YES(?,O(n^3))

Problem:
 active(f(x)) -> mark(x)
 top(active(c())) -> top(mark(c()))
 top(mark(x)) -> top(check(x))
 check(f(x)) -> f(check(x))
 check(x) -> start(match(f(X()),x))
 match(f(x),f(y)) -> f(match(x,y))
 match(X(),x) -> proper(x)
 proper(c()) -> ok(c())
 proper(f(x)) -> f(proper(x))
 f(ok(x)) -> ok(f(x))
 start(ok(x)) -> found(x)
 f(found(x)) -> found(f(x))
 top(found(x)) -> top(active(x))
 active(f(x)) -> f(active(x))
 f(mark(x)) -> mark(f(x))

Proof:
 RT Transformation Processor:
  strict:
   active(f(x)) -> mark(x)
   top(active(c())) -> top(mark(c()))
   top(mark(x)) -> top(check(x))
   check(f(x)) -> f(check(x))
   check(x) -> start(match(f(X()),x))
   match(f(x),f(y)) -> f(match(x,y))
   match(X(),x) -> proper(x)
   proper(c()) -> ok(c())
   proper(f(x)) -> f(proper(x))
   f(ok(x)) -> ok(f(x))
   start(ok(x)) -> found(x)
   f(found(x)) -> found(f(x))
   top(found(x)) -> top(active(x))
   active(f(x)) -> f(active(x))
   f(mark(x)) -> mark(f(x))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [found](x0) = x0 + 9,
    
    [ok](x0) = x0,
    
    [proper](x0) = x0 + 18,
    
    [start](x0) = x0 + 7,
    
    [match](x0, x1) = x0 + x1 + 8,
    
    [X] = 1,
    
    [check](x0) = x0,
    
    [top](x0) = x0 + 7,
    
    [c] = 30,
    
    [mark](x0) = x0 + 2,
    
    [active](x0) = x0,
    
    [f](x0) = x0
   orientation:
    active(f(x)) = x >= x + 2 = mark(x)
    
    top(active(c())) = 37 >= 39 = top(mark(c()))
    
    top(mark(x)) = x + 9 >= x + 7 = top(check(x))
    
    check(f(x)) = x >= x = f(check(x))
    
    check(x) = x >= x + 16 = start(match(f(X()),x))
    
    match(f(x),f(y)) = x + y + 8 >= x + y + 8 = f(match(x,y))
    
    match(X(),x) = x + 9 >= x + 18 = proper(x)
    
    proper(c()) = 48 >= 30 = ok(c())
    
    proper(f(x)) = x + 18 >= x + 18 = f(proper(x))
    
    f(ok(x)) = x >= x = ok(f(x))
    
    start(ok(x)) = x + 7 >= x + 9 = found(x)
    
    f(found(x)) = x + 9 >= x + 9 = found(f(x))
    
    top(found(x)) = x + 16 >= x + 7 = top(active(x))
    
    active(f(x)) = x >= x = f(active(x))
    
    f(mark(x)) = x + 2 >= x + 2 = mark(f(x))
   problem:
    strict:
     active(f(x)) -> mark(x)
     top(active(c())) -> top(mark(c()))
     check(f(x)) -> f(check(x))
     check(x) -> start(match(f(X()),x))
     match(f(x),f(y)) -> f(match(x,y))
     match(X(),x) -> proper(x)
     proper(f(x)) -> f(proper(x))
     f(ok(x)) -> ok(f(x))
     start(ok(x)) -> found(x)
     f(found(x)) -> found(f(x))
     active(f(x)) -> f(active(x))
     f(mark(x)) -> mark(f(x))
    weak:
     top(mark(x)) -> top(check(x))
     proper(c()) -> ok(c())
     top(found(x)) -> top(active(x))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [found](x0) = x0 + 1,
     
     [ok](x0) = x0 + 5,
     
     [proper](x0) = x0 + 5,
     
     [start](x0) = x0 + 16,
     
     [match](x0, x1) = x0 + x1 + 13,
     
     [X] = 5,
     
     [check](x0) = x0 + 4,
     
     [top](x0) = x0 + 1,
     
     [c] = 13,
     
     [mark](x0) = x0 + 4,
     
     [active](x0) = x0,
     
     [f](x0) = x0
    orientation:
     active(f(x)) = x >= x + 4 = mark(x)
     
     top(active(c())) = 14 >= 18 = top(mark(c()))
     
     check(f(x)) = x + 4 >= x + 4 = f(check(x))
     
     check(x) = x + 4 >= x + 34 = start(match(f(X()),x))
     
     match(f(x),f(y)) = x + y + 13 >= x + y + 13 = f(match(x,y))
     
