YES

Problem:
 U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
 U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
 plus(N,0()) -> N
 plus(N,s(M)) -> U11(tt(),M,N)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   U11#(tt(),M,N) -> activate#(N)
   U11#(tt(),M,N) -> activate#(M)
   U11#(tt(),M,N) -> U12#(tt(),activate(M),activate(N))
   U12#(tt(),M,N) -> activate#(M)
   U12#(tt(),M,N) -> activate#(N)
   U12#(tt(),M,N) -> plus#(activate(N),activate(M))
   plus#(N,s(M)) -> U11#(tt(),M,N)
  TRS:
   U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
   U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
   plus(N,0()) -> N
   plus(N,s(M)) -> U11(tt(),M,N)
   activate(X) -> X
  KBO Processor:
   argument filtering:
    pi(tt) = []
    pi(U11) = [0,1,2]
    pi(activate) = 0
    pi(U12) = [0,1,2]
    pi(plus) = [0,1]
    pi(s) = [0]
    pi(0) = []
    pi(U11#) = [0,1,2]
    pi(activate#) = [0]
    pi(U12#) = [1,2]
    pi(plus#) = [0,1]
   weight function:
    w0 = 1
    w(activate#) = w(0) = w(s) = w(plus) = w(U12) = w(U11) = w(tt) = 1
    w(plus#) = w(U12#) = w(U11#) = w(activate) = 0
   precedence:
    U12# ~ 0 ~ plus > plus# ~ U11 > U12 > activate# ~ U11# ~ s ~ activate ~ tt
   problem:
    DPs:
     
    TRS:
     U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
     U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
     plus(N,0()) -> N
     plus(N,s(M)) -> U11(tt(),M,N)
     activate(X) -> X
   Qed