YES

Problem:
 f(a(),a()) -> f(a(),b())
 f(a(),b()) -> f(s(a()),c())
 f(s(X),c()) -> f(X,c())
 f(c(),c()) -> f(a(),a())

Proof:
 DP Processor:
  DPs:
   f#(a(),a()) -> f#(a(),b())
   f#(a(),b()) -> f#(s(a()),c())
   f#(s(X),c()) -> f#(X,c())
   f#(c(),c()) -> f#(a(),a())
  TRS:
   f(a(),a()) -> f(a(),b())
   f(a(),b()) -> f(s(a()),c())
   f(s(X),c()) -> f(X,c())
   f(c(),c()) -> f(a(),a())
  EDG Processor:
   DPs:
    f#(a(),a()) -> f#(a(),b())
    f#(a(),b()) -> f#(s(a()),c())
    f#(s(X),c()) -> f#(X,c())
    f#(c(),c()) -> f#(a(),a())
   TRS:
    f(a(),a()) -> f(a(),b())
    f(a(),b()) -> f(s(a()),c())
    f(s(X),c()) -> f(X,c())
    f(c(),c()) -> f(a(),a())
   graph:
    f#(c(),c()) -> f#(a(),a()) -> f#(a(),a()) -> f#(a(),b())
    f#(s(X),c()) -> f#(X,c()) -> f#(s(X),c()) -> f#(X,c())
    f#(s(X),c()) -> f#(X,c()) -> f#(c(),c()) -> f#(a(),a())
    f#(a(),b()) -> f#(s(a()),c()) -> f#(s(X),c()) -> f#(X,c())
    f#(a(),a()) -> f#(a(),b()) -> f#(a(),b()) -> f#(s(a()),c())
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [f#](x0, x1) = x0,
     
     [c] = 1,
     
     [s](x0) = x0,
     
     [b] = 0,
     
     [f](x0, x1) = x0 + 1,
     
     [a] = 0
    orientation:
     f#(a(),a()) = 0 >= 0 = f#(a(),b())
     
     f#(a(),b()) = 0 >= 0 = f#(s(a()),c())
     
     f#(s(X),c()) = X >= X = f#(X,c())
     
     f#(c(),c()) = 1 >= 0 = f#(a(),a())
     
     f(a(),a()) = 1 >= 1 = f(a(),b())
     
     f(a(),b()) = 1 >= 1 = f(s(a()),c())
     
     f(s(X),c()) = X + 1 >= X + 1 = f(X,c())
     
     f(c(),c()) = 2 >= 1 = f(a(),a())
    problem:
     DPs:
      f#(a(),a()) -> f#(a(),b())
      f#(a(),b()) -> f#(s(a()),c())
      f#(s(X),c()) -> f#(X,c())
     TRS:
      f(a(),a()) -> f(a(),b())
      f(a(),b()) -> f(s(a()),c())
      f(s(X),c()) -> f(X,c())
      f(c(),c()) -> f(a(),a())
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = x0 + x1 + 1,
      
      [c] = 0,
      
      [s](x0) = x0 + 1,
      
      [b] = 1,
      
      [f](x0, x1) = 1,
      
      [a] = 1
     orientation:
      f#(a(),a()) = 3 >= 3 = f#(a(),b())
      
      f#(a(),b()) = 3 >= 3 = f#(s(a()),c())
      
      f#(s(X),c()) = X + 2 >= X + 1 = f#(X,c())
      
      f(a(),a()) = 1 >= 1 = f(a(),b())
      
      f(a(),b()) = 1 >= 1 = f(s(a()),c())
      
      f(s(X),c()) = 1 >= 1 = f(X,c())
      
      f(c(),c()) = 1 >= 1 = f(a(),a())
     problem:
      DPs:
       f#(a(),a()) -> f#(a(),b())
       f#(a(),b()) -> f#(s(a()),c())
      TRS:
       f(a(),a()) -> f(a(),b())
       f(a(),b()) -> f(s(a()),c())
       f(s(X),c()) -> f(X,c())
       f(c(),c()) -> f(a(),a())
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x1,
       
       [c] = 0,
       
       [s](x0) = 0,
       
       [b] = 1,
       
       [f](x0, x1) = 0,
       
       [a] = 1
      orientation:
       f#(a(),a()) = 1 >= 1 = f#(a(),b())
       
       f#(a(),b()) = 1 >= 0 = f#(s(a()),c())
       
       f(a(),a()) = 0 >= 0 = f(a(),b())
       
       f(a(),b()) = 0 >= 0 = f(s(a()),c())
       
       f(s(X),c()) = 0 >= 0 = f(X,c())
       
       f(c(),c()) = 0 >= 0 = f(a(),a())
      problem:
       DPs:
        f#(a(),a()) -> f#(a(),b())
       TRS:
        f(a(),a()) -> f(a(),b())
        f(a(),b()) -> f(s(a()),c())
        f(s(X),c()) -> f(X,c())
        f(c(),c()) -> f(a(),a())
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0, x1) = x1,
        
        [c] = 0,
        
        [s](x0) = 0,
        
        [b] = 0,
        
        [f](x0, x1) = 0,
        
        [a] = 1
       orientation:
        f#(a(),a()) = 1 >= 0 = f#(a(),b())
        
        f(a(),a()) = 0 >= 0 = f(a(),b())
        
        f(a(),b()) = 0 >= 0 = f(s(a()),c())
        
        f(s(X),c()) = 0 >= 0 = f(X,c())
        
        f(c(),c()) = 0 >= 0 = f(a(),a())
       problem:
        DPs:
         
        TRS:
         f(a(),a()) -> f(a(),b())
         f(a(),b()) -> f(s(a()),c())
         f(s(X),c()) -> f(X,c())
         f(c(),c()) -> f(a(),a())
       Qed