YES(?,O(n^1)) Problem: d(x) -> e(u(x)) d(u(x)) -> c(x) c(u(x)) -> b(x) v(e(x)) -> x b(u(x)) -> a(e(x)) Proof: RT Transformation Processor: strict: d(x) -> e(u(x)) d(u(x)) -> c(x) c(u(x)) -> b(x) v(e(x)) -> x b(u(x)) -> a(e(x)) weak: Matrix Interpretation Processor: dimension: 1 interpretation: [a](x0) = x0 + 15, [v](x0) = x0 + 15, [b](x0) = x0 + 3, [c](x0) = x0 + 2, [e](x0) = x0 + 1, [u](x0) = x0 + 16, [d](x0) = x0 orientation: d(x) = x >= x + 17 = e(u(x)) d(u(x)) = x + 16 >= x + 2 = c(x) c(u(x)) = x + 18 >= x + 3 = b(x) v(e(x)) = x + 16 >= x = x b(u(x)) = x + 19 >= x + 16 = a(e(x)) problem: strict: d(x) -> e(u(x)) weak: d(u(x)) -> c(x) c(u(x)) -> b(x) v(e(x)) -> x b(u(x)) -> a(e(x)) Matrix Interpretation Processor: dimension: 1 interpretation: [a](x0) = x0 + 19, [v](x0) = x0, [b](x0) = x0 + 31, [c](x0) = x0 + 29, [e](x0) = x0 + 14, [u](x0) = x0 + 2, [d](x0) = x0 + 27 orientation: d(x) = x + 27 >= x + 16 = e(u(x)) d(u(x)) = x + 29 >= x + 29 = c(x) c(u(x)) = x + 31 >= x + 31 = b(x) v(e(x)) = x + 14 >= x = x b(u(x)) = x + 33 >= x + 33 = a(e(x)) problem: strict: weak: d(x) -> e(u(x)) d(u(x)) -> c(x) c(u(x)) -> b(x) v(e(x)) -> x b(u(x)) -> a(e(x)) Qed