YES(?,O(n^1)) 0.16/0.25 YES(?,O(n^1)) 0.16/0.25 0.16/0.25 Problem: 0.16/0.25 app(app(app(compose(),f),g),x) -> app(f,app(g,x)) 0.16/0.25 0.16/0.25 Proof: 0.16/0.25 Uncurry Processor: 0.16/0.25 compose3(f,g,x) -> app(f,app(g,x)) 0.16/0.25 app(compose2(x4,x3),x5) -> compose3(x4,x3,x5) 0.16/0.25 app(compose1(x4),x5) -> compose2(x4,x5) 0.16/0.25 app(compose(),x5) -> compose1(x5) 0.16/0.25 Complexity Transformation Processor: 0.16/0.25 strict: 0.16/0.25 compose3(f,g,x) -> app(f,app(g,x)) 0.16/0.25 app(compose2(x4,x3),x5) -> compose3(x4,x3,x5) 0.16/0.25 app(compose1(x4),x5) -> compose2(x4,x5) 0.16/0.25 app(compose(),x5) -> compose1(x5) 0.16/0.25 weak: 0.16/0.25 0.16/0.25 Matrix Interpretation Processor: dim=1 0.16/0.25 0.16/0.25 max_matrix: 0.16/0.25 1 0.16/0.25 interpretation: 0.16/0.25 [compose1](x0) = x0 + 18, 0.16/0.25 0.16/0.25 [compose3](x0, x1, x2) = x0 + x1 + x2, 0.16/0.25 0.16/0.25 [compose2](x0, x1) = x0 + x1 + 130, 0.16/0.25 0.16/0.25 [app](x0, x1) = x0 + x1 + 120, 0.16/0.25 0.16/0.25 [compose] = 7 0.16/0.25 orientation: 0.16/0.25 compose3(f,g,x) = f + g + x >= f + g + x + 240 = app(f,app(g,x)) 0.16/0.25 0.16/0.25 app(compose2(x4,x3),x5) = x3 + x4 + x5 + 250 >= x3 + x4 + x5 = compose3(x4,x3,x5) 0.16/0.25 0.16/0.25 app(compose1(x4),x5) = x4 + x5 + 138 >= x4 + x5 + 130 = compose2(x4,x5) 0.16/0.25 0.16/0.25 app(compose(),x5) = x5 + 127 >= x5 + 18 = compose1(x5) 0.16/0.25 problem: 0.16/0.25 strict: 0.16/0.25 compose3(f,g,x) -> app(f,app(g,x)) 0.16/0.25 weak: 0.16/0.25 app(compose2(x4,x3),x5) -> compose3(x4,x3,x5) 0.16/0.25 app(compose1(x4),x5) -> compose2(x4,x5) 0.16/0.25 app(compose(),x5) -> compose1(x5) 0.16/0.25 Matrix Interpretation Processor: dim=1 0.16/0.25 0.16/0.25 max_matrix: 0.16/0.25 1 0.16/0.25 interpretation: 0.16/0.25 [compose1](x0) = x0 + 1, 0.16/0.25 0.16/0.25 [compose3](x0, x1, x2) = x0 + x1 + x2 + 1, 0.16/0.25 0.16/0.25 [compose2](x0, x1) = x0 + x1 + 1, 0.16/0.25 0.16/0.25 [app](x0, x1) = x0 + x1, 0.16/0.25 0.16/0.25 [compose] = 1 0.16/0.25 orientation: 0.16/0.25 compose3(f,g,x) = f + g + x + 1 >= f + g + x = app(f,app(g,x)) 0.16/0.25 0.16/0.25 app(compose2(x4,x3),x5) = x3 + x4 + x5 + 1 >= x3 + x4 + x5 + 1 = compose3(x4,x3,x5) 0.16/0.25 0.16/0.25 app(compose1(x4),x5) = x4 + x5 + 1 >= x4 + x5 + 1 = compose2(x4,x5) 0.16/0.25 0.16/0.25 app(compose(),x5) = x5 + 1 >= x5 + 1 = compose1(x5) 0.16/0.25 problem: 0.16/0.25 strict: 0.16/0.25 0.16/0.25 weak: 0.16/0.25 compose3(f,g,x) -> app(f,app(g,x)) 0.16/0.25 app(compose2(x4,x3),x5) -> compose3(x4,x3,x5) 0.16/0.25 app(compose1(x4),x5) -> compose2(x4,x5) 0.16/0.25 app(compose(),x5) -> compose1(x5) 0.16/0.25 Qed 0.16/0.26 EOF