YES

Problem:
 a(b(x)) -> a(c(b(x)))

Proof:
 DP Processor:
  DPs:
   a#(b(x)) -> a#(c(b(x)))
  TRS:
   a(b(x)) -> a(c(b(x)))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [a#](x0) = 1x0 + 0,
    
    [c](x0) = -5x0 + 1,
    
    [a](x0) = x0 + 0,
    
    [b](x0) = 15x0 + 14
   orientation:
    a#(b(x)) = 16x + 15 >= 11x + 10 = a#(c(b(x)))
    
    a(b(x)) = 15x + 14 >= 10x + 9 = a(c(b(x)))
   problem:
    DPs:
     
    TRS:
     a(b(x)) -> a(c(b(x)))
   Qed