     match(X(),x) = x + 18 >= x + 5 = proper(x)
     
     proper(f(x)) = x + 5 >= x + 5 = f(proper(x))
     
     f(ok(x)) = x + 5 >= x + 5 = ok(f(x))
     
     start(ok(x)) = x + 21 >= x + 1 = found(x)
     
     f(found(x)) = x + 1 >= x + 1 = found(f(x))
     
     active(f(x)) = x >= x = f(active(x))
     
     f(mark(x)) = x + 4 >= x + 4 = mark(f(x))
     
     top(mark(x)) = x + 5 >= x + 5 = top(check(x))
     
     proper(c()) = 18 >= 18 = ok(c())
     
     top(found(x)) = x + 2 >= x + 1 = top(active(x))
    problem:
     strict:
      active(f(x)) -> mark(x)
      top(active(c())) -> top(mark(c()))
      check(f(x)) -> f(check(x))
      check(x) -> start(match(f(X()),x))
      match(f(x),f(y)) -> f(match(x,y))
      proper(f(x)) -> f(proper(x))
      f(ok(x)) -> ok(f(x))
      f(found(x)) -> found(f(x))
      active(f(x)) -> f(active(x))
      f(mark(x)) -> mark(f(x))
     weak:
      match(X(),x) -> proper(x)
      start(ok(x)) -> found(x)
      top(mark(x)) -> top(check(x))
      proper(c()) -> ok(c())
      top(found(x)) -> top(active(x))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [found](x0) = x0 + 17,
      
      [ok](x0) = x0,
      
      [proper](x0) = x0 + 18,
      
      [start](x0) = x0 + 26,
      
      [match](x0, x1) = x0 + x1 + 10,
      
      [X] = 8,
      
      [check](x0) = x0 + 2,
      
      [top](x0) = x0 + 2,
      
      [c] = 9,
      
      [mark](x0) = x0 + 2,
      
      [active](x0) = x0 + 7,
      
      [f](x0) = x0 + 8
     orientation:
      active(f(x)) = x + 15 >= x + 2 = mark(x)
      
      top(active(c())) = 18 >= 13 = top(mark(c()))
      
      check(f(x)) = x + 10 >= x + 10 = f(check(x))
      
      check(x) = x + 2 >= x + 52 = start(match(f(X()),x))
      
      match(f(x),f(y)) = x + y + 26 >= x + y + 18 = f(match(x,y))
      
      proper(f(x)) = x + 26 >= x + 26 = f(proper(x))
      
      f(ok(x)) = x + 8 >= x + 8 = ok(f(x))
      
      f(found(x)) = x + 25 >= x + 25 = found(f(x))
      
      active(f(x)) = x + 15 >= x + 15 = f(active(x))
      
      f(mark(x)) = x + 10 >= x + 10 = mark(f(x))
      
      match(X(),x) = x + 18 >= x + 18 = proper(x)
      
      start(ok(x)) = x + 26 >= x + 17 = found(x)
      
      top(mark(x)) = x + 4 >= x + 4 = top(check(x))
      
      proper(c()) = 27 >= 9 = ok(c())
      
      top(found(x)) = x + 19 >= x + 9 = top(active(x))
     problem:
      strict:
       check(f(x)) -> f(check(x))
       check(x) -> start(match(f(X()),x))
       proper(f(x)) -> f(proper(x))
       f(ok(x)) -> ok(f(x))
       f(found(x)) -> found(f(x))
       active(f(x)) -> f(active(x))
       f(mark(x)) -> mark(f(x))
      weak:
       active(f(x)) -> mark(x)
       top(active(c())) -> top(mark(c()))
       match(f(x),f(y)) -> f(match(x,y))
       match(X(),x) -> proper(x)
       start(ok(x)) -> found(x)
       top(mark(x)) -> top(check(x))
       proper(c()) -> ok(c())
       top(found(x)) -> top(active(x))
     Matrix Interpretation Processor:
      dimension: 3
      interpretation:
                     [1 4 0]  
       [found](x0) = [0 0 0]x0
                     [0 0 1]  ,
       
                  [1 4 0]  
       [ok](x0) = [0 0 0]x0
                  [0 0 1]  ,
       
                      [1 0 0]  
       [proper](x0) = [0 0 0]x0
                      [0 0 1]  ,
       
                     [1 0 0]  
       [start](x0) = [0 0 0]x0
                     [0 0 1]  ,
       
                         [1 0 0]     [1 0 0]     [0]
       [match](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [5]
                         [0 0 0]     [0 0 1]     [0],
       
             [0]
       [X] = [0]
             [0],
       
                     [1 0 0]  
       [check](x0) = [0 0 0]x0
                     [0 0 1]  ,
       
                   [1 0 0]     [0]
       [top](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [7],
       
