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 (kb):
  ?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: joinable
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [c] = 0,
     
     [?2](x0, x1, x2) = 2x0 + 2x1 + 6x2 + 5,
     
     [f](x0, x1) = 4x0 + 6x1 + 5,
     
     [?3](x0, x1) = 4x0 + x1,
     
     [?1](x0, x1, x2, x3) = 2x0 + x1 + 4x2 + 2x3 + 5,
     
     [d] = 0,
     
     [g](x0) = x0
    orientation:
     ?1(z,x,y,z) = x + 4y + 4z + 5 >= x = x
     
     ?2(z,x,y) = 2x + 6y + 2z + 5 >= x + 6y + 2z + 5 = ?1(g(y),x,y,z)
     
     f(x,y) = 4x + 6y + 5 >= 4x + 6y + 5 = ?2(g(x),x,y)
     
     ?3(c(),x) = x >= 0 = c()
     
     g(x) = x >= x = ?3(d(),x)
    problem:
     ?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)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [c] = 0,
      
      [?2](x0, x1, x2) = x0 + 2x1 + 3x2 + 3,
      
      [f](x0, x1) = 5x0 + 3x1 + 4,
      
      [?3](x0, x1) = 2x0 + 2x1,
      
      [?1](x0, x1, x2, x3) = x0 + 2x1 + x2 + x3 + 2,
      
      [d] = 0,
      
      [g](x0) = 2x0
     orientation:
      ?2(z,x,y) = 2x + 3y + z + 3 >= 2x + 3y + z + 2 = ?1(g(y),x,y,z)
      
      f(x,y) = 5x + 3y + 4 >= 4x + 3y + 3 = ?2(g(x),x,y)
      
      ?3(c(),x) = 2x >= 0 = c()
      
      g(x) = 2x >= 2x = ?3(d(),x)
     problem:
      ?3(c(),x) -> c()
      g(x) -> ?3(d(),x)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [c] = 4,
       
       [?3](x0, x1) = 2x0 + 4x1,
       
       [d] = 0,
       
       [g](x0) = 5x0
      orientation:
       ?3(c(),x) = 4x + 8 >= 4 = c()
       
       g(x) = 5x >= 4x = ?3(d(),x)
      problem:
       g(x) -> ?3(d(),x)
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [?3](x0, x1) = x0 + x1,
        
        [d] = 0,
        
        [g](x0) = x0 + 1
       orientation:
        g(x) = x + 1 >= x = ?3(d(),x)
       problem:
        
       Qed