28.36/7.02 YES 28.36/7.03 28.36/7.03 Problem: 28.36/7.03 strict: 28.36/7.03 n(s(x1)) -> s(x1) 28.36/7.03 o(s(x1)) -> s(x1) 28.36/7.03 n(o(p(x1))) -> o(n(x1)) 28.36/7.03 weak: 28.36/7.03 t(x1) -> t(c(n(x1))) 28.36/7.03 p(s(x1)) -> s(x1) 28.36/7.03 o(n(x1)) -> n(o(x1)) 28.36/7.03 p(n(x1)) -> m(p(x1)) 28.36/7.03 p(m(x1)) -> m(p(x1)) 28.36/7.03 o(m(x1)) -> n(o(x1)) 28.36/7.03 n(p(x1)) -> p(n(x1)) 28.36/7.03 c(p(x1)) -> p(c(x1)) 28.36/7.03 c(m(x1)) -> m(c(x1)) 28.36/7.03 c(n(x1)) -> n(c(x1)) 28.36/7.03 c(o(x1)) -> o(c(x1)) 28.36/7.03 c(o(x1)) -> o(x1) 28.36/7.03 28.36/7.03 Proof: 28.36/7.03 Arctic Interpretation Processor: 28.36/7.03 dimension: 1 28.36/7.03 interpretation: 28.36/7.03 [m](x0) = x0, 28.36/7.03 28.36/7.03 [c](x0) = x0, 28.36/7.03 28.36/7.03 [t](x0) = 4x0, 28.36/7.03 28.36/7.03 [p](x0) = 10x0, 28.36/7.03 28.36/7.03 [o](x0) = x0, 28.36/7.03 28.36/7.03 [n](x0) = x0, 28.36/7.03 28.36/7.03 [s](x0) = 5x0 28.36/7.03 orientation: 28.36/7.03 n(s(x1)) = 5x1 >= 5x1 = s(x1) 28.36/7.03 28.36/7.03 o(s(x1)) = 5x1 >= 5x1 = s(x1) 28.36/7.03 28.36/7.03 n(o(p(x1))) = 10x1 >= x1 = o(n(x1)) 28.36/7.03 28.36/7.03 t(x1) = 4x1 >= 4x1 = t(c(n(x1))) 28.36/7.03 28.36/7.03 p(s(x1)) = 15x1 >= 5x1 = s(x1) 28.36/7.03 28.36/7.03 o(n(x1)) = x1 >= x1 = n(o(x1)) 28.36/7.03 28.36/7.03 p(n(x1)) = 10x1 >= 10x1 = m(p(x1)) 28.36/7.03 28.36/7.03 p(m(x1)) = 10x1 >= 10x1 = m(p(x1)) 28.36/7.03 28.36/7.03 o(m(x1)) = x1 >= x1 = n(o(x1)) 28.36/7.03 28.36/7.03 n(p(x1)) = 10x1 >= 10x1 = p(n(x1)) 28.36/7.03 28.36/7.03 c(p(x1)) = 10x1 >= 10x1 = p(c(x1)) 28.36/7.03 28.36/7.03 c(m(x1)) = x1 >= x1 = m(c(x1)) 28.36/7.03 28.36/7.03 c(n(x1)) = x1 >= x1 = n(c(x1)) 28.36/7.03 28.36/7.03 c(o(x1)) = x1 >= x1 = o(c(x1)) 28.36/7.03 28.36/7.03 c(o(x1)) = x1 >= x1 = o(x1) 28.36/7.03 problem: 28.36/7.03 strict: 28.36/7.03 n(s(x1)) -> s(x1) 28.36/7.03 o(s(x1)) -> s(x1) 28.36/7.03 weak: 28.36/7.03 t(x1) -> t(c(n(x1))) 28.36/7.03 o(n(x1)) -> n(o(x1)) 28.36/7.03 p(n(x1)) -> m(p(x1)) 28.36/7.03 p(m(x1)) -> m(p(x1)) 28.36/7.03 o(m(x1)) -> n(o(x1)) 28.36/7.03 n(p(x1)) -> p(n(x1)) 28.36/7.03 c(p(x1)) -> p(c(x1)) 28.36/7.03 c(m(x1)) -> m(c(x1)) 28.36/7.03 c(n(x1)) -> n(c(x1)) 