YES

Problem:
 and(tt(),X) -> activate(X)
 plus(N,0()) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0()) -> 0()
 x(N,s(M)) -> plus(x(N,M),N)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   and#(tt(),X) -> activate#(X)
   plus#(N,s(M)) -> plus#(N,M)
   x#(N,s(M)) -> x#(N,M)
   x#(N,s(M)) -> plus#(x(N,M),N)
  TRS:
   and(tt(),X) -> activate(X)
   plus(N,0()) -> N
   plus(N,s(M)) -> s(plus(N,M))
   x(N,0()) -> 0()
   x(N,s(M)) -> plus(x(N,M),N)
   activate(X) -> X
  TDG Processor:
   DPs:
    and#(tt(),X) -> activate#(X)
    plus#(N,s(M)) -> plus#(N,M)
    x#(N,s(M)) -> x#(N,M)
    x#(N,s(M)) -> plus#(x(N,M),N)
   TRS:
    and(tt(),X) -> activate(X)
    plus(N,0()) -> N
    plus(N,s(M)) -> s(plus(N,M))
    x(N,0()) -> 0()
    x(N,s(M)) -> plus(x(N,M),N)
    activate(X) -> X
   graph:
    x#(N,s(M)) -> x#(N,M) -> x#(N,s(M)) -> plus#(x(N,M),N)
    x#(N,s(M)) -> x#(N,M) -> x#(N,s(M)) -> x#(N,M)
    x#(N,s(M)) -> plus#(x(N,M),N) -> plus#(N,s(M)) -> plus#(N,M)
    plus#(N,s(M)) -> plus#(N,M) -> plus#(N,s(M)) -> plus#(N,M)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/16
    DPs:
     x#(N,s(M)) -> x#(N,M)
    TRS:
     and(tt(),X) -> activate(X)
     plus(N,0()) -> N
     plus(N,s(M)) -> s(plus(N,M))
     x(N,0()) -> 0()
     x(N,s(M)) -> plus(x(N,M),N)
     activate(X) -> X
    LPO Processor:
     argument filtering:
      pi(tt) = []
      pi(and) = [1]
      pi(activate) = 0
      pi(0) = []
      pi(plus) = [0,1]
      pi(s) = [0]
      pi(x) = [0,1]
      pi(x#) = 1
     precedence:
      x > plus > x# ~ s ~ 0 ~ activate ~ and ~ tt
     problem:
      DPs:
       
      TRS:
       and(tt(),X) -> activate(X)
       plus(N,0()) -> N
       plus(N,s(M)) -> s(plus(N,M))
       x(N,0()) -> 0()
       x(N,s(M)) -> plus(x(N,M),N)
       activate(X) -> X
     Qed
    
    DPs:
     plus#(N,s(M)) -> plus#(N,M)
    TRS:
     and(tt(),X) -> activate(X)
     plus(N,0()) -> N
     plus(N,s(M)) -> s(plus(N,M))
     x(N,0()) -> 0()
     x(N,s(M)) -> plus(x(N,M),N)
     activate(X) -> X
    LPO Processor:
     argument filtering:
      pi(tt) = []
      pi(and) = [1]
      pi(activate) = 0
      pi(0) = []
      pi(plus) = [0,1]
      pi(s) = [0]
      pi(x) = [0,1]
      pi(plus#) = 1
     precedence:
      x > plus > plus# ~ s ~ 0 ~ activate ~ and ~ tt
     problem:
      DPs:
       
      TRS:
       and(tt(),X) -> activate(X)
       plus(N,0()) -> N
       plus(N,s(M)) -> s(plus(N,M))
       x(N,0()) -> 0()
       x(N,s(M)) -> plus(x(N,M),N)
       activate(X) -> X
     Qed