YES

Proof:
This system is quasi-decreasing.
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(g(x)) -> x
  g(s(x)) -> g(x)
  s(x) -> x
  g(x) -> x
  f(x) -> x

 DP Processor:
  DPs:
   g#(s(x)) -> g#(x)
  TRS:
   f(g(x)) -> x
   g(s(x)) -> g(x)
   s(x) -> x
   g(x) -> x
   f(x) -> x
  Subterm Criterion Processor:
   simple projection:
    pi(g#) = 0
   problem:
    DPs:
     
    TRS:
     f(g(x)) -> x
     g(s(x)) -> g(x)
     s(x) -> x
     g(x) -> x
     f(x) -> x
   Qed