Problem: -(+(x,-(x))) -> 0() +(x,-(x)) -> 0() -(+(0(),0())) -> 0() +(0(),0()) -> 0() -(0()) -> 0() Proof: Church Rosser Transformation Processor (kb): -(+(x,-(x))) -> 0() +(x,-(x)) -> 0() -(+(0(),0())) -> 0() +(0(),0()) -> 0() -(0()) -> 0() critical peaks: joinable Matrix Interpretation Processor: dim=1 interpretation: [+](x0, x1) = 7x0 + 5x1, [-](x0) = x0 + 2, [0] = 1 orientation: -(+(x,-(x))) = 12x + 12 >= 1 = 0() +(x,-(x)) = 12x + 10 >= 1 = 0() -(+(0(),0())) = 14 >= 1 = 0() +(0(),0()) = 12 >= 1 = 0() -(0()) = 3 >= 1 = 0() problem: Qed