YES

Problem:
 top(free(x)) -> top(check(new(x)))
 new(free(x)) -> free(new(x))
 old(free(x)) -> free(old(x))
 new(serve()) -> free(serve())
 old(serve()) -> free(serve())
 check(free(x)) -> free(check(x))
 check(new(x)) -> new(check(x))
 check(old(x)) -> old(check(x))
 check(old(x)) -> old(x)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [old](x0) = 4x0,
   
   [top](x0) = 2x0 + 1,
   
   [check](x0) = x0,
   
   [serve] = 4,
   
   [free](x0) = 2x0,
   
   [new](x0) = 2x0
  orientation:
   top(free(x)) = 4x + 1 >= 4x + 1 = top(check(new(x)))
   
   new(free(x)) = 4x >= 4x = free(new(x))
   
   old(free(x)) = 8x >= 8x = free(old(x))
   
   new(serve()) = 8 >= 8 = free(serve())
   
   old(serve()) = 16 >= 8 = free(serve())
   
   check(free(x)) = 2x >= 2x = free(check(x))
   
   check(new(x)) = 2x >= 2x = new(check(x))
   
   check(old(x)) = 4x >= 4x = old(check(x))
   
   check(old(x)) = 4x >= 4x = old(x)
  problem:
   top(free(x)) -> top(check(new(x)))
   new(free(x)) -> free(new(x))
   old(free(x)) -> free(old(x))
   new(serve()) -> free(serve())
   check(free(x)) -> free(check(x))
   check(new(x)) -> new(check(x))
   check(old(x)) -> old(check(x))
   check(old(x)) -> old(x)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                [1 0 0]     [1]
    [old](x0) = [0 1 0]x0 + [0]
                [0 0 0]     [0],
    
                [1 1 1]  
    [top](x0) = [1 0 1]x0
                [0 0 0]  ,
    
                  [1 0 0]  
    [check](x0) = [0 1 0]x0
                  [0 0 0]  ,
    
              [0]
    [serve] = [1]
              [1],
    
                 [1 1 0]     [0]
    [free](x0) = [0 0 0]x0 + [1]
                 [0 0 1]     [0],
    
                [1 0 1]  
    [new](x0) = [0 1 0]x0
                [0 0 1]  
   orientation:
                   [1 1 1]    [1]    [1 1 1]                      
    top(free(x)) = [1 1 1]x + [0] >= [1 0 1]x = top(check(new(x)))
                   [0 0 0]    [0]    [0 0 0]                      
    
                   [1 1 1]    [0]    [1 1 1]    [0]               
    new(free(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = free(new(x))
                   [0 0 1]    [0]    [0 0 1]    [0]               
    
                   [1 1 0]    [1]    [1 1 0]    [1]               
    old(free(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = free(old(x))
                   [0 0 0]    [0]    [0 0 0]    [0]               
    
                   [1]    [1]                
    new(serve()) = [1] >= [1] = free(serve())
                   [1]    [1]                
    
                     [1 1 0]    [0]    [1 1 0]    [0]                 
    check(free(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = free(check(x))
                     [0 0 0]    [0]    [0 0 0]    [0]                 
    
                    [1 0 1]     [1 0 0]                 
    check(new(x)) = [0 1 0]x >= [0 1 0]x = new(check(x))
                    [0 0 0]     [0 0 0]                 
    
                    [1 0 0]    [1]    [1 0 0]    [1]                
    check(old(x)) = [0 1 0]x + [0] >= [0 1 0]x + [0] = old(check(x))
                    [0 0 0]    [0]    [0 0 0]    [0]                
    
                    [1 0 0]    [1]    [1 0 0]    [1]         
    check(old(x)) = [0 1 0]x + [0] >= [0 1 0]x + [0] = old(x)
                    [0 0 0]    [0]    [0 0 0]    [0]         
   problem:
    new(free(x)) -> free(new(x))
    old(free(x)) -> free(old(x))
    new(serve()) -> free(serve())
    check(free(x)) -> free(check(x))
    check(new(x)) -> new(check(x))
    check(old(x)) -> old(check(x))
    check(old(x)) -> old(x)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 1 0]  
     [old](x0) = [0 1 0]x0
                 [1 0 0]  ,
     
