Problem: W(B(x)) -> W(x) B(I(x)) -> J(x) W(I(x)) -> W(J(x)) Proof: Church Rosser Transformation Processor (critical pair closing system, Thm 2.11): W(I(x20)) -> W(J(x20)) critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [W](x0) = 4x0 + 2, [J](x0) = x0 + 1, [I](x0) = x0 + 2 orientation: W(I(x20)) = 4x20 + 10 >= 4x20 + 6 = W(J(x20)) problem: Qed