YES

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:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 1 1]  
   [found](x0) = [0 0 0]x0
                 [0 0 0]  ,
   
              [1 0 0]  
   [ok](x0) = [0 1 1]x0
              [0 1 0]  ,
   
                  [1 0 0]     [0]
   [proper](x0) = [0 0 0]x0 + [1]
                  [0 0 0]     [1],
   
                 [1 1 0]     [0]
   [start](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [0],
   
                     [1 0 0]     [1 0 0]     [0]
   [match](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0]
                     [0 0 0]     [0 0 0]     [1],
   
         [0]
   [X] = [1]
         [0],
   
                 [1 0 0]     [0]
   [check](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [0],
   
               [1 0 1]  
   [top](x0) = [0 0 0]x0
               [1 0 0]  ,
   
         [0]
   [c] = [1]
         [0],
   
                [1 0 0]  
   [mark](x0) = [0 0 0]x0
                [0 0 0]  ,
   
                  [1 0 0]  
   [active](x0) = [1 0 0]x0
                  [0 1 0]  ,
   
             [1 0 0]  
   [f](x0) = [0 0 0]x0
             [0 0 0]  
  orientation:
                  [1 0 0]     [1 0 0]           
   active(f(x)) = [1 0 0]x >= [0 0 0]x = mark(x)
                  [0 0 0]     [0 0 0]           
   
                      [1]    [0]                 
   top(active(c())) = [0] >= [0] = top(mark(c()))
                      [0]    [0]                 
   
                  [1 0 0]     [1 0 0]                 
   top(mark(x)) = [0 0 0]x >= [0 0 0]x = top(check(x))
                  [1 0 0]     [1 0 0]                 
   
                 [1 0 0]    [0]    [1 0 0]               
   check(f(x)) = [0 0 0]x + [1] >= [0 0 0]x = f(check(x))
                 [0 0 0]    [0]    [0 0 0]               
   
              [1 0 0]    [0]    [1 0 0]    [0]                         
   check(x) = [0 0 0]x + [1] >= [0 0 0]x + [1] = start(match(f(X()),x))
              [0 0 0]    [0]    [0 0 0]    [0]                         
   
                      [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]                 
   match(f(x),f(y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = f(match(x,y))
                      [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]                 
   
                  [1 0 0]    [0]    [1 0 0]    [0]            
   match(X(),x) = [0 0 0]x + [1] >= [0 0 0]x + [1] = proper(x)
                  [0 0 0]    [1]    [0 0 0]    [1]            
   
                 [0]    [0]          
   proper(c()) = [1] >= [1] = ok(c())
                 [1]    [1]          
   
                  [1 0 0]    [0]    [1 0 0]                
   proper(f(x)) = [0 0 0]x + [1] >= [0 0 0]x = f(proper(x))
                  [0 0 0]    [1]    [0 0 0]                
   
              [1 0 0]     [1 0 0]            
   f(ok(x)) = [0 0 0]x >= [0 0 0]x = ok(f(x))
              [0 0 0]     [0 0 0]            
   
                  [1 1 1]    [0]    [1 1 1]            
   start(ok(x)) = [0 0 0]x + [1] >= [0 0 0]x = found(x)
                  [0 0 0]    [0]    [0 0 0]            
   
                 [1 1 1]     [1 0 0]               
   f(found(x)) = [0 0 0]x >= [0 0 0]x = found(f(x))
                 [0 0 0]     [0 0 0]               
   
                   [1 1 1]     [1 1 0]                  
   top(found(x)) = [0 0 0]x >= [0 0 0]x = top(active(x))
                   [1 1 1]     [1 0 0]                  
   
                  [1 0 0]     [1 0 0]                
   active(f(x)) = [1 0 0]x >= [0 0 0]x = f(active(x))
                  [0 0 0]     [0 0 0]                
   
