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(l, x) -> e
  f(x) -> ?1(d, x)
  h(x, x) -> A

 sorted: (order)
 0:?1(l(),x) -> e()
   f(x) -> ?1(d(),x)
 1:h(x,x) -> A()
 -----
 sorts
   [0>1, 1>2, 1>5, 1>9, 3>4, 3>8, 5>6, 5>7, 9>10]
 sort attachment (non-strict)
   ?1 : 5 x 9 -> 1
   l : 7
   e : 2
   f : 10 -> 0
   d : 6
   h : 8 x 8 -> 3
   A : 4
 -----
 0:?1(l(),x) -> e()
   f(x) -> ?1(d(),x)
   Church Rosser Transformation Processor:
    strict:
     ?1(l(),x) -> e()
     f(x) -> ?1(d(),x)
    weak:
     
    critical peaks: 0
    Closedness Processor (*strongly -- <=7 steps*):
     strict:
      
     weak:
      
     Qed
 
 
 1:h(x,x) -> A()
   Church Rosser Transformation Processor (kb):
    h(x,x) -> A()
    critical peaks: joinable
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [h](x0, x1) = x0 + 2x1 + 4,
       
       [A] = 0
      orientation:
       h(x,x) = 3x + 4 >= 0 = A()
      problem:
       
      Qed