YES

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

Proof:
 DP Processor:
  DPs:
   and#(tt(),X) -> activate#(X)
   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))
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [plus#](x0, x1) = 5x1 + 1,
    
    [activate#](x0) = 0,
    
    [and#](x0, x1) = 3x0 + 4x1 + 3,
    
    [s](x0) = x0 + 3,
    
    [plus](x0, x1) = x0 + 6x1 + 1,
    
    [0] = 5,
    
    [activate](x0) = x0 + 4,
    
    [and](x0, x1) = x1 + 4,
    
    [tt] = 6
   orientation:
    and#(tt(),X) = 4X + 21 >= 0 = activate#(X)
    
    plus#(N,s(M)) = 5M + 16 >= 5M + 1 = plus#(N,M)
    
    and(tt(),X) = X + 4 >= X + 4 = activate(X)
    
    plus(N,0()) = N + 31 >= N = N
    
    plus(N,s(M)) = 6M + N + 19 >= 6M + N + 4 = s(plus(N,M))
    
    activate(X) = X + 4 >= X = X
   problem:
    DPs:
     
    TRS:
     and(tt(),X) -> activate(X)
     plus(N,0()) -> N
     plus(N,s(M)) -> s(plus(N,M))
     activate(X) -> X
   Qed