YES

Problem:
 active(f(X)) -> mark(if(X,c(),f(true())))
 active(if(true(),X,Y)) -> mark(X)
 active(if(false(),X,Y)) -> mark(Y)
 mark(f(X)) -> active(f(mark(X)))
 mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
 mark(c()) -> active(c())
 mark(true()) -> active(true())
 mark(false()) -> active(false())
 f(mark(X)) -> f(X)
 f(active(X)) -> f(X)
 if(mark(X1),X2,X3) -> if(X1,X2,X3)
 if(X1,mark(X2),X3) -> if(X1,X2,X3)
 if(X1,X2,mark(X3)) -> if(X1,X2,X3)
 if(active(X1),X2,X3) -> if(X1,X2,X3)
 if(X1,active(X2),X3) -> if(X1,X2,X3)
 if(X1,X2,active(X3)) -> if(X1,X2,X3)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [false] = 4,
   
   [mark](x0) = x0,
   
   [if](x0, x1, x2) = x0 + x1 + 2x2,
   
   [true] = 0,
   
   [c] = 0,
   
   [active](x0) = x0,
   
   [f](x0) = x0
  orientation:
   active(f(X)) = X >= X = mark(if(X,c(),f(true())))
   
   active(if(true(),X,Y)) = X + 2Y >= X = mark(X)
   
   active(if(false(),X,Y)) = X + 2Y + 4 >= Y = mark(Y)
   
   mark(f(X)) = X >= X = active(f(mark(X)))
   
   mark(if(X1,X2,X3)) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = active(if(mark(X1),mark(X2),X3))
   
   mark(c()) = 0 >= 0 = active(c())
   
   mark(true()) = 0 >= 0 = active(true())
   
   mark(false()) = 4 >= 4 = active(false())
   
   f(mark(X)) = X >= X = f(X)
   
   f(active(X)) = X >= X = f(X)
   
   if(mark(X1),X2,X3) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = if(X1,X2,X3)
   
   if(X1,mark(X2),X3) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = if(X1,X2,X3)
   
   if(X1,X2,mark(X3)) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = if(X1,X2,X3)
   
   if(active(X1),X2,X3) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = if(X1,X2,X3)
   
   if(X1,active(X2),X3) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = if(X1,X2,X3)
   
   if(X1,X2,active(X3)) = X1 + X2 + 2X3 >= X1 + X2 + 2X3 = if(X1,X2,X3)
  problem:
   active(f(X)) -> mark(if(X,c(),f(true())))
   active(if(true(),X,Y)) -> mark(X)
   mark(f(X)) -> active(f(mark(X)))
   mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
   mark(c()) -> active(c())
   mark(true()) -> active(true())
   mark(false()) -> active(false())
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
   if(mark(X1),X2,X3) -> if(X1,X2,X3)
   if(X1,mark(X2),X3) -> if(X1,X2,X3)
   if(X1,X2,mark(X3)) -> if(X1,X2,X3)
   if(active(X1),X2,X3) -> if(X1,X2,X3)
   if(X1,active(X2),X3) -> if(X1,X2,X3)
   if(X1,X2,active(X3)) -> if(X1,X2,X3)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [0]
    [false] = [0]
              [0],
    
                 [1 0 1]  
    [mark](x0) = [0 1 0]x0
                 [0 0 0]  ,
    
                       [1 0 1]     [1 0 1]     [1 0 0]  
    [if](x0, x1, x2) = [0 0 0]x0 + [0 1 0]x1 + [0 0 0]x2
                       [0 0 0]     [0 1 0]     [0 0 0]  ,
    
             [0]
    [true] = [0]
             [0],
    
          [0]
    [c] = [0]
          [0],
    
                   [1 0 1]  
    [active](x0) = [0 1 0]x0
                   [0 0 0]  ,
    
              [1 0 1]     [0]
    [f](x0) = [0 0 0]x0 + [0]
              [0 1 0]     [1]
   orientation:
                   [1 1 1]    [1]    [1 0 1]                             
    active(f(X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(if(X,c(),f(true())))
                   [0 0 0]    [0]    [0 0 0]                             
    
                             [1 1 1]    [1 0 0]     [1 0 1]           
    active(if(true(),X,Y)) = [0 1 0]X + [0 0 0]Y >= [0 1 0]X = mark(X)
                             [0 0 0]    [0 0 0]     [0 0 0]           
    
                 [1 1 1]    [1]    [1 1 1]    [1]                     
    mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(f(mark(X)))
                 [0 0 0]    [0]    [0 0 0]    [0]                     
    
