0.53/0.57 YES 0.53/0.57 0.53/0.57 Problem: 0.53/0.57 f(g(h(x))) -> g(f(h(g(x)))) 0.53/0.57 f(x) -> x 0.53/0.57 g(x) -> x 0.53/0.57 h(x) -> x 0.53/0.57 0.53/0.57 Proof: 0.53/0.57 Church Rosser Transformation Processor (critical pair closing system, Thm 2.11): 0.53/0.57 g(x33) -> x33 0.53/0.57 f(x35) -> x35 0.53/0.57 h(x59) -> x59 0.53/0.57 critical peaks: joinable 0.53/0.57 Matrix Interpretation Processor: dim=1 0.53/0.57 0.53/0.57 interpretation: 0.53/0.57 [g](x0) = x0 + 1, 0.53/0.57 0.53/0.57 [h](x0) = x0 + 1, 0.53/0.57 0.53/0.57 [f](x0) = x0 + 1 0.53/0.57 orientation: 0.53/0.57 g(x33) = x33 + 1 >= x33 = x33 0.53/0.57 0.53/0.57 f(x35) = x35 + 1 >= x35 = x35 0.53/0.57 0.53/0.57 h(x59) = x59 + 1 >= x59 = x59 0.53/0.57 problem: 0.53/0.57 0.53/0.57 Qed 0.63/0.58 EOF