             [1]
       [c] = [0]
             [4],
       
                    [1 0 0]     [0]
       [mark](x0) = [0 0 0]x0 + [0]
                    [0 0 1]     [4],
       
                      [1 0 0]     [0]
       [active](x0) = [0 0 0]x0 + [3]
                      [0 0 1]     [0],
       
                 [1 0 1]     [0]
       [f](x0) = [0 0 0]x0 + [0]
                 [0 0 1]     [4]
      orientation:
                     [1 0 1]    [0]    [1 0 1]    [0]              
       check(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(check(x))
                     [0 0 1]    [4]    [0 0 1]    [4]              
       
                  [1 0 0]     [1 0 0]                          
       check(x) = [0 0 0]x >= [0 0 0]x = start(match(f(X()),x))
                  [0 0 1]     [0 0 1]                          
       
                      [1 0 1]    [0]    [1 0 1]    [0]               
       proper(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(proper(x))
                      [0 0 1]    [4]    [0 0 1]    [4]               
       
                  [1 4 1]    [0]    [1 0 1]    [0]           
       f(ok(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = ok(f(x))
                  [0 0 1]    [4]    [0 0 1]    [4]           
       
                     [1 4 1]    [0]    [1 0 1]    [0]              
       f(found(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = found(f(x))
                     [0 0 1]    [4]    [0 0 1]    [4]              
       
                      [1 0 1]    [0]    [1 0 1]    [0]               
       active(f(x)) = [0 0 0]x + [3] >= [0 0 0]x + [0] = f(active(x))
                      [0 0 1]    [4]    [0 0 1]    [4]               
       
                    [1 0 1]    [4]    [1 0 1]    [0]             
       f(mark(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = mark(f(x))
                    [0 0 1]    [8]    [0 0 1]    [8]             
       
                      [1 0 1]    [0]    [1 0 0]    [0]          
       active(f(x)) = [0 0 0]x + [3] >= [0 0 0]x + [0] = mark(x)
                      [0 0 1]    [4]    [0 0 1]    [4]          
       
                          [1]    [1]                 
       top(active(c())) = [0] >= [0] = top(mark(c()))
                          [7]    [7]                 
       
                          [1 0 1]    [1 0 1]    [0]    [1 0 0]    [1 0 1]    [0]                
       match(f(x),f(y)) = [0 0 0]x + [0 0 0]y + [5] >= [0 0 0]x + [0 0 0]y + [0] = f(match(x,y))
                          [0 0 0]    [0 0 1]    [4]    [0 0 0]    [0 0 1]    [4]                
       
                      [1 0 0]    [0]    [1 0 0]             
       match(X(),x) = [0 0 0]x + [5] >= [0 0 0]x = proper(x)
                      [0 0 1]    [0]    [0 0 1]             
       
                      [1 4 0]     [1 4 0]            
       start(ok(x)) = [0 0 0]x >= [0 0 0]x = found(x)
                      [0 0 1]     [0 0 1]            
       
                      [1 0 0]    [0]    [1 0 0]    [0]                
       top(mark(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = top(check(x))
                      [0 0 0]    [7]    [0 0 0]    [7]                
       
                     [1]    [1]          
       proper(c()) = [0] >= [0] = ok(c())
                     [4]    [4]          
       
                       [1 4 0]    [0]    [1 0 0]    [0]                 
       top(found(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = top(active(x))
                       [0 0 0]    [7]    [0 0 0]    [7]                 
      problem:
       strict:
        check(f(x)) -> f(check(x))
        check(x) -> start(match(f(X()),x))
        proper(f(x)) -> f(proper(x))
        f(ok(x)) -> ok(f(x))
        f(found(x)) -> found(f(x))
        active(f(x)) -> f(active(x))
       weak:
        f(mark(x)) -> mark(f(x))
        active(f(x)) -> mark(x)
        top(active(c())) -> top(mark(c()))
        match(f(x),f(y)) -> f(match(x,y))
        match(X(),x) -> proper(x)
        start(ok(x)) -> found(x)
        top(mark(x)) -> top(check(x))
        proper(c()) -> ok(c())
        top(found(x)) -> top(active(x))
      Matrix Interpretation Processor:
       dimension: 2
       interpretation:
                           [8]
        [found](x0) = x0 + [0],
        
