Problem: b(w(x)) -> w(w(w(b(x)))) w(b(x)) -> b(x) b(b(x)) -> w(w(w(w(x)))) w(w(x)) -> w(x) Proof: Church Rosser Transformation Processor (kb): b(w(x)) -> w(w(w(b(x)))) w(b(x)) -> b(x) b(b(x)) -> w(w(w(w(x)))) w(w(x)) -> w(x) critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [b](x0) = 5x0 + 3, [w](x0) = x0 + 4 orientation: b(w(x)) = 5x + 23 >= 5x + 15 = w(w(w(b(x)))) w(b(x)) = 5x + 7 >= 5x + 3 = b(x) b(b(x)) = 25x + 18 >= x + 16 = w(w(w(w(x)))) w(w(x)) = x + 8 >= x + 4 = w(x) problem: Qed