Problem: W(B(x)) -> W(x) B(I(x)) -> J(x) W(I(x)) -> W(J(x)) Proof: Church Rosser Transformation Processor (kb): W(B(x)) -> W(x) B(I(x)) -> J(x) W(I(x)) -> W(J(x)) critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [J](x0) = 2x0 + 5, [I](x0) = 3x0 + 5, [W](x0) = 5x0 + 4, [B](x0) = 5x0 orientation: W(B(x)) = 25x + 4 >= 5x + 4 = W(x) B(I(x)) = 15x + 25 >= 2x + 5 = J(x) W(I(x)) = 15x + 29 >= 10x + 29 = W(J(x)) problem: W(B(x)) -> W(x) W(I(x)) -> W(J(x)) Matrix Interpretation Processor: dim=1 interpretation: [J](x0) = x0, [I](x0) = x0 + 5, [W](x0) = x0, [B](x0) = x0 orientation: W(B(x)) = x >= x = W(x) W(I(x)) = x + 5 >= x = W(J(x)) problem: W(B(x)) -> W(x) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [W](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [B](x0) = [0 0 0]x0 + [0] [0 0 0] [0] orientation: [1 0 0] [1] [1 0 0] W(B(x)) = [0 0 0]x + [0] >= [0 0 0]x = W(x) [0 0 0] [0] [0 0 0] problem: Qed