                [1 0 0]     [1 0 0]              
   f(mark(x)) = [0 0 0]x >= [0 0 0]x = mark(f(x))
                [0 0 0]     [0 0 0]              
  problem:
   active(f(x)) -> mark(x)
   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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [found](x0) = 3x0,
    
    [ok](x0) = 2x0,
    
    [proper](x0) = 3x0,
    
    [start](x0) = 2x0,
    
    [match](x0, x1) = 2x0 + 3x1,
    
    [X] = 0,
    
    [check](x0) = 6x0,
    
    [top](x0) = x0,
    
    [c] = 1,
    
    [mark](x0) = 6x0,
    
    [active](x0) = 3x0,
    
    [f](x0) = 2x0
   orientation:
    active(f(x)) = 6x >= 6x = mark(x)
    
    top(mark(x)) = 6x >= 6x = top(check(x))
    
    check(f(x)) = 12x >= 12x = f(check(x))
    
    check(x) = 6x >= 6x = start(match(f(X()),x))
    
    match(f(x),f(y)) = 4x + 6y >= 4x + 6y = f(match(x,y))
    
    match(X(),x) = 3x >= 3x = proper(x)
    
    proper(c()) = 3 >= 2 = ok(c())
    
    proper(f(x)) = 6x >= 6x = f(proper(x))
    
    f(ok(x)) = 4x >= 4x = ok(f(x))
    
    start(ok(x)) = 4x >= 3x = found(x)
    
    f(found(x)) = 6x >= 6x = found(f(x))
    
    top(found(x)) = 3x >= 3x = top(active(x))
    
    active(f(x)) = 6x >= 6x = f(active(x))
    
    f(mark(x)) = 12x >= 12x = mark(f(x))
   problem:
    active(f(x)) -> mark(x)
    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(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))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [found](x0) = 4x0 + 3,
     
     [ok](x0) = 4x0 + 4,
     
     [proper](x0) = 2x0,
     
     [start](x0) = x0 + 2,
     
     [match](x0, x1) = x0 + 2x1,
     
     [X] = 0,
     
     [check](x0) = 6x0 + 5,
     
     [top](x0) = x0 + 2,
     
     [mark](x0) = 6x0 + 5,
     
     [active](x0) = 4x0 + 2,
     
     [f](x0) = 2x0 + 1
    orientation:
     active(f(x)) = 8x + 6 >= 6x + 5 = mark(x)
     
     top(mark(x)) = 6x + 7 >= 6x + 7 = top(check(x))
     
     check(f(x)) = 12x + 11 >= 12x + 11 = f(check(x))
     
     check(x) = 6x + 5 >= 2x + 3 = start(match(f(X()),x))
     
     match(f(x),f(y)) = 2x + 4y + 3 >= 2x + 4y + 1 = f(match(x,y))
     
     match(X(),x) = 2x >= 2x = proper(x)
     
     proper(f(x)) = 4x + 2 >= 4x + 1 = f(proper(x))
     
     f(ok(x)) = 8x + 9 >= 8x + 8 = ok(f(x))
     
     start(ok(x)) = 4x + 6 >= 4x + 3 = found(x)
     
     f(found(x)) = 8x + 7 >= 8x + 7 = found(f(x))
     
     top(found(x)) = 4x + 5 >= 4x + 4 = top(active(x))
     
     active(f(x)) = 8x + 6 >= 8x + 5 = f(active(x))
     
