YES

Proof:
This system is quasi-decreasing.
By \cite{O02}, p. 214, Proposition 7.2.50.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to U(R).
Call external tool:
ttt2 - trs 30
Input:
  pin(a) -> pout(b)
  pin(b) -> pout(c)
  tc(x) -> x
  ?2(y, x) -> y
  ?1(pout(z), x) -> ?2(tc(z), x)
  tc(x) -> ?1(pin(x), x)

 LPO Processor:
  precedence:
   a > b > pout > tc > ?1 > z ~ ?2 ~ c ~ pin
  problem:
   
  Qed