Problem: f(x,x) -> a() f(x,g(x)) -> b() Proof: Church Rosser Transformation Processor (kb): f(x,x) -> a() f(x,g(x)) -> b() critical peaks: joinable Matrix Interpretation Processor: dim=3 interpretation: [0] [b] = [0] [0], [1 0 0] [0] [g](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [a] = [0] [0], [1 0 0] [1 0 1] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [2 0 1] [0] f(x,x) = [0 0 0]x >= [0] = a() [0 0 0] [0] [2 0 0] [1] [0] f(x,g(x)) = [0 0 0]x + [0] >= [0] = b() [0 0 0] [0] [0] problem: f(x,x) -> a() Matrix Interpretation Processor: dim=3 interpretation: [0] [a] = [0] [0], [1 0 0] [1 0 0] [1] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0] orientation: [2 0 0] [1] [0] f(x,x) = [0 0 0]x + [0] >= [0] = a() [0 0 0] [0] [0] problem: Qed