                     
     [check](x0) = x0
                     ,
     
               [0]
     [serve] = [0]
               [1],
     
                       [0]
     [free](x0) = x0 + [1]
                       [0],
     
                 [1 1 1]     [0]
     [new](x0) = [0 1 1]x0 + [0]
                 [0 0 0]     [1]
    orientation:
                    [1 1 1]    [1]    [1 1 1]    [0]               
     new(free(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = free(new(x))
                    [0 0 0]    [1]    [0 0 0]    [1]               
     
                    [1 1 0]    [1]    [1 1 0]    [0]               
     old(free(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = free(old(x))
                    [1 0 0]    [0]    [1 0 0]    [0]               
     
                    [1]    [0]                
     new(serve()) = [1] >= [1] = free(serve())
                    [1]    [1]                
     
                          [0]        [0]                 
     check(free(x)) = x + [1] >= x + [1] = free(check(x))
                          [0]        [0]                 
     
                     [1 1 1]    [0]    [1 1 1]    [0]                
     check(new(x)) = [0 1 1]x + [0] >= [0 1 1]x + [0] = new(check(x))
                     [0 0 0]    [1]    [0 0 0]    [1]                
     
                     [1 1 0]     [1 1 0]                 
     check(old(x)) = [0 1 0]x >= [0 1 0]x = old(check(x))
                     [1 0 0]     [1 0 0]                 
     
                     [1 1 0]     [1 1 0]          
     check(old(x)) = [0 1 0]x >= [0 1 0]x = old(x)
                     [1 0 0]     [1 0 0]          
    problem:
     check(free(x)) -> free(check(x))
     check(new(x)) -> new(check(x))
     check(old(x)) -> old(check(x))
     check(old(x)) -> old(x)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [old](x0) = 5x0 + 4,
      
      [check](x0) = 6x0 + 5,
      
      [free](x0) = 4x0 + 3,
      
      [new](x0) = 3x0 + 2
     orientation:
      check(free(x)) = 24x + 23 >= 24x + 23 = free(check(x))
      
      check(new(x)) = 18x + 17 >= 18x + 17 = new(check(x))
      
      check(old(x)) = 30x + 29 >= 30x + 29 = old(check(x))
      
      check(old(x)) = 30x + 29 >= 5x + 4 = old(x)
     problem:
      check(free(x)) -> free(check(x))
      check(new(x)) -> new(check(x))
      check(old(x)) -> old(check(x))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [old](x0) = 4x0 + 4,
       
       [check](x0) = 4x0 + 4,
       
       [free](x0) = x0 + 1,
       
       [new](x0) = x0
      orientation:
       check(free(x)) = 4x + 8 >= 4x + 5 = free(check(x))
       
       check(new(x)) = 4x + 4 >= 4x + 4 = new(check(x))
       
       check(old(x)) = 16x + 20 >= 16x + 20 = old(check(x))
      problem:
       check(new(x)) -> new(check(x))
       check(old(x)) -> old(check(x))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [old](x0) = 5x0 + 3,
        
        [check](x0) = 4x0 + 1,
        
        [new](x0) = 4x0 + 1
       orientation:
        check(new(x)) = 16x + 5 >= 16x + 5 = new(check(x))
        
        check(old(x)) = 20x + 13 >= 20x + 8 = old(check(x))
       problem:
        check(new(x)) -> new(check(x))
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                       [1 1 0]  
         [check](x0) = [0 1 0]x0
                       [0 0 0]  ,
         
                     [1 0 0]     [0]
         [new](x0) = [0 1 0]x0 + [1]
                     [0 0 0]     [0]
        orientation:
                         [1 1 0]    [1]    [1 1 0]    [0]                
         check(new(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = new(check(x))
                         [0 0 0]    [0]    [0 0 0]    [0]                
        problem:
         
        Qed