YES

Proof:
This system is confluent.
By \cite{ALS94}, Theorem 4.1.
This system is of type 3 or smaller.
This system is strongly deterministic.
There are no critical pairs.
By \cite{A14}, Theorem 11.5.9.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to V(R) + Emb.
Call external tool:
ttt2 - trs 30
Input:
  f(x, x') -> g(x', x')
  f(x, x') -> x'
  f(x, x') -> x
  h(x, x', x'') -> c
  h(x, x', x'') -> x''
  h(x, x', x'') -> x'
  h(x, x', x'') -> x
  h(x, y, z) -> x
  h(x, y, z) -> y
  h(x, y, z) -> z
  g(x, y) -> x
  g(x, y) -> y
  f(x, y) -> x
  f(x, y) -> y

 DP Processor:
  DPs:
   f#(x,x') -> g#(x',x')
  TRS:
   f(x,x') -> g(x',x')
   f(x,x') -> x'
   f(x,x') -> x
   h(x,x',x'') -> c()
   h(x,x',x'') -> x''
   h(x,x',x'') -> x'
   h(x,x',x'') -> x
   h(x,y,z) -> x
   h(x,y,z) -> y
   h(x,y,z) -> z
   g(x,y) -> x
   g(x,y) -> y
   f(x,y) -> x
   f(x,y) -> y
  TDG Processor:
   DPs:
    f#(x,x') -> g#(x',x')
   TRS:
    f(x,x') -> g(x',x')
    f(x,x') -> x'
    f(x,x') -> x
    h(x,x',x'') -> c()
    h(x,x',x'') -> x''
    h(x,x',x'') -> x'
    h(x,x',x'') -> x
    h(x,y,z) -> x
    h(x,y,z) -> y
    h(x,y,z) -> z
    g(x,y) -> x
    g(x,y) -> y
    f(x,y) -> x
    f(x,y) -> y
   graph:
    
   Qed
This system is deterministic.
This system is not weakly left-linear.
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.