YES

Proof:
This system is confluent.
By \cite{GNG13}, Theorem 9.
This system is deterministic.
This system is weakly left-linear.
System R transformed to optimized U(R).
This system is not orthogonal.
Call external tool:
csi - trs 30
Input:
  ?1(z, x, y, z) -> x
  ?2(z, x, y) -> ?1(g(y), x, y, z)
  f(x, y) -> ?2(g(x), x, y)
  ?3(c, x) -> c
  g(x) -> ?3(d, x)

 Church Rosser Transformation Processor (to relative problem):
  strict:
   ?1(z,x,y,z) -> x
   ?2(z,x,y) -> ?1(g(y),x,y,z)
   f(x,y) -> ?2(g(x),x,y)
   ?3(c(),x) -> c()
   g(x) -> ?3(d(),x)
  weak:
   
  original problem:
   ?1(z,x,y,z) -> x
   ?2(z,x,y) -> ?1(g(y),x,y,z)
   f(x,y) -> ?2(g(x),x,y)
   ?3(c(),x) -> c()
   g(x) -> ?3(d(),x)
  critical peaks: 
   LPO Processor:
    precedence:
     f > ?2 > g > d ~ ?3 ~ c ~ ?1
    problem:
     strict:
      
     weak:
      
     original problem:
      ?1(z,x,y,z) -> x
      ?2(z,x,y) -> ?1(g(y),x,y,z)
      f(x,y) -> ?2(g(x),x,y)
      ?3(c(),x) -> c()
      g(x) -> ?3(d(),x)
    KH confluence processor
     Split input TRS into two TRSs S and T:
     
     TRS S:
      ?1(z,x,y,z) -> x
     
     TRS T:
      ?2(z,x,y) -> ?1(g(y),x,y,z)
      f(x,y) -> ?2(g(x),x,y)
      ?3(c(),x) -> c()
      g(x) -> ?3(d(),x)
     
     As established above, T/S is terminating.
     T is strongly non-overlapping on S and S is strongly non-overlapping on T
     
     Please install theorem prover 'Prover9' and 'Mace4' for handling more TRSs.
     
      All S-critical pairs are joinable.
     
     We have to check confluence of S.
     
     Church Rosser Transformation Processor (kb):
      ?1(z,x,y,z) -> x
      critical peaks: joinable
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [?1](x0, x1, x2, x3) = x0 + 2x1 + 4x2 + 2x3 + 1
        orientation:
         ?1(z,x,y,z) = 2x + 4y + 3z + 1 >= x = x
        problem:
         
        Qed
This system is not normal.
This system is oriented.
This system is of type 3 or smaller.
This system is not right-stable.
This system is conditional.