                         [1 0 1]     [1 1 1]     [1 0 0]      [1 0 1]     [1 1 1]     [1 0 0]                                     
    mark(if(X1,X2,X3)) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 = active(if(mark(X1),mark(X2),X3))
                         [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                                     
    
                [0]    [0]              
    mark(c()) = [0] >= [0] = active(c())
                [0]    [0]              
    
                   [0]    [0]                 
    mark(true()) = [0] >= [0] = active(true())
                   [0]    [0]                 
    
                    [0]    [0]                  
    mark(false()) = [0] >= [0] = active(false())
                    [0]    [0]                  
    
                 [1 0 1]    [0]    [1 0 1]    [0]       
    f(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(X)
                 [0 1 0]    [1]    [0 1 0]    [1]       
    
                   [1 0 1]    [0]    [1 0 1]    [0]       
    f(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(X)
                   [0 1 0]    [1]    [0 1 0]    [1]       
    
                         [1 0 1]     [1 0 1]     [1 0 0]      [1 0 1]     [1 0 1]     [1 0 0]                 
    if(mark(X1),X2,X3) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 = if(X1,X2,X3)
                         [0 0 0]     [0 1 0]     [0 0 0]      [0 0 0]     [0 1 0]     [0 0 0]                 
    
                         [1 0 1]     [1 0 1]     [1 0 0]      [1 0 1]     [1 0 1]     [1 0 0]                 
    if(X1,mark(X2),X3) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 = if(X1,X2,X3)
                         [0 0 0]     [0 1 0]     [0 0 0]      [0 0 0]     [0 1 0]     [0 0 0]                 
    
                         [1 0 1]     [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]     [1 0 0]                 
    if(X1,X2,mark(X3)) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 = if(X1,X2,X3)
                         [0 0 0]     [0 1 0]     [0 0 0]      [0 0 0]     [0 1 0]     [0 0 0]                 
    
                           [1 0 1]     [1 0 1]     [1 0 0]      [1 0 1]     [1 0 1]     [1 0 0]                 
    if(active(X1),X2,X3) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 = if(X1,X2,X3)
                           [0 0 0]     [0 1 0]     [0 0 0]      [0 0 0]     [0 1 0]     [0 0 0]                 
    
                           [1 0 1]     [1 0 1]     [1 0 0]      [1 0 1]     [1 0 1]     [1 0 0]                 
    if(X1,active(X2),X3) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 = if(X1,X2,X3)
                           [0 0 0]     [0 1 0]     [0 0 0]      [0 0 0]     [0 1 0]     [0 0 0]                 
    
                           [1 0 1]     [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]     [1 0 0]                 
    if(X1,X2,active(X3)) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 = if(X1,X2,X3)
                           [0 0 0]     [0 1 0]     [0 0 0]      [0 0 0]     [0 1 0]     [0 0 0]                 
   problem:
    active(if(true(),X,Y)) -> mark(X)
    mark(f(X)) -> active(f(mark(X)))
    mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
    mark(c()) -> active(c())
    mark(true()) -> active(true())
    mark(false()) -> active(false())
    f(mark(X)) -> f(X)
    f(active(X)) -> f(X)
    if(mark(X1),X2,X3) -> if(X1,X2,X3)
    if(X1,mark(X2),X3) -> if(X1,X2,X3)
    if(X1,X2,mark(X3)) -> if(X1,X2,X3)
    if(active(X1),X2,X3) -> if(X1,X2,X3)
    if(X1,active(X2),X3) -> if(X1,X2,X3)
    if(X1,X2,active(X3)) -> if(X1,X2,X3)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [false] = 0,
     
     [mark](x0) = x0,
     
     [if](x0, x1, x2) = x0 + 6x1 + 2x2,
     
     [true] = 5,
     
     [c] = 0,
     
     [active](x0) = x0,
     
     [f](x0) = 4x0 + 2
    orientation:
     active(if(true(),X,Y)) = 6X + 2Y + 5 >= X = mark(X)
     
     mark(f(X)) = 4X + 2 >= 4X + 2 = active(f(mark(X)))
     
     mark(if(X1,X2,X3)) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = active(if(mark(X1),mark(X2),X3))
     
     mark(c()) = 0 >= 0 = active(c())
     
     mark(true()) = 5 >= 5 = active(true())
     
     mark(false()) = 0 >= 0 = active(false())
     
     f(mark(X)) = 4X + 2 >= 4X + 2 = f(X)
     
