YES

Problem:
 U11(tt(),N) -> activate(N)
 U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
 and(tt(),X) -> activate(X)
 isNat(n__0()) -> tt()
 isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
 isNat(n__s(V1)) -> isNat(activate(V1))
 plus(N,0()) -> U11(isNat(N),N)
 plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
 0() -> n__0()
 plus(X1,X2) -> n__plus(X1,X2)
 isNat(X) -> n__isNat(X)
 s(X) -> n__s(X)
 activate(n__0()) -> 0()
 activate(n__plus(X1,X2)) -> plus(X1,X2)
 activate(n__isNat(X)) -> isNat(X)
 activate(n__s(X)) -> s(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   U11#(tt(),N) -> activate#(N)
   U21#(tt(),M,N) -> activate#(M)
   U21#(tt(),M,N) -> activate#(N)
   U21#(tt(),M,N) -> plus#(activate(N),activate(M))
   U21#(tt(),M,N) -> s#(plus(activate(N),activate(M)))
   and#(tt(),X) -> activate#(X)
   isNat#(n__plus(V1,V2)) -> activate#(V2)
   isNat#(n__plus(V1,V2)) -> activate#(V1)
   isNat#(n__plus(V1,V2)) -> isNat#(activate(V1))
   isNat#(n__plus(V1,V2)) -> and#(isNat(activate(V1)),n__isNat(activate(V2)))
   isNat#(n__s(V1)) -> activate#(V1)
   isNat#(n__s(V1)) -> isNat#(activate(V1))
   plus#(N,0()) -> isNat#(N)
   plus#(N,0()) -> U11#(isNat(N),N)
   plus#(N,s(M)) -> isNat#(M)
   plus#(N,s(M)) -> and#(isNat(M),n__isNat(N))
   plus#(N,s(M)) -> U21#(and(isNat(M),n__isNat(N)),M,N)
   activate#(n__0()) -> 0#()
   activate#(n__plus(X1,X2)) -> plus#(X1,X2)
   activate#(n__isNat(X)) -> isNat#(X)
   activate#(n__s(X)) -> s#(X)
  TRS:
   U11(tt(),N) -> activate(N)
   U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
   and(tt(),X) -> activate(X)
   isNat(n__0()) -> tt()
   isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
   isNat(n__s(V1)) -> isNat(activate(V1))
   plus(N,0()) -> U11(isNat(N),N)
   plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
   0() -> n__0()
   plus(X1,X2) -> n__plus(X1,X2)
   isNat(X) -> n__isNat(X)
   s(X) -> n__s(X)
   activate(n__0()) -> 0()
   activate(n__plus(X1,X2)) -> plus(X1,X2)
   activate(n__isNat(X)) -> isNat(X)
   activate(n__s(X)) -> s(X)
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    U11(tt(),N) -> activate(N)
    U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
    and(tt(),X) -> activate(X)
    isNat(n__0()) -> tt()
    isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
    isNat(n__s(V1)) -> isNat(activate(V1))
    plus(N,0()) -> U11(isNat(N),N)
    plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
    0() -> n__0()
    plus(X1,X2) -> n__plus(X1,X2)
    isNat(X) -> n__isNat(X)
    s(X) -> n__s(X)
    activate(n__0()) -> 0()
    activate(n__plus(X1,X2)) -> plus(X1,X2)
    activate(n__isNat(X)) -> isNat(X)
    activate(n__s(X)) -> s(X)
    activate(X) -> X
   interpretation:
    [0#] = 0,
    
    [isNat#](x0) = x0,
    
    [and#](x0, x1) = x1 + 2,
    
    [s#](x0) = x0,
    
    [plus#](x0, x1) = 4x0 + 4x1 + 3,
    
    [U21#](x0, x1, x2) = 4x1 + 4x2 + 4,
    
    [activate#](x0) = x0 + 1,
    
    [U11#](x0, x1) = x1 + 5,
    
    [0] = 1,
    
    [n__s](x0) = x0 + 2,
    
    [n__isNat](x0) = 4x0,
    
    [n__plus](x0, x1) = 4x0 + 4x1 + 3,
    
    [isNat](x0) = 4x0,
    
    [n__0] = 1,
    
    [and](x0, x1) = 4x0 + 4x1 + 1,
    
    [s](x0) = x0 + 2,
    
    [plus](x0, x1) = 4x0 + 4x1 + 3,
    
    [U21](x0, x1, x2) = 4x1 + 4x2 + 5,
    
    [activate](x0) = x0,
    
    [U11](x0, x1) = 4x1 + 7,
    
    [tt] = 0
   orientation:
    U11#(tt(),N) = N + 5 >= N + 1 = activate#(N)
    
    U21#(tt(),M,N) = 4M + 4N + 4 >= M + 1 = activate#(M)
    
    U21#(tt(),M,N) = 4M + 4N + 4 >= N + 1 = activate#(N)
    
    U21#(tt(),M,N) = 4M + 4N + 4 >= 4M + 4N + 3 = plus#(activate(N),activate(M))
    
    U21#(tt(),M,N) = 4M + 4N + 4 >= 4M + 4N + 3 = s#(plus(activate(N),activate(M)))
    
    and#(tt(),X) = X + 2 >= X + 1 = activate#(X)
    
    isNat#(n__plus(V1,V2)) = 4V1