                     
        [ok](x0) = x0,
        
                       [1 2]     [0]
        [proper](x0) = [0 1]x0 + [2],
        
                           [8]
        [start](x0) = x0 + [2],
        
                          [1 0]     [1 2]     [0]
        [match](x0, x1) = [0 0]x0 + [0 1]x1 + [2],
        
              [0]
        [X] = [0],
        
                      [1 2]     [8]
        [check](x0) = [0 1]x0 + [4],
        
                    [1 0]     [0]
        [top](x0) = [0 0]x0 + [4],
        
              [12]
        [c] = [0 ],
        
                     [1 2]     [8]
        [mark](x0) = [0 1]x0 + [4],
        
                            [8]
        [active](x0) = x0 + [0],
        
                  [1 2]     [0]
        [f](x0) = [0 1]x0 + [4]
       orientation:
                      [1 4]    [16]    [1 4]    [16]              
        check(f(x)) = [0 1]x + [8 ] >= [0 1]x + [8 ] = f(check(x))
        
                   [1 2]    [8]    [1 2]    [8]                         
        check(x) = [0 1]x + [4] >= [0 1]x + [4] = start(match(f(X()),x))
        
                       [1 4]    [8]    [1 4]    [4]               
        proper(f(x)) = [0 1]x + [6] >= [0 1]x + [6] = f(proper(x))
        
                   [1 2]    [0]    [1 2]    [0]           
        f(ok(x)) = [0 1]x + [4] >= [0 1]x + [4] = ok(f(x))
        
                      [1 2]    [8]    [1 2]    [8]              
        f(found(x)) = [0 1]x + [4] >= [0 1]x + [4] = found(f(x))
        
                       [1 2]    [8]    [1 2]    [8]               
        active(f(x)) = [0 1]x + [4] >= [0 1]x + [4] = f(active(x))
        
                     [1 4]    [16]    [1 4]    [16]             
        f(mark(x)) = [0 1]x + [8 ] >= [0 1]x + [8 ] = mark(f(x))
        
                       [1 2]    [8]    [1 2]    [8]          
        active(f(x)) = [0 1]x + [4] >= [0 1]x + [4] = mark(x)
        
                           [20]    [20]                 
        top(active(c())) = [4 ] >= [4 ] = top(mark(c()))
        
                           [1 2]    [1 4]    [8]    [1 0]    [1 4]    [4]                
        match(f(x),f(y)) = [0 0]x + [0 1]y + [6] >= [0 0]x + [0 1]y + [6] = f(match(x,y))
        
                       [1 2]    [0]    [1 2]    [0]            
        match(X(),x) = [0 1]x + [2] >= [0 1]x + [2] = proper(x)
        
                           [8]        [8]           
        start(ok(x)) = x + [2] >= x + [0] = found(x)
        
                       [1 2]    [8]    [1 2]    [8]                
        top(mark(x)) = [0 0]x + [4] >= [0 0]x + [4] = top(check(x))
        
                      [12]    [12]          
        proper(c()) = [2 ] >= [0 ] = ok(c())
        
                        [1 0]    [8]    [1 0]    [8]                 
        top(found(x)) = [0 0]x + [4] >= [0 0]x + [4] = top(active(x))
       problem:
        strict:
         check(f(x)) -> f(check(x))
         check(x) -> start(match(f(X()),x))
         f(ok(x)) -> ok(f(x))
         f(found(x)) -> found(f(x))
         active(f(x)) -> f(active(x))
        weak:
         proper(f(x)) -> f(proper(x))
         f(mark(x)) -> mark(f(x))
         active(f(x)) -> mark(x)
         top(active(c())) -> top(mark(c()))
         match(f(x),f(y)) -> f(match(x,y))
         match(X(),x) -> proper(x)
         start(ok(x)) -> found(x)
         top(mark(x)) -> top(check(x))
         proper(c()) -> ok(c())
         top(found(x)) -> top(active(x))
       Matrix Interpretation Processor:
        dimension: 2
        interpretation:
                         
         [found](x0) = x0,
         
                      
         [ok](x0) = x0,
         
                          
         [proper](x0) = x0,
         
                         
         [start](x0) = x0,
         
                           [1 0]       
         [match](x0, x1) = [0 0]x0 + x1,
         
               [0]
         [X] = [0],
         
                       [1 1]  
         [check](x0) = [0 1]x0,
         
                     [1 0]     [0]
         [top](x0) = [0 0]x0 + [8],
         
               [8]
         [c] = [0],
         
                      [1 1]     [0]
         [mark](x0) = [0 1]x0 + [1],
         
                          
         [active](x0) = x0,
         
                   [1 4]     [0]
         [f](x0) = [0 1]x0 + [2]
        orientation:
                       [1 5]    [2]    [1 5]    [0]              
         check(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(check(x))
         
                    [1 1]                               
         check(x) = [0 1]x >= x = start(match(f(X()),x))
         
                    [1 4]    [0]    [1 4]    [0]           
         f(ok(x)) = [0 1]x + [2] >= [0 1]x + [2] = ok(f(x))
         