28.36/7.03 c(o(x1)) -> o(c(x1)) 28.36/7.03 c(o(x1)) -> o(x1) 28.36/7.03 String Reversal Processor: 28.36/7.03 strict: 28.36/7.03 s(n(x1)) -> s(x1) 28.36/7.03 s(o(x1)) -> s(x1) 28.36/7.03 weak: 28.36/7.03 t(x1) -> n(c(t(x1))) 28.36/7.03 n(o(x1)) -> o(n(x1)) 28.36/7.03 n(p(x1)) -> p(m(x1)) 28.36/7.03 m(p(x1)) -> p(m(x1)) 28.36/7.03 m(o(x1)) -> o(n(x1)) 28.36/7.03 p(n(x1)) -> n(p(x1)) 28.36/7.03 p(c(x1)) -> c(p(x1)) 28.36/7.03 m(c(x1)) -> c(m(x1)) 28.36/7.03 n(c(x1)) -> c(n(x1)) 28.36/7.03 o(c(x1)) -> c(o(x1)) 28.36/7.03 o(c(x1)) -> o(x1) 28.36/7.03 Arctic Interpretation Processor: 28.36/7.03 dimension: 1 28.36/7.03 interpretation: 28.36/7.03 [m](x0) = x0, 28.36/7.03 28.36/7.03 [c](x0) = x0, 28.36/7.03 28.36/7.03 [t](x0) = 9x0, 28.36/7.03 28.36/7.03 [p](x0) = 3x0, 28.36/7.03 28.36/7.03 [o](x0) = 1x0, 28.36/7.03 28.36/7.03 [n](x0) = x0, 28.36/7.03 28.36/7.03 [s](x0) = 15x0 28.36/7.03 orientation: 28.36/7.03 s(n(x1)) = 15x1 >= 15x1 = s(x1) 28.36/7.03 28.36/7.03 s(o(x1)) = 16x1 >= 15x1 = s(x1) 28.36/7.03 28.36/7.03 t(x1) = 9x1 >= 9x1 = n(c(t(x1))) 28.36/7.03 28.36/7.03 n(o(x1)) = 1x1 >= 1x1 = o(n(x1)) 28.36/7.03 28.36/7.03 n(p(x1)) = 3x1 >= 3x1 = p(m(x1)) 28.36/7.03 28.36/7.03 m(p(x1)) = 3x1 >= 3x1 = p(m(x1)) 28.36/7.03 28.36/7.03 m(o(x1)) = 1x1 >= 1x1 = o(n(x1)) 28.36/7.03 28.36/7.03 p(n(x1)) = 3x1 >= 3x1 = n(p(x1)) 28.36/7.03 28.36/7.03 p(c(x1)) = 3x1 >= 3x1 = c(p(x1)) 28.36/7.03 28.36/7.03 m(c(x1)) = x1 >= x1 = c(m(x1)) 28.36/7.03 28.36/7.03 n(c(x1)) = x1 >= x1 = c(n(x1)) 28.36/7.03 28.36/7.03 o(c(x1)) = 1x1 >= 1x1 = c(o(x1)) 28.36/7.03 28.36/7.03 o(c(x1)) = 1x1 >= 1x1 = o(x1) 28.36/7.03 problem: 28.36/7.03 strict: 28.36/7.03 s(n(x1)) -> s(x1) 28.36/7.03 weak: 28.36/7.03 t(x1) -> n(c(t(x1))) 28.36/7.03 n(o(x1)) -> o(n(x1)) 28.36/7.03 n(p(x1)) -> p(m(x1)) 28.36/7.03 m(p(x1)) -> p(m(x1)) 28.36/7.03 m(o(x1)) -> o(n(x1)) 28.36/7.03 p(n(x1)) -> n(p(x1)) 28.36/7.03 p(c(x1)) -> c(p(x1)) 28.36/7.03 m(c(x1)) -> c(m(x1)) 28.36/7.03 n(c(x1)) -> c(n(x1)) 28.36/7.03 o(c(x1)) -> c(o(x1)) 28.36/7.03 o(c(x1)) -> o(x1) 28.36/7.03 String Reversal Processor: 28.36/7.03 strict: 28.36/7.03 n(s(x1)) -> s(x1) 28.36/7.03 weak: 28.36/7.03 