     f(mark(x)) = 12x + 11 >= 12x + 11 = mark(f(x))
    problem:
     top(mark(x)) -> top(check(x))
     check(f(x)) -> f(check(x))
     match(X(),x) -> proper(x)
     f(found(x)) -> found(f(x))
     f(mark(x)) -> mark(f(x))
    DP Processor:
     DPs:
      top#(mark(x)) -> check#(x)
      top#(mark(x)) -> top#(check(x))
      check#(f(x)) -> check#(x)
      check#(f(x)) -> f#(check(x))
      f#(found(x)) -> f#(x)
      f#(mark(x)) -> f#(x)
     TRS:
      top(mark(x)) -> top(check(x))
      check(f(x)) -> f(check(x))
      match(X(),x) -> proper(x)
      f(found(x)) -> found(f(x))
      f(mark(x)) -> mark(f(x))
     TDG Processor:
      DPs:
       top#(mark(x)) -> check#(x)
       top#(mark(x)) -> top#(check(x))
       check#(f(x)) -> check#(x)
       check#(f(x)) -> f#(check(x))
       f#(found(x)) -> f#(x)
       f#(mark(x)) -> f#(x)
      TRS:
       top(mark(x)) -> top(check(x))
       check(f(x)) -> f(check(x))
       match(X(),x) -> proper(x)
       f(found(x)) -> found(f(x))
       f(mark(x)) -> mark(f(x))
      graph:
       f#(found(x)) -> f#(x) -> f#(mark(x)) -> f#(x)
       f#(found(x)) -> f#(x) -> f#(found(x)) -> f#(x)
       f#(mark(x)) -> f#(x) -> f#(mark(x)) -> f#(x)
       f#(mark(x)) -> f#(x) -> f#(found(x)) -> f#(x)
       check#(f(x)) -> f#(check(x)) -> f#(mark(x)) -> f#(x)
       check#(f(x)) -> f#(check(x)) -> f#(found(x)) -> f#(x)
       check#(f(x)) -> check#(x) -> check#(f(x)) -> f#(check(x))
       check#(f(x)) -> check#(x) -> check#(f(x)) -> check#(x)
       top#(mark(x)) -> check#(x) -> check#(f(x)) -> f#(check(x))
       top#(mark(x)) -> check#(x) -> check#(f(x)) -> check#(x)
       top#(mark(x)) -> top#(check(x)) ->
       top#(mark(x)) -> top#(check(x))
       top#(mark(x)) -> top#(check(x)) -> top#(mark(x)) -> check#(x)
      SCC Processor:
       #sccs: 3
       #rules: 4
       #arcs: 12/36
       DPs:
        top#(mark(x)) -> top#(check(x))
       TRS:
        top(mark(x)) -> top(check(x))
        check(f(x)) -> f(check(x))
        match(X(),x) -> proper(x)
        f(found(x)) -> found(f(x))
        f(mark(x)) -> mark(f(x))
       CDG Processor:
        DPs:
         top#(mark(x)) -> top#(check(x))
        TRS:
         top(mark(x)) -> top(check(x))
         check(f(x)) -> f(check(x))
         match(X(),x) -> proper(x)
         f(found(x)) -> found(f(x))
         f(mark(x)) -> mark(f(x))
        graph:
         
        Qed
       
       DPs:
        check#(f(x)) -> check#(x)
       TRS:
        top(mark(x)) -> top(check(x))
        check(f(x)) -> f(check(x))
        match(X(),x) -> proper(x)
        f(found(x)) -> found(f(x))
        f(mark(x)) -> mark(f(x))
       Subterm Criterion Processor:
        simple projection:
         pi(check#) = 0
        problem:
         DPs:
          
         TRS:
          top(mark(x)) -> top(check(x))
          check(f(x)) -> f(check(x))
          match(X(),x) -> proper(x)
          f(found(x)) -> found(f(x))
          f(mark(x)) -> mark(f(x))
        Qed
       
       DPs:
        f#(found(x)) -> f#(x)
        f#(mark(x)) -> f#(x)
       TRS:
        top(mark(x)) -> top(check(x))
        check(f(x)) -> f(check(x))
        match(X(),x) -> proper(x)
        f(found(x)) -> found(f(x))
        f(mark(x)) -> mark(f(x))
       Subterm Criterion Processor:
        simple projection:
         pi(f#) = 0
        problem:
         DPs:
          
         TRS:
          top(mark(x)) -> top(check(x))
          check(f(x)) -> f(check(x))
          match(X(),x) -> proper(x)
          f(found(x)) -> found(f(x))
          f(mark(x)) -> mark(f(x))
        Qed