                       [1 4]    [0]    [1 4]    [0]              
         f(found(x)) = [0 1]x + [2] >= [0 1]x + [2] = found(f(x))
         
                        [1 4]    [0]    [1 4]    [0]               
         active(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(active(x))
         
                        [1 4]    [0]    [1 4]    [0]               
         proper(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(proper(x))
         
                      [1 5]    [4]    [1 5]    [2]             
         f(mark(x)) = [0 1]x + [3] >= [0 1]x + [3] = mark(f(x))
         
                        [1 4]    [0]    [1 1]    [0]          
         active(f(x)) = [0 1]x + [2] >= [0 1]x + [1] = mark(x)
         
                            [8]    [8]                 
         top(active(c())) = [8] >= [8] = top(mark(c()))
         
                            [1 4]    [1 4]    [0]    [1 0]    [1 4]    [0]                
         match(f(x),f(y)) = [0 0]x + [0 1]y + [2] >= [0 0]x + [0 1]y + [2] = f(match(x,y))
         
                                          
         match(X(),x) = x >= x = proper(x)
         
                                         
         start(ok(x)) = x >= x = found(x)
         
                        [1 1]    [0]    [1 1]    [0]                
         top(mark(x)) = [0 0]x + [8] >= [0 0]x + [8] = top(check(x))
         
                       [8]    [8]          
         proper(c()) = [0] >= [0] = ok(c())
         
                         [1 0]    [0]    [1 0]    [0]                 
         top(found(x)) = [0 0]x + [8] >= [0 0]x + [8] = top(active(x))
        problem:
         strict:
          check(x) -> start(match(f(X()),x))
          f(ok(x)) -> ok(f(x))
          f(found(x)) -> found(f(x))
          active(f(x)) -> f(active(x))
         weak:
          check(f(x)) -> f(check(x))
          proper(f(x)) -> f(proper(x))
          f(mark(x)) -> mark(f(x))
          active(f(x)) -> mark(x)
          top(active(c())) -> top(mark(c()))
          match(f(x),f(y)) -> f(match(x,y))
          match(X(),x) -> proper(x)
          start(ok(x)) -> found(x)
          top(mark(x)) -> top(check(x))
          proper(c()) -> ok(c())
          top(found(x)) -> top(active(x))
        Matrix Interpretation Processor:
         dimension: 2
         interpretation:
                          
          [found](x0) = x0,
          
                          [0]
          [ok](x0) = x0 + [4],
          
                         [1 2]     [0]
          [proper](x0) = [0 1]x0 + [4],
          
                          
          [start](x0) = x0,
          
                            [1 0]     [1 2]     [0]
          [match](x0, x1) = [0 0]x0 + [0 1]x1 + [4],
          
                [0]
          [X] = [0],
          
                        [1 2]     [0]
          [check](x0) = [0 1]x0 + [4],
          
                      [1 0]     [0 ]
          [top](x0) = [0 0]x0 + [14],
          
                [8]
          [c] = [0],
          
                       [1 2]     [0]
          [mark](x0) = [0 1]x0 + [4],
          
                           
          [active](x0) = x0,
          
                    [1 4]     [0]
          [f](x0) = [0 1]x0 + [8]
         orientation:
                     [1 2]    [0]    [1 2]    [0]                         
          check(x) = [0 1]x + [4] >= [0 1]x + [4] = start(match(f(X()),x))
          
                     [1 4]    [16]    [1 4]    [0 ]           
          f(ok(x)) = [0 1]x + [12] >= [0 1]x + [12] = ok(f(x))
          
                        [1 4]    [0]    [1 4]    [0]              
          f(found(x)) = [0 1]x + [8] >= [0 1]x + [8] = found(f(x))
          
                         [1 4]    [0]    [1 4]    [0]               
          active(f(x)) = [0 1]x + [8] >= [0 1]x + [8] = f(active(x))
          
                        [1 6]    [16]    [1 6]    [16]              
          check(f(x)) = [0 1]x + [12] >= [0 1]x + [12] = f(check(x))
          
                         [1 6]    [16]    [1 6]    [16]               
          proper(f(x)) = [0 1]x + [12] >= [0 1]x + [12] = f(proper(x))
          
                       [1 6]    [16]    [1 6]    [16]             
          f(mark(x)) = [0 1]x + [12] >= [0 1]x + [12] = mark(f(x))
          
                         [1 4]    [0]    [1 2]    [0]          
          active(f(x)) = [0 1]x + [8] >= [0 1]x + [4] = mark(x)
          
                             [8 ]    [8 ]                 
          top(active(c())) = [14] >= [14] = top(mark(c()))
          
