YES

Problem:
 rev(nil()) -> nil()
 rev(.(x,y)) -> ++(rev(y),.(x,nil()))
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(nil()) -> true()
 null(.(x,y)) -> false()
 ++(nil(),y) -> y
 ++(.(x,y),z) -> .(x,++(y,z))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [car](x0) = 2x0 + 3,
   
   [false] = 0,
   
   [rev](x0) = 4x0,
   
   [++](x0, x1) = x0 + 4x1,
   
   [cdr](x0) = 4x0,
   
   [nil] = 0,
   
   [true] = 0,
   
   [null](x0) = 2x0,
   
   [.](x0, x1) = 4x0 + x1
  orientation:
   rev(nil()) = 0 >= 0 = nil()
   
   rev(.(x,y)) = 16x + 4y >= 16x + 4y = ++(rev(y),.(x,nil()))
   
   car(.(x,y)) = 8x + 2y + 3 >= x = x
   
   cdr(.(x,y)) = 16x + 4y >= y = y
   
   null(nil()) = 0 >= 0 = true()
   
   null(.(x,y)) = 8x + 2y >= 0 = false()
   
   ++(nil(),y) = 4y >= y = y
   
   ++(.(x,y),z) = 4x + y + 4z >= 4x + y + 4z = .(x,++(y,z))
  problem:
   rev(nil()) -> nil()
   rev(.(x,y)) -> ++(rev(y),.(x,nil()))
   cdr(.(x,y)) -> y
   null(nil()) -> true()
   null(.(x,y)) -> false()
   ++(nil(),y) -> y
   ++(.(x,y),z) -> .(x,++(y,z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [false] = 0,
    
    [rev](x0) = x0 + 2,
    
    [++](x0, x1) = x0 + x1,
    
    [cdr](x0) = 2x0,
    
    [nil] = 0,
    
    [true] = 0,
    
    [null](x0) = 2x0 + 6,
    
    [.](x0, x1) = 4x0 + x1 + 6
   orientation:
    rev(nil()) = 2 >= 0 = nil()
    
    rev(.(x,y)) = 4x + y + 8 >= 4x + y + 8 = ++(rev(y),.(x,nil()))
    
    cdr(.(x,y)) = 8x + 2y + 12 >= y = y
    
    null(nil()) = 6 >= 0 = true()
    
    null(.(x,y)) = 8x + 2y + 18 >= 0 = false()
    
    ++(nil(),y) = y >= y = y
    
    ++(.(x,y),z) = 4x + y + z + 6 >= 4x + y + z + 6 = .(x,++(y,z))
   problem:
    rev(.(x,y)) -> ++(rev(y),.(x,nil()))
    ++(nil(),y) -> y
    ++(.(x,y),z) -> .(x,++(y,z))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 0 1]     [0]
     [rev](x0) = [0 0 0]x0 + [1]
                 [0 0 1]     [0],
     
                    [1 0 0]     [1 1 0]     [0]
     [++](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1]
                    [0 0 1]     [0 0 1]     [0],
     
             [1]
     [nil] = [0]
             [0],
     
                   [1 0 0]     [1 0 0]     [0]
     [.](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                   [0 1 0]     [0 0 1]     [1]
    orientation:
                   [1 1 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]    [1]                        
     rev(.(x,y)) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = ++(rev(y),.(x,nil()))
                   [0 1 0]    [0 0 1]    [1]    [0 1 0]    [0 0 1]    [1]                        
     
                   [1 1 0]    [1]         
     ++(nil(),y) = [0 1 0]y + [1] >= y = y
                   [0 0 1]    [0]         
     
                    [1 0 0]    [1 0 0]    [1 1 0]    [0]    [1 0 0]    [1 0 0]    [1 1 0]    [0]               
     ++(.(x,y),z) = [0 0 0]x + [0 0 0]y + [0 1 0]z + [1] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] = .(x,++(y,z))
                    [0 1 0]    [0 0 1]    [0 0 1]    [1]    [0 1 0]    [0 0 1]    [0 0 1]    [1]               
    problem:
     rev(.(x,y)) -> ++(rev(y),.(x,nil()))
     ++(.(x,y),z) -> .(x,++(y,z))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [rev](x0) = 7x0 + 6,
      
      [++](x0, x1) = x0 + x1,
      
      [nil] = 2,
      
      [.](x0, x1) = 2x0 + x1 + 2
     orientation:
      rev(.(x,y)) = 14x + 7y + 20 >= 2x + 7y + 10 = ++(rev(y),.(x,nil()))
      
      ++(.(x,y),z) = 2x + y + z + 2 >= 2x + y + z + 2 = .(x,++(y,z))
     problem:
      ++(.(x,y),z) -> .(x,++(y,z))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                      [1 1 0]     [1 0 0]  
       [++](x0, x1) = [0 1 1]x0 + [0 0 0]x1
                      [0 0 0]     [1 0 0]  ,
       
                     [1 0 0]          [0]
       [.](x0, x1) = [0 0 0]x0 + x1 + [1]
                     [0 0 0]          [0]
      orientation:
                      [1 0 0]    [1 1 0]    [1 0 0]    [1]    [1 0 0]    [1 1 0]    [1 0 0]    [0]               
       ++(.(x,y),z) = [0 0 0]x + [0 1 1]y + [0 0 0]z + [1] >= [0 0 0]x + [0 1 1]y + [0 0 0]z + [1] = .(x,++(y,z))
                      [0 0 0]    [0 0 0]    [1 0 0]    [0]    [0 0 0]    [0 0 0]    [1 0 0]    [0]               
      problem:
       
      Qed