YES

Problem:
 f(i(x),g(a())) -> f(j(x,x),g(b()))
 b() -> a()
 i(x) -> j(x,x)

Proof:
 Church Rosser Transformation Processor (kb):
  f(i(x),g(a())) -> f(j(x,x),g(b()))
  b() -> a()
  i(x) -> j(x,x)
  critical peaks: joinable
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [j](x0, x1) = x0 + 6x1 + 2,
     
     [a] = 0,
     
     [f](x0, x1) = x0 + 2x1 + 3,
     
     [b] = 0,
     
     [i](x0) = 7x0 + 4,
     
     [g](x0) = 4x0
    orientation:
     f(i(x),g(a())) = 7x + 7 >= 7x + 5 = f(j(x,x),g(b()))
     
     b() = 0 >= 0 = a()
     
     i(x) = 7x + 4 >= 7x + 2 = j(x,x)
    problem:
     b() -> a()
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [a] = 0,
      
      [b] = 1
     orientation:
      b() = 1 >= 0 = a()
     problem:
      
     Qed