                             [1 4]    [1 6]    [16]    [1 0]    [1 6]    [16]                
          match(f(x),f(y)) = [0 0]x + [0 1]y + [12] >= [0 0]x + [0 1]y + [12] = f(match(x,y))
          
                         [1 2]    [0]    [1 2]    [0]            
          match(X(),x) = [0 1]x + [4] >= [0 1]x + [4] = proper(x)
          
                             [0]                
          start(ok(x)) = x + [4] >= x = found(x)
          
                         [1 2]    [0 ]    [1 2]    [0 ]                
          top(mark(x)) = [0 0]x + [14] >= [0 0]x + [14] = top(check(x))
          
                        [8]    [8]          
          proper(c()) = [4] >= [4] = ok(c())
          
                          [1 0]    [0 ]    [1 0]    [0 ]                 
          top(found(x)) = [0 0]x + [14] >= [0 0]x + [14] = top(active(x))
         problem:
          strict:
           check(x) -> start(match(f(X()),x))
           f(found(x)) -> found(f(x))
           active(f(x)) -> f(active(x))
          weak:
           f(ok(x)) -> ok(f(x))
           check(f(x)) -> f(check(x))
           proper(f(x)) -> f(proper(x))
           f(mark(x)) -> mark(f(x))
           active(f(x)) -> mark(x)
           top(active(c())) -> top(mark(c()))
           match(f(x),f(y)) -> f(match(x,y))
           match(X(),x) -> proper(x)
           start(ok(x)) -> found(x)
           top(mark(x)) -> top(check(x))
           proper(c()) -> ok(c())
           top(found(x)) -> top(active(x))
         Matrix Interpretation Processor:
          dimension: 2
          interpretation:
                         [1 8]     [0]
           [found](x0) = [0 1]x0 + [1],
           
                        
           [ok](x0) = x0,
           
                            
           [proper](x0) = x0,
           
                         [1 8]     [0]
           [start](x0) = [0 1]x0 + [1],
           
                             [1 0]       
           [match](x0, x1) = [0 0]x0 + x1,
           
                 [0]
           [X] = [0],
           
                         [1 8]     [0]
           [check](x0) = [0 1]x0 + [1],
           
                       [1 8]     [0]
           [top](x0) = [0 0]x0 + [1],
           
                 [0]
           [c] = [0],
           
                        [1 8]     [0]
           [mark](x0) = [0 1]x0 + [1],
           
                          [1 1]     [8]
           [active](x0) = [0 1]x0 + [0],
           
                     [1 8]     [0]
           [f](x0) = [0 1]x0 + [1]
          orientation:
                      [1 8]    [0]    [1 8]    [0]                         
           check(x) = [0 1]x + [1] >= [0 1]x + [1] = start(match(f(X()),x))
           
                         [1  16]    [8]    [1  16]    [8]              
           f(found(x)) = [0  1 ]x + [2] >= [0  1 ]x + [2] = found(f(x))
           
                          [1 9]    [9]    [1 9]    [8]               
           active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(active(x))
           
                      [1 8]    [0]    [1 8]    [0]           
           f(ok(x)) = [0 1]x + [1] >= [0 1]x + [1] = ok(f(x))
           
                         [1  16]    [8]    [1  16]    [8]              
           check(f(x)) = [0  1 ]x + [2] >= [0  1 ]x + [2] = f(check(x))
           
                          [1 8]    [0]    [1 8]    [0]               
           proper(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(proper(x))
           
                        [1  16]    [8]    [1  16]    [8]             
           f(mark(x)) = [0  1 ]x + [2] >= [0  1 ]x + [2] = mark(f(x))
           
                          [1 9]    [9]    [1 8]    [0]          
           active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = mark(x)
           
                              [8]    [8]                 
           top(active(c())) = [1] >= [1] = top(mark(c()))
           
                              [1 8]    [1 8]    [0]    [1 0]    [1 8]    [0]                
           match(f(x),f(y)) = [0 0]x + [0 1]y + [1] >= [0 0]x + [0 1]y + [1] = f(match(x,y))
           
                                            
           match(X(),x) = x >= x = proper(x)
           
                          [1 8]    [0]    [1 8]    [0]           
           start(ok(x)) = [0 1]x + [1] >= [0 1]x + [1] = found(x)
           
                          [1  16]    [8]    [1  16]    [8]                
           top(mark(x)) = [0  0 ]x + [1] >= [0  0 ]x + [1] = top(check(x))
           
                         [0]    [0]          
           proper(c()) = [0] >= [0] = ok(c())
           
