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: [J](x0) = x0 + 1, [I](x0) = x0 + 4, [W](x0) = x0 + 7 orientation: W(I(x20)) = x20 + 11 >= x20 + 8 = W(J(x20)) problem: Qed