YES

Problem:
 a__U11(tt(),M,N) -> a__U12(tt(),M,N)
 a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
 a__plus(N,0()) -> mark(N)
 a__plus(N,s(M)) -> a__U11(tt(),M,N)
 mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
 mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
 mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
 mark(tt()) -> tt()
 mark(s(X)) -> s(mark(X))
 mark(0()) -> 0()
 a__U11(X1,X2,X3) -> U11(X1,X2,X3)
 a__U12(X1,X2,X3) -> U12(X1,X2,X3)
 a__plus(X1,X2) -> plus(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__U11#(tt(),M,N) -> a__U12#(tt(),M,N)
   a__U12#(tt(),M,N) -> mark#(M)
   a__U12#(tt(),M,N) -> mark#(N)
   a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M))
   a__plus#(N,0()) -> mark#(N)
   a__plus#(N,s(M)) -> a__U11#(tt(),M,N)
   mark#(U11(X1,X2,X3)) -> mark#(X1)
   mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3)
   mark#(U12(X1,X2,X3)) -> mark#(X1)
   mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3)
   mark#(plus(X1,X2)) -> mark#(X2)
   mark#(plus(X1,X2)) -> mark#(X1)
   mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
   mark#(s(X)) -> mark#(X)
  TRS:
   a__U11(tt(),M,N) -> a__U12(tt(),M,N)
   a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
   a__plus(N,0()) -> mark(N)
   a__plus(N,s(M)) -> a__U11(tt(),M,N)
   mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
   mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
   mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
   mark(tt()) -> tt()
   mark(s(X)) -> s(mark(X))
   mark(0()) -> 0()
   a__U11(X1,X2,X3) -> U11(X1,X2,X3)
   a__U12(X1,X2,X3) -> U12(X1,X2,X3)
   a__plus(X1,X2) -> plus(X1,X2)
  KBO Processor:
   argument filtering:
    pi(tt) = []
    pi(a__U11) = [0,1,2]
    pi(a__U12) = [0,1,2]
    pi(mark) = [0]
    pi(a__plus) = [0,1]
    pi(s) = [0]
    pi(0) = []
    pi(U11) = [0,1,2]
    pi(U12) = [0,1,2]
    pi(plus) = [0,1]
    pi(a__U11#) = [0,1,2]
    pi(a__U12#) = [1,2]
    pi(mark#) = 0
    pi(a__plus#) = [0,1]
   weight function:
    w0 = 1
    w(a__U12#) = w(plus) = w(U12) = w(U11) = w(0) = w(s) = w(a__plus) = w(
    a__U12) = w(a__U11) = w(tt) = 1
    w(a__plus#) = w(mark#) = w(a__U11#) = w(mark) = 0
   precedence:
    mark > a__plus > a__U11 > a__plus# > a__U11# ~ a__U12 > mark# ~ a__U12# ~ 
    plus ~ U12 ~ U11 ~ 0 ~ s ~ tt
   problem:
    DPs:
     
    TRS:
     a__U11(tt(),M,N) -> a__U12(tt(),M,N)
     a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
     a__plus(N,0()) -> mark(N)
     a__plus(N,s(M)) -> a__U11(tt(),M,N)
     mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
     mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
     mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
     mark(tt()) -> tt()
     mark(s(X)) -> s(mark(X))
     mark(0()) -> 0()
     a__U11(X1,X2,X3) -> U11(X1,X2,X3)
     a__U12(X1,X2,X3) -> U12(X1,X2,X3)
     a__plus(X1,X2) -> plus(X1,X2)
   Qed