 d(x1) -> b(x1) 5.63/1.93 f(f(x1)) -> g(a(x1)) 5.63/1.93 Matrix Interpretation Processor: dim=1 5.63/1.93 5.63/1.93 interpretation: 5.63/1.93 [g](x0) = x0, 5.63/1.93 5.63/1.93 [f](x0) = x0 + 4, 5.63/1.93 5.63/1.93 [d](x0) = x0 + 8, 5.63/1.93 5.63/1.93 [b](x0) = x0 + 8, 5.63/1.93 5.63/1.93 [c](x0) = x0 + 8, 5.63/1.93 5.63/1.93 [a](x0) = x0 + 8 5.63/1.93 orientation: 5.63/1.93 a(a(x1)) = x1 + 16 >= x1 + 16 = b(c(x1)) 5.63/1.93 5.63/1.93 b(b(x1)) = x1 + 16 >= x1 + 16 = c(d(x1)) 5.63/1.93 5.63/1.93 b(x1) = x1 + 8 >= x1 + 8 = a(x1) 5.63/1.93 5.63/1.93 c(c(x1)) = x1 + 16 >= x1 + 12 = d(f(x1)) 5.63/1.93 5.63/1.93 d(d(x1)) = x1 + 16 >= x1 + 12 = f(f(f(x1))) 5.63/1.93 5.63/1.93 d(x1) = x1 + 8 >= x1 + 8 = b(x1) 5.63/1.93 5.63/1.93 f(f(x1)) = x1 + 8 >= x1 + 8 = g(a(x1)) 5.63/1.93 problem: 5.63/1.93 a(a(x1)) -> b(c(x1)) 5.63/1.93 b(b(x1)) -> c(d(x1)) 5.63/1.93 b(x1) -> a(x1) 5.63/1.93 d(x1) -> b(x1) 5.63/1.93 f(f(x1)) -> g(a(x1)) 5.63/1.93 String Reversal Processor: 5.63/1.93 a(a(x1)) -> c(b(x1)) 5.63/1.93 b(b(x1)) -> d(c(x1)) 5.63/1.93 b(x1) -> a(x1) 5.63/1.93 d(x1) -> b(x1) 5.63/1.93 f(f(x1)) -> a(g(x1)) 5.63/1.93 KBO Processor: 5.63/1.93 weight function: 5.63/1.93 w0 = 1 5.63/1.93 w(g) = w(f) = w(d) = w(b) = w(a) = 1 5.63/1.93 w(c) = 0 5.63/1.93 precedence: 5.63/1.93 c > d > f > b > g ~ a 5.63/1.93 problem: 5.63/1.93 5.63/1.93 Qed 6.35/1.94 EOF