                           [1  16]    [8]    [1 9]    [8]                 
           top(found(x)) = [0  0 ]x + [1] >= [0 0]x + [1] = top(active(x))
          problem:
           strict:
            check(x) -> start(match(f(X()),x))
            f(found(x)) -> found(f(x))
           weak:
            active(f(x)) -> f(active(x))
            f(ok(x)) -> ok(f(x))
            check(f(x)) -> f(check(x))
            proper(f(x)) -> f(proper(x))
            f(mark(x)) -> mark(f(x))
            active(f(x)) -> mark(x)
            top(active(c())) -> top(mark(c()))
            match(f(x),f(y)) -> f(match(x,y))
            match(X(),x) -> proper(x)
            start(ok(x)) -> found(x)
            top(mark(x)) -> top(check(x))
            proper(c()) -> ok(c())
            top(found(x)) -> top(active(x))
          Matrix Interpretation Processor:
           dimension: 2
           interpretation:
                               [0]
            [found](x0) = x0 + [4],
            
                         
            [ok](x0) = x0,
            
                             
            [proper](x0) = x0,
            
                          [1 1]     [0]
            [start](x0) = [0 1]x0 + [4],
            
                              [1 0]       
            [match](x0, x1) = [0 0]x0 + x1,
            
                  [0]
            [X] = [0],
            
                          [1 4]     [0]
            [check](x0) = [0 1]x0 + [4],
            
                        [1 0]     [0]
            [top](x0) = [0 0]x0 + [2],
            
                  [2]
            [c] = [0],
            
                         [1 4]     [0]
            [mark](x0) = [0 1]x0 + [4],
            
                             
            [active](x0) = x0,
            
                      [1 4]     [0]
            [f](x0) = [0 1]x0 + [4]
           orientation:
                       [1 4]    [0]    [1 1]    [0]                         
            check(x) = [0 1]x + [4] >= [0 1]x + [4] = start(match(f(X()),x))
            
                          [1 4]    [16]    [1 4]    [0]              
            f(found(x)) = [0 1]x + [8 ] >= [0 1]x + [8] = found(f(x))
            
                           [1 4]    [0]    [1 4]    [0]               
            active(f(x)) = [0 1]x + [4] >= [0 1]x + [4] = f(active(x))
            
                       [1 4]    [0]    [1 4]    [0]           
            f(ok(x)) = [0 1]x + [4] >= [0 1]x + [4] = ok(f(x))
            
                          [1 8]    [16]    [1 8]    [16]              
            check(f(x)) = [0 1]x + [8 ] >= [0 1]x + [8 ] = f(check(x))
            
                           [1 4]    [0]    [1 4]    [0]               
            proper(f(x)) = [0 1]x + [4] >= [0 1]x + [4] = f(proper(x))
            
                         [1 8]    [16]    [1 8]    [16]             
            f(mark(x)) = [0 1]x + [8 ] >= [0 1]x + [8 ] = mark(f(x))
            
                           [1 4]    [0]    [1 4]    [0]          
            active(f(x)) = [0 1]x + [4] >= [0 1]x + [4] = mark(x)
            
                               [2]    [2]                 
            top(active(c())) = [2] >= [2] = top(mark(c()))
            
                               [1 4]    [1 4]    [0]    [1 0]    [1 4]    [0]                
            match(f(x),f(y)) = [0 0]x + [0 1]y + [4] >= [0 0]x + [0 1]y + [4] = f(match(x,y))
            
                                             
            match(X(),x) = x >= x = proper(x)
            
                           [1 1]    [0]        [0]           
            start(ok(x)) = [0 1]x + [4] >= x + [4] = found(x)
            
                           [1 4]    [0]    [1 4]    [0]                
            top(mark(x)) = [0 0]x + [2] >= [0 0]x + [2] = top(check(x))
            
                          [2]    [2]          
            proper(c()) = [0] >= [0] = ok(c())
            
                            [1 0]    [0]    [1 0]    [0]                 
            top(found(x)) = [0 0]x + [2] >= [0 0]x + [2] = top(active(x))
           problem:
            strict:
             check(x) -> start(match(f(X()),x))
            weak:
             f(found(x)) -> found(f(x))
             active(f(x)) -> f(active(x))
             f(ok(x)) -> ok(f(x))
             check(f(x)) -> f(check(x))
             proper(f(x)) -> f(proper(x))
             f(mark(x)) -> mark(f(x))
             active(f(x)) -> mark(x)
             top(active(c())) -> top(mark(c()))
             match(f(x),f(y)) -> f(match(x,y))
             match(X(),x) -> proper(x)
             start(ok(x)) -> found(x)
             top(mark(x)) -> top(check(x))
             proper(c()) -> ok(c())
             top(found(x)) -> top(active(x))
           Matrix Interpretation Processor:
            dimension: 3
            interpretation:
                           [1 0 2]     [1]
             [found](x0) = [0 1 0]x0 + [0]
                           [0 0 0]     [0],
             