t(x1) -> t(c(n(x1))) 28.36/7.03 o(n(x1)) -> n(o(x1)) 28.36/7.03 p(n(x1)) -> m(p(x1)) 28.36/7.03 p(m(x1)) -> m(p(x1)) 28.36/7.03 o(m(x1)) -> n(o(x1)) 28.36/7.03 n(p(x1)) -> p(n(x1)) 28.36/7.03 c(p(x1)) -> p(c(x1)) 28.36/7.03 c(m(x1)) -> m(c(x1)) 28.36/7.03 c(n(x1)) -> n(c(x1)) 28.36/7.03 c(o(x1)) -> o(c(x1)) 28.36/7.03 c(o(x1)) -> o(x1) 28.36/7.03 Matrix Interpretation Processor: dim=2 28.36/7.03 28.36/7.03 interpretation: 28.36/7.03 [1 0] [0] 28.36/7.03 [m](x0) = [0 2]x0 + [1], 28.36/7.03 28.36/7.03 28.36/7.03 [c](x0) = x0, 28.36/7.03 28.36/7.03 [1 0] [2] 28.36/7.03 [t](x0) = [1 0]x0 + [0], 28.36/7.03 28.36/7.03 [2 0] 28.36/7.03 [p](x0) = [0 1]x0, 28.36/7.03 28.36/7.03 [2 1] 28.36/7.03 [o](x0) = [0 1]x0, 28.36/7.03 28.36/7.03 [1 0] [0] 28.36/7.03 [n](x0) = [0 2]x0 + [1], 28.36/7.03 28.36/7.03 28.36/7.03 [s](x0) = x0 28.36/7.03 orientation: 28.36/7.03 [1 0] [0] 28.36/7.03 n(s(x1)) = [0 2]x1 + [1] >= x1 = s(x1) 28.36/7.03 28.36/7.03 [1 0] [2] [1 0] [2] 28.38/7.04 t(x1) = [1 0]x1 + [0] >= [1 0]x1 + [0] = t(c(n(x1))) 28.38/7.04 28.38/7.04 [2 2] [1] [2 1] [0] 28.38/7.04 o(n(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = n(o(x1)) 28.38/7.04 28.38/7.04 [2 0] [0] [2 0] [0] 28.38/7.04 p(n(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = m(p(x1)) 28.38/7.04 28.38/7.04 [2 0] [0] [2 0] [0] 28.38/7.04 p(m(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = m(p(x1)) 28.38/7.04 28.38/7.04 [2 2] [1] [2 1] [0] 28.38/7.04 o(m(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = n(o(x1)) 28.38/7.04 28.38/7.04 [2 0] [0] [2 0] [0] 28.38/7.04 n(p(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = p(n(x1)) 28.38/7.04 28.38/7.04 [2 0] [2 0] 28.38/7.04 c(p(x1)) = [0 1]x1 >= [0 1]x1 = p(c(x1)) 28.38/7.04 28.38/7.04 [1 0] [0] [1 0] [0] 28.38/7.04 c(m(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = m(c(x1)) 28.38/7.04 28.38/7.04 [1 0] [0] [1 0] [0] 28.38/7.04 c(n(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = n(c(x1)) 28.38/7.04 28.38/7.04 [2 1] [2 1] 28.38/7.04 c(o(x1)) = [0 1]x1 >= [0 1]x1 = o(c(x1)) 28.38/7.04 28.38/7.04 [2 1] [2 1] 28.38/7.04 c(o(x1)) = [0 1]x1 >= [0 1]x1 = o(x1) 28.38/7.04 problem: 