     f(active(X)) = 4X + 2 >= 4X + 2 = f(X)
     
     if(mark(X1),X2,X3) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = if(X1,X2,X3)
     
     if(X1,mark(X2),X3) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = if(X1,X2,X3)
     
     if(X1,X2,mark(X3)) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = if(X1,X2,X3)
     
     if(active(X1),X2,X3) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = if(X1,X2,X3)
     
     if(X1,active(X2),X3) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = if(X1,X2,X3)
     
     if(X1,X2,active(X3)) = X1 + 6X2 + 2X3 >= X1 + 6X2 + 2X3 = if(X1,X2,X3)
    problem:
     mark(f(X)) -> active(f(mark(X)))
     mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
     mark(c()) -> active(c())
     mark(true()) -> active(true())
     mark(false()) -> active(false())
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     if(mark(X1),X2,X3) -> if(X1,X2,X3)
     if(X1,mark(X2),X3) -> if(X1,X2,X3)
     if(X1,X2,mark(X3)) -> if(X1,X2,X3)
     if(active(X1),X2,X3) -> if(X1,X2,X3)
     if(X1,active(X2),X3) -> if(X1,X2,X3)
     if(X1,X2,active(X3)) -> if(X1,X2,X3)
    DP Processor:
     DPs:
      mark#(f(X)) -> mark#(X)
      mark#(f(X)) -> f#(mark(X))
      mark#(if(X1,X2,X3)) -> mark#(X2)
      mark#(if(X1,X2,X3)) -> mark#(X1)
      mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
      f#(mark(X)) -> f#(X)
      f#(active(X)) -> f#(X)
      if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
      if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
      if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
      if#(active(X1),X2,X3) -> if#(X1,X2,X3)
      if#(X1,active(X2),X3) -> if#(X1,X2,X3)
      if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
     TRS:
      mark(f(X)) -> active(f(mark(X)))
      mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
      mark(c()) -> active(c())
      mark(true()) -> active(true())
      mark(false()) -> active(false())
      f(mark(X)) -> f(X)
      f(active(X)) -> f(X)
      if(mark(X1),X2,X3) -> if(X1,X2,X3)
      if(X1,mark(X2),X3) -> if(X1,X2,X3)
      if(X1,X2,mark(X3)) -> if(X1,X2,X3)
      if(active(X1),X2,X3) -> if(X1,X2,X3)
      if(X1,active(X2),X3) -> if(X1,X2,X3)
      if(X1,X2,active(X3)) -> if(X1,X2,X3)
     TDG Processor:
      DPs:
       mark#(f(X)) -> mark#(X)
       mark#(f(X)) -> f#(mark(X))
       mark#(if(X1,X2,X3)) -> mark#(X2)
       mark#(if(X1,X2,X3)) -> mark#(X1)
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
       f#(mark(X)) -> f#(X)
       f#(active(X)) -> f#(X)
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
       if#(active(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,active(X2),X3) -> if#(X1,X2,X3)
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
      TRS:
       mark(f(X)) -> active(f(mark(X)))
       mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
       mark(c()) -> active(c())
       mark(true()) -> active(true())
       mark(false()) -> active(false())
       f(mark(X)) -> f(X)
       f(active(X)) -> f(X)
       if(mark(X1),X2,X3) -> if(X1,X2,X3)
       if(X1,mark(X2),X3) -> if(X1,X2,X3)
       if(X1,X2,mark(X3)) -> if(X1,X2,X3)
       if(active(X1),X2,X3) -> if(X1,X2,X3)
       if(X1,active(X2),X3) -> if(X1,X2,X3)
       if(X1,X2,active(X3)) -> if(X1,X2,X3)
      graph:
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(X1,active(X2),X3) -> if#(X1,X2,X3)
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(active(X1),X2,X3) -> if#(X1,X2,X3)
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
       if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
       if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(X1,active(X2),X3) -> if#(X1,X2,X3)
       if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(active(X1),X2,X3) -> if#(X1,X2,X3)
       if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
       if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
       if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
       if#(X1,active(X2),X3) -> if#(X1,X2,X3)
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
       if#(active(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
       if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
       if#(X1,active(X2),X3) -> if#(X1,X2,X3)
       if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
       if#(active(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
       if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
       if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
       if#(X1,active(X2),X3) -> if#(X1,X2,X3)
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
       if#(active(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
       if#(X1,active(X2),X3) -> if#(X1,X2,X3)
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
       if#(active(X1),X2,X3) -> if#(X1,X2,X3)
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
       f#(mark(X)) -> f#(X) -> f#(active(X)) -> f#(X)
       f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
       f#(active(X)) -> f#(X) -> f#(active(X)) -> f#(X)
       f#(active(X)) -> f#(X) ->
       f#(mark(X)) -> f#(X)
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
       if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
       if#(X1,active(X2),X3) -> if#(X1,X2,X3)
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
       if#(active(X1),X2,X3) -> if#(X1,X2,X3)
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
       if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
       if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
       mark#(if(X1,X2,X3)) -> mark#(X2) ->
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
       mark#(if(X1,X2,X3)) -> mark#(X2) ->
       mark#(if(X1,X2,X3)) -> mark#(X1)
       mark#(if(X1,X2,X3)) -> mark#(X2) ->
       mark#(if(X1,X2,X3)) -> mark#(X2)
       mark#(if(X1,X2,X3)) -> mark#(X2) ->
       mark#(f(X)) -> f#(mark(X))
       mark#(if(X1,X2,X3)) -> mark#(X2) -> mark#(f(X)) -> mark#(X)
       mark#(if(X1,X2,X3)) -> mark#(X1) ->
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
       mark#(if(X1,X2,X3)) -> mark#(X1) ->
       mark#(if(X1,X2,X3)) -> mark#(X1)
       mark#(if(X1,X2,X3)) -> mark#(X1) ->
       mark#(if(X1,X2,X3)) -> mark#(X2)
       mark#(if(X1,X2,X3)) -> mark#(X1) ->
       mark#(f(X)) -> f#(mark(X))
       mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(f(X)) -> mark#(X)
       mark#(f(X)) -> f#(mark(X)) -> f#(active(X)) -> f#(X)
       mark#(f(X)) -> f#(mark(X)) -> f#(mark(X)) -> f#(X)
       mark#(f(X)) -> mark#(X) ->
       mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
       mark#(f(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
       mark#(f(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X2)
       mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X))
       mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
      SCC Processor:
       #sccs: 3
       #rules: 11
       #arcs: 63/169
       DPs:
        mark#(if(X1,X2,X3)) -> mark#(X2)
        mark#(f(X)) -> mark#(X)
        mark#(if(X1,X2,X3)) -> mark#(X1)
       TRS:
        mark(f(X)) -> active(f(mark(X)))
        mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
        mark(c()) -> active(c())
        mark(true()) -> active(true())
        mark(false()) -> active(false())
        f(mark(X)) -> f(X)
        f(active(X)) -> f(X)
        if(mark(X1),X2,X3) -> if(X1,X2,X3)
        if(X1,mark(X2),X3) -> if(X1,X2,X3)
        if(X1,X2,mark(X3)) -> if(X1,X2,X3)
        if(active(X1),X2,X3) -> if(X1,X2,X3)
        if(X1,active(X2),X3) -> if(X1,X2,X3)
        if(X1,X2,active(X3)) -> if(X1,X2,X3)
       Subterm Criterion Processor:
        simple projection:
         pi(mark#) = 0
        problem:
         DPs:
          
