YES

Problem:
 g(x,a(),b()) -> g(b(),b(),a())

Proof:
 DP Processor:
  DPs:
   g#(x,a(),b()) -> g#(b(),b(),a())
  TRS:
   g(x,a(),b()) -> g(b(),b(),a())
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [g#](x0, x1, x2) = x2,
    
    [g](x0, x1, x2) = -2x0 + 5x2,
    
    [b] = 1,
    
    [a] = 0
   orientation:
    g#(x,a(),b()) = 1 >= 0 = g#(b(),b(),a())
    
    g(x,a(),b()) = -2x + 6 >= 5 = g(b(),b(),a())
   problem:
    DPs:
     
    TRS:
     g(x,a(),b()) -> g(b(),b(),a())
   Qed