28.38/7.04 strict: 28.38/7.04 n(s(x1)) -> s(x1) 28.38/7.04 weak: 28.38/7.04 t(x1) -> t(c(n(x1))) 28.38/7.04 p(n(x1)) -> m(p(x1)) 28.38/7.04 p(m(x1)) -> m(p(x1)) 28.38/7.04 n(p(x1)) -> p(n(x1)) 28.38/7.04 c(p(x1)) -> p(c(x1)) 28.38/7.04 c(m(x1)) -> m(c(x1)) 28.38/7.04 c(n(x1)) -> n(c(x1)) 28.38/7.04 c(o(x1)) -> o(c(x1)) 28.38/7.04 c(o(x1)) -> o(x1) 28.38/7.04 Matrix Interpretation Processor: dim=2 28.38/7.04 28.38/7.04 interpretation: 28.38/7.04 [1 0] 28.38/7.04 [m](x0) = [0 0]x0, 28.38/7.04 28.38/7.04 [1 0] 28.38/7.04 [c](x0) = [0 0]x0, 28.38/7.04 28.38/7.04 [1 2] [2] 28.38/7.04 [t](x0) = [0 2]x0 + [2], 28.38/7.04 28.38/7.04 28.38/7.04 [p](x0) = x0, 28.38/7.04 28.38/7.04 [2 1] 28.38/7.04 [o](x0) = [0 0]x0, 28.38/7.04 28.38/7.04 [1 2] 28.38/7.04 [n](x0) = [0 2]x0, 28.38/7.04 28.38/7.04 [1 2] [0] 28.38/7.04 [s](x0) = [0 0]x0 + [1] 28.38/7.04 orientation: 28.38/7.04 [1 2] [2] [1 2] [0] 28.38/7.04 n(s(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [1] = s(x1) 28.38/7.04 28.38/7.04 [1 2] [2] [1 2] [2] 28.38/7.04 t(x1) = [0 2]x1 + [2] >= [0 0]x1 + [2] = t(c(n(x1))) 28.38/7.04 28.38/7.04 [1 2] [1 0] 28.38/7.04 p(n(x1)) = [0 2]x1 >= [0 0]x1 = m(p(x1)) 28.38/7.04 28.38/7.04 [1 0] [1 0] 28.38/7.04 p(m(x1)) = [0 0]x1 >= [0 0]x1 = m(p(x1)) 28.38/7.04 28.38/7.04 [1 2] [1 2] 28.38/7.04 n(p(x1)) = [0 2]x1 >= [0 2]x1 = p(n(x1)) 28.38/7.04 28.38/7.04 [1 0] [1 0] 28.38/7.04 c(p(x1)) = [0 0]x1 >= [0 0]x1 = p(c(x1)) 28.38/7.04 28.38/7.04 [1 0] [1 0] 28.38/7.04 c(m(x1)) = [0 0]x1 >= [0 0]x1 = m(c(x1)) 28.38/7.04 28.38/7.04 [1 2] [1 0] 28.38/7.04 c(n(x1)) = [0 0]x1 >= [0 0]x1 = n(c(x1)) 28.38/7.04 28.38/7.04 [2 1] [2 0] 28.38/7.04 c(o(x1)) = [0 0]x1 >= [0 0]x1 = o(c(x1)) 28.38/7.04 28.38/7.04 [2 1] [2 1] 28.38/7.04 c(o(x1)) = [0 0]x1 >= [0 0]x1 = o(x1) 28.38/7.04 problem: 28.38/7.04 strict: 28.38/7.04 28.38/7.04 weak: 28.38/7.04 t(x1) -> t(c(n(x1))) 28.38/7.04 p(n(x1)) -> m(p(x1)) 28.38/7.04 p(m(x1)) -> m(p(x1)) 28.38/7.04 n(p(x1)) -> p(n(x1)) 28.38/7.04 c(p(x1)) -> p(c(x1)) 28.38/7.04 c(m(x1)) -> m(c(x1)) 28.38/7.04 c(n(x1)) -> n(c(x1)) 28.38/7.04 c(o(x1)) -> o(c(x1)) 28.38/7.04 c(o(x1)) -> o(x1) 28.38/7.04 Qed 28.38/7.04 EOF