                             [1]
             [ok](x0) = x0 + [0]
                             [0],
             
                            [1 0 0]     [1]
             [proper](x0) = [0 1 0]x0 + [0]
                            [0 0 0]     [4],
             
                           [1 0 2]  
             [start](x0) = [0 1 0]x0
                           [0 0 1]  ,
             
                               [1 0 0]     [1 0 0]     [1]
             [match](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0]
                               [0 0 1]     [0 0 0]     [0],
             
                   [0]
             [X] = [0]
                   [4],
             
                           [1 0 0]     [3]
             [check](x0) = [0 1 0]x0 + [0]
                           [0 0 0]     [0],
             
                         [1 2 2]     [1]
             [top](x0) = [0 0 0]x0 + [1]
                         [0 0 0]     [0],
             
                   [2]
             [c] = [1]
                   [4],
             
                          [1 4 0]     [2]
             [mark](x0) = [0 0 0]x0 + [1]
                          [0 0 0]     [0],
             
                                 [1]
             [active](x0) = x0 + [0]
                                 [0],
             
                       [1 4 0]     [1]
             [f](x0) = [0 0 0]x0 + [1]
                       [0 0 0]     [0]
            orientation:
                        [1 0 0]    [3]    [1 0 0]    [2]                         
             check(x) = [0 1 0]x + [0] >= [0 1 0]x + [0] = start(match(f(X()),x))
                        [0 0 0]    [0]    [0 0 0]    [0]                         
             
                           [1 4 2]    [2]    [1 4 0]    [2]              
             f(found(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = found(f(x))
                           [0 0 0]    [0]    [0 0 0]    [0]              
             
                            [1 4 0]    [2]    [1 4 0]    [2]               
             active(f(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = f(active(x))
                            [0 0 0]    [0]    [0 0 0]    [0]               
             
                        [1 4 0]    [2]    [1 4 0]    [2]           
             f(ok(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = ok(f(x))
                        [0 0 0]    [0]    [0 0 0]    [0]           
             
                           [1 4 0]    [4]    [1 4 0]    [4]              
             check(f(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = f(check(x))
                           [0 0 0]    [0]    [0 0 0]    [0]              
             
                            [1 4 0]    [2]    [1 4 0]    [2]               
             proper(f(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = f(proper(x))
                            [0 0 0]    [4]    [0 0 0]    [0]               
             
                          [1 4 0]    [7]    [1 4 0]    [7]             
             f(mark(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = mark(f(x))
                          [0 0 0]    [0]    [0 0 0]    [0]             
             
                            [1 4 0]    [2]    [1 4 0]    [2]          
             active(f(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = mark(x)
                            [0 0 0]    [0]    [0 0 0]    [0]          
             
                                [14]    [11]                 
             top(active(c())) = [1 ] >= [1 ] = top(mark(c()))
                                [0 ]    [0 ]                 
             
                                [1 4 0]    [1 4 0]    [3]    [1 0 0]    [1 4 0]    [2]                
             match(f(x),f(y)) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = f(match(x,y))
                                [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                
             
                            [1 0 0]    [1]    [1 0 0]    [1]            
             match(X(),x) = [0 1 0]x + [0] >= [0 1 0]x + [0] = proper(x)
                            [0 0 0]    [4]    [0 0 0]    [4]            
             
                            [1 0 2]    [1]    [1 0 2]    [1]           
             start(ok(x)) = [0 1 0]x + [0] >= [0 1 0]x + [0] = found(x)
                            [0 0 1]    [0]    [0 0 0]    [0]           
             
                            [1 4 0]    [5]    [1 2 0]    [4]                
             top(mark(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = top(check(x))
                            [0 0 0]    [0]    [0 0 0]    [0]                
             
                           [3]    [3]          
             proper(c()) = [1] >= [1] = ok(c())
                           [4]    [4]          
             
                             [1 2 2]    [2]    [1 2 2]    [2]                 
             top(found(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = top(active(x))
                             [0 0 0]    [0]    [0 0 0]    [0]                 
            problem:
             strict:
              
             weak:
              check(x) -> start(match(f(X()),x))
              f(found(x)) -> found(f(x))
              active(f(x)) -> f(active(x))
              f(ok(x)) -> ok(f(x))
              check(f(x)) -> f(check(x))
              proper(f(x)) -> f(proper(x))
              f(mark(x)) -> mark(f(x))
              active(f(x)) -> mark(x)
              top(active(c())) -> top(mark(c()))
              match(f(x),f(y)) -> f(match(x,y))
              match(X(),x) -> proper(x)
              start(ok(x)) -> found(x)
              top(mark(x)) -> top(check(x))
              proper(c()) -> ok(c())
              top(found(x)) -> top(active(x))
            Qed