YES

Problem:
 a__and(tt(),X) -> mark(X)
 a__plus(N,0()) -> mark(N)
 a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
 mark(tt()) -> tt()
 mark(0()) -> 0()
 mark(s(X)) -> s(mark(X))
 a__and(X1,X2) -> and(X1,X2)
 a__plus(X1,X2) -> plus(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__and#(tt(),X) -> mark#(X)
   a__plus#(N,0()) -> mark#(N)
   a__plus#(N,s(M)) -> mark#(M)
   a__plus#(N,s(M)) -> mark#(N)
   a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
   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__and(tt(),X) -> mark(X)
   a__plus(N,0()) -> mark(N)
   a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
   mark(tt()) -> tt()
   mark(0()) -> 0()
   mark(s(X)) -> s(mark(X))
   a__and(X1,X2) -> and(X1,X2)
   a__plus(X1,X2) -> plus(X1,X2)
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    a__and(tt(),X) -> mark(X)
    a__plus(N,0()) -> mark(N)
    a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
    mark(and(X1,X2)) -> a__and(mark(X1),X2)
    mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    mark(tt()) -> tt()
    mark(0()) -> 0()
    mark(s(X)) -> s(mark(X))
    a__and(X1,X2) -> and(X1,X2)
    a__plus(X1,X2) -> plus(X1,X2)
   interpretation:
    [a__plus#](x0, x1) = x0 + x1 + 1/2,
    
    [mark#](x0) = x0,
    
    [a__and#](x0, x1) = x1 + 1/2,
    
    [plus](x0, x1) = x0 + x1 + 1,
    
    [and](x0, x1) = 2x0 + x1 + 2,
    
    [s](x0) = x0 + 2,
    
    [a__plus](x0, x1) = x0 + x1 + 1,
    
    [0] = 0,
    
    [mark](x0) = x0,
    
    [a__and](x0, x1) = 2x0 + x1 + 2,
    
    [tt] = 0
   orientation:
    a__and#(tt(),X) = X + 1/2 >= X = mark#(X)
    
    a__plus#(N,0()) = N + 1/2 >= N = mark#(N)
    
    a__plus#(N,s(M)) = M + N + 5/2 >= M = mark#(M)
    
    a__plus#(N,s(M)) = M + N + 5/2 >= N = mark#(N)
    
    a__plus#(N,s(M)) = M + N + 5/2 >= M + N + 1/2 = a__plus#(mark(N),mark(M))
    
    mark#(and(X1,X2)) = 2X1 + X2 + 2 >= X1 = mark#(X1)
    
    mark#(and(X1,X2)) = 2X1 + X2 + 2 >= X2 + 1/2 = a__and#(mark(X1),X2)
    
    mark#(plus(X1,X2)) = X1 + X2 + 1 >= X2 = mark#(X2)
    
    mark#(plus(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1)
    
    mark#(plus(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1/2 = a__plus#(mark(X1),mark(X2))
    
    mark#(s(X)) = X + 2 >= X = mark#(X)
    
    a__and(tt(),X) = X + 2 >= X = mark(X)
    
    a__plus(N,0()) = N + 1 >= N = mark(N)
    
    a__plus(N,s(M)) = M + N + 3 >= M + N + 3 = s(a__plus(mark(N),mark(M)))
    
    mark(and(X1,X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = a__and(mark(X1),X2)
    
    mark(plus(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = a__plus(mark(X1),mark(X2))
    
    mark(tt()) = 0 >= 0 = tt()
    
    mark(0()) = 0 >= 0 = 0()
    
    mark(s(X)) = X + 2 >= X + 2 = s(mark(X))
    
    a__and(X1,X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = and(X1,X2)
    
    a__plus(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = plus(X1,X2)
   problem:
    DPs:
     
    TRS:
     a__and(tt(),X) -> mark(X)
     a__plus(N,0()) -> mark(N)
     a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
     mark(tt()) -> tt()
     mark(0()) -> 0()
     mark(s(X)) -> s(mark(X))
     a__and(X1,X2) -> and(X1,X2)
     a__plus(X1,X2) -> plus(X1,X2)
   Qed