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)
  Arctic Interpretation Processor:
   dimension: 1
   usable rules:
    
   interpretation:
    [mark#](x0) = 8x0,
    
    [a__h#](x0) = 1,
    
    [a__c#](x0) = 0,
    
    [a__f#](x0) = 1,
    
    [h](x0) = 5x0 + 13,
    
    [c](x0) = x0 + -6,
    
    [mark](x0) = x0 + 1,
    
    [a__h](x0) = 15x0 + -15,
    
    [d](x0) = x0 + 9,
    
    [a__c](x0) = 7x0 + -16,
    
    [g](x0) = -15x0 + 15,
    
    [a__f](x0) = x0 + 12,
    
    [f](x0) = 1x0 + 8
   orientation:
    a__f#(f(X)) = 1 >= 0 = a__c#(f(g(f(X))))
    
    a__h#(X) = 1 >= 0 = a__c#(d(X))
    
    mark#(f(X)) = 9X + 16 >= 8X = mark#(X)
    
    mark#(f(X)) = 9X + 16 >= 1 = a__f#(mark(X))
    
    mark#(c(X)) = 8X + 2 >= 0 = a__c#(X)
    
    mark#(h(X)) = 13X + 21 >= 8X = mark#(X)
    
    mark#(h(X)) = 13X + 21 >= 1 = a__h#(mark(X))
    
    a__f(f(X)) = 1X + 12 >= -6X + 23 = a__c(f(g(f(X))))
    
    a__c(X) = 7X + -16 >= X + 9 = d(X)
    
    a__h(X) = 15X + -15 >= 7X + 16 = a__c(d(X))
    
    mark(f(X)) = 1X + 8 >= X + 12 = a__f(mark(X))
    
    mark(c(X)) = X + 1 >= 7X + -16 = a__c(X)
    
    mark(h(X)) = 5X + 13 >= 15X + 16 = a__h(mark(X))
    
    mark(g(X)) = -15X + 15 >= -15X + 15 = g(X)
    
    mark(d(X)) = X + 9 >= X + 9 = d(X)
    
    a__f(X) = X + 12 >= 1X + 8 = f(X)
    
    a__c(X) = 7X + -16 >= X + -6 = c(X)
    
    a__h(X) = 15X + -15 >= 5X + 13 = h(X)
   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