YES

Problem:
 a__f(f(X)) -> a__c(f(g(f(X))))
 a__c(X) -> d(X)
 a__h(X) -> a__c(d(X))
 mark(f(X)) -> a__f(mark(X))
 mark(c(X)) -> a__c(X)
 mark(h(X)) -> a__h(mark(X))
 mark(g(X)) -> g(X)
 mark(d(X)) -> d(X)
 a__f(X) -> f(X)
 a__c(X) -> c(X)
 a__h(X) -> h(X)

Proof:
 DP Processor:
  DPs:
   a__f#(f(X)) -> a__c#(f(g(f(X))))
   a__h#(X) -> a__c#(d(X))
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> a__f#(mark(X))
   mark#(c(X)) -> a__c#(X)
   mark#(h(X)) -> mark#(X)
   mark#(h(X)) -> a__h#(mark(X))
  TRS:
   a__f(f(X)) -> a__c(f(g(f(X))))
   a__c(X) -> d(X)
   a__h(X) -> a__c(d(X))
   mark(f(X)) -> a__f(mark(X))
   mark(c(X)) -> a__c(X)
   mark(h(X)) -> a__h(mark(X))
   mark(g(X)) -> g(X)
   mark(d(X)) -> d(X)
   a__f(X) -> f(X)
   a__c(X) -> c(X)
   a__h(X) -> h(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
    [mark#](x0) = [0 1 1]x0 + [1],
    
    [a__h#](x0) = [1],
    
    [a__c#](x0) = [0],
    
    [a__f#](x0) = [0 0 1]x0,
    
              [0 0 0]     [0]
    [h](x0) = [1 0 0]x0 + [0]
              [0 1 1]     [1],
    
              [0 0 0]  
    [c](x0) = [0 0 0]x0
              [0 0 1]  ,
    
                 [0 0 0]  
    [mark](x0) = [0 0 0]x0
                 [1 1 1]  ,
    
                 [0 1 0]     [0]
    [a__h](x0) = [1 0 0]x0 + [0]
                 [0 1 1]     [1],
    
              [0 0 0]  
    [d](x0) = [0 0 0]x0
              [0 0 1]  ,
    
                 [0 0 0]  
    [a__c](x0) = [0 0 0]x0
                 [0 0 1]  ,
    
              [0]
    [g](x0) = [0]
              [1],
    
                 [0 0 0]     [0]
    [a__f](x0) = [1 1 0]x0 + [0]
                 [1 1 1]     [1],
    
              [0 0 0]     [0]
    [f](x0) = [1 1 0]x0 + [0]
              [0 1 1]     [1]
   orientation:
    a__f#(f(X)) = [0 1 1]X + [1] >= [0] = a__c#(f(g(f(X))))
    
    a__h#(X) = [1] >= [0] = a__c#(d(X))
    
    mark#(f(X)) = [1 2 1]X + [2] >= [0 1 1]X + [1] = mark#(X)
    
    mark#(f(X)) = [1 2 1]X + [2] >= [1 1 1]X = a__f#(mark(X))
    
    mark#(c(X)) = [0 0 1]X + [1] >= [0] = a__c#(X)
    
    mark#(h(X)) = [1 1 1]X + [2] >= [0 1 1]X + [1] = mark#(X)
    
    mark#(h(X)) = [1 1 1]X + [2] >= [1] = a__h#(mark(X))
    
                 [0 0 0]    [0]    [0]                   
    a__f(f(X)) = [1 1 0]X + [0] >= [0] = a__c(f(g(f(X))))
                 [1 2 1]    [2]    [2]                   
    
              [0 0 0]     [0 0 0]        
    a__c(X) = [0 0 0]X >= [0 0 0]X = d(X)
              [0 0 1]     [0 0 1]        
    
              [0 1 0]    [0]    [0 0 0]              
    a__h(X) = [1 0 0]X + [0] >= [0 0 0]X = a__c(d(X))
              [0 1 1]    [1]    [0 0 1]              
    
                 [0 0 0]    [0]    [0 0 0]    [0]                
    mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__f(mark(X))
                 [1 2 1]    [1]    [1 1 1]    [1]                
    
                 [0 0 0]     [0 0 0]           
    mark(c(X)) = [0 0 0]X >= [0 0 0]X = a__c(X)
                 [0 0 1]     [0 0 1]           
    
                 [0 0 0]    [0]    [0 0 0]    [0]                
    mark(h(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__h(mark(X))
                 [1 1 1]    [1]    [1 1 1]    [1]                
    
                 [0]    [0]       
    mark(g(X)) = [0] >= [0] = g(X)
                 [1]    [1]       
    
                 [0 0 0]     [0 0 0]        
    mark(d(X)) = [0 0 0]X >= [0 0 0]X = d(X)
                 [0 0 1]     [0 0 1]        
    
              [0 0 0]    [0]    [0 0 0]    [0]       
    a__f(X) = [1 1 0]X + [0] >= [1 1 0]X + [0] = f(X)
              [1 1 1]    [1]    [0 1 1]    [1]       
    
              [0 0 0]     [0 0 0]        
    a__c(X) = [0 0 0]X >= [0 0 0]X = c(X)
              [0 0 1]     [0 0 1]        
    
              [0 1 0]    [0]    [0 0 0]    [0]       
    a__h(X) = [1 0 0]X + [0] >= [1 0 0]X + [0] = h(X)
              [0 1 1]    [1]    [0 1 1]    [1]       
   problem:
    DPs:
     
    TRS:
     a__f(f(X)) -> a__c(f(g(f(X))))
     a__c(X) -> d(X)
     a__h(X) -> a__c(d(X))
     mark(f(X)) -> a__f(mark(X))
     mark(c(X)) -> a__c(X)
     mark(h(X)) -> a__h(mark(X))
     mark(g(X)) -> g(X)
     mark(d(X)) -> d(X)
     a__f(X) -> f(X)
     a__c(X) -> c(X)
     a__h(X) -> h(X)
   Qed