         TRS:
          mark(f(X)) -> active(f(mark(X)))
          mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
          mark(c()) -> active(c())
          mark(true()) -> active(true())
          mark(false()) -> active(false())
          f(mark(X)) -> f(X)
          f(active(X)) -> f(X)
          if(mark(X1),X2,X3) -> if(X1,X2,X3)
          if(X1,mark(X2),X3) -> if(X1,X2,X3)
          if(X1,X2,mark(X3)) -> if(X1,X2,X3)
          if(active(X1),X2,X3) -> if(X1,X2,X3)
          if(X1,active(X2),X3) -> if(X1,X2,X3)
          if(X1,X2,active(X3)) -> if(X1,X2,X3)
        Qed
       
       DPs:
        f#(mark(X)) -> f#(X)
        f#(active(X)) -> f#(X)
       TRS:
        mark(f(X)) -> active(f(mark(X)))
        mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
        mark(c()) -> active(c())
        mark(true()) -> active(true())
        mark(false()) -> active(false())
        f(mark(X)) -> f(X)
        f(active(X)) -> f(X)
        if(mark(X1),X2,X3) -> if(X1,X2,X3)
        if(X1,mark(X2),X3) -> if(X1,X2,X3)
        if(X1,X2,mark(X3)) -> if(X1,X2,X3)
        if(active(X1),X2,X3) -> if(X1,X2,X3)
        if(X1,active(X2),X3) -> if(X1,X2,X3)
        if(X1,X2,active(X3)) -> if(X1,X2,X3)
       Subterm Criterion Processor:
        simple projection:
         pi(f#) = 0
        problem:
         DPs:
          
