MAYBE

Problem:
 ap(ap(g(),x),y) -> y
 ap(f(),x) -> ap(f(),app(g(),x))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                   [1 0 0]     [1 0 0]  
   [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 1 1]  ,
   
         [1]
   [f] = [0]
         [0],
   
                  [1 0 1]     [1 0 0]  
   [ap](x0, x1) = [0 0 0]x0 + [0 1 1]x1
                  [0 0 0]     [0 1 1]  ,
   
         [0]
   [g] = [0]
         [1]
  orientation:
                     [1 1 1]    [1 0 0]    [1]         
   ap(ap(g(),x),y) = [0 0 0]x + [0 1 1]y + [0] >= y = y
                     [0 0 0]    [0 1 1]    [0]         
   
               [1 0 0]    [1]    [1 0 0]    [1]                     
   ap(f(),x) = [0 1 1]x + [0] >= [0 1 1]x + [0] = ap(f(),app(g(),x))
               [0 1 1]    [0]    [0 1 1]    [0]                     
  problem:
   ap(f(),x) -> ap(f(),app(g(),x))
  DP Processor:
   DPs:
    ap#(f(),x) -> ap#(f(),app(g(),x))
   TRS:
    ap(f(),x) -> ap(f(),app(g(),x))
   Open