         TRS:
          mark(f(X)) -> active(f(mark(X)))
          mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
          mark(c()) -> active(c())
          mark(true()) -> active(true())
          mark(false()) -> active(false())
          f(mark(X)) -> f(X)
          f(active(X)) -> f(X)
          if(mark(X1),X2,X3) -> if(X1,X2,X3)
          if(X1,mark(X2),X3) -> if(X1,X2,X3)
          if(X1,X2,mark(X3)) -> if(X1,X2,X3)
          if(active(X1),X2,X3) -> if(X1,X2,X3)
          if(X1,active(X2),X3) -> if(X1,X2,X3)
          if(X1,X2,active(X3)) -> if(X1,X2,X3)
        Qed
       
       DPs:
        if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
        if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
        if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
        if#(active(X1),X2,X3) -> if#(X1,X2,X3)
        if#(X1,active(X2),X3) -> if#(X1,X2,X3)
        if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
       TRS:
        mark(f(X)) -> active(f(mark(X)))
        mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
        mark(c()) -> active(c())
        mark(true()) -> active(true())
        mark(false()) -> active(false())
        f(mark(X)) -> f(X)
        f(active(X)) -> f(X)
        if(mark(X1),X2,X3) -> if(X1,X2,X3)
        if(X1,mark(X2),X3) -> if(X1,X2,X3)
        if(X1,X2,mark(X3)) -> if(X1,X2,X3)
        if(active(X1),X2,X3) -> if(X1,X2,X3)
        if(X1,active(X2),X3) -> if(X1,X2,X3)
        if(X1,X2,active(X3)) -> if(X1,X2,X3)
       Subterm Criterion Processor:
        simple projection:
         pi(if#) = 2
        problem:
         DPs:
          if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
          if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
          if#(active(X1),X2,X3) -> if#(X1,X2,X3)
          if#(X1,active(X2),X3) -> if#(X1,X2,X3)
         TRS:
          mark(f(X)) -> active(f(mark(X)))
          mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
          mark(c()) -> active(c())
          mark(true()) -> active(true())
          mark(false()) -> active(false())
          f(mark(X)) -> f(X)
          f(active(X)) -> f(X)
          if(mark(X1),X2,X3) -> if(X1,X2,X3)
          if(X1,mark(X2),X3) -> if(X1,X2,X3)
          if(X1,X2,mark(X3)) -> if(X1,X2,X3)
          if(active(X1),X2,X3) -> if(X1,X2,X3)
          if(X1,active(X2),X3) -> if(X1,X2,X3)
          if(X1,X2,active(X3)) -> if(X1,X2,X3)
        Subterm Criterion Processor:
         simple projection:
          pi(if#) = 1
         problem:
          DPs:
           if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
           if#(active(X1),X2,X3) -> if#(X1,X2,X3)
          TRS:
           mark(f(X)) -> active(f(mark(X)))
           mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
           mark(c()) -> active(c())
           mark(true()) -> active(true())
           mark(false()) -> active(false())
           f(mark(X)) -> f(X)
           f(active(X)) -> f(X)
           if(mark(X1),X2,X3) -> if(X1,X2,X3)
           if(X1,mark(X2),X3) -> if(X1,X2,X3)
           if(X1,X2,mark(X3)) -> if(X1,X2,X3)
           if(active(X1),X2,X3) -> if(X1,X2,X3)
           if(X1,active(X2),X3) -> if(X1,X2,X3)
           if(X1,X2,active(X3)) -> if(X1,X2,X3)
         Subterm Criterion Processor:
          simple projection:
           pi(if#) = 0
          problem:
           DPs:
            
           TRS:
            mark(f(X)) -> active(f(mark(X)))
            mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
            mark(c()) -> active(c())
            mark(true()) -> active(true())
            mark(false()) -> active(false())
            f(mark(X)) -> f(X)
            f(active(X)) -> f(X)
            if(mark(X1),X2,X3) -> if(X1,X2,X3)
            if(X1,mark(X2),X3) -> if(X1,X2,X3)
            if(X1,X2,mark(X3)) -> if(X1,X2,X3)
            if(active(X1),X2,X3) -> if(X1,X2,X3)
            if(X1,active(X2),X3) -> if(X1,X2,X3)
            if(X1,X2,active(X3)) -> if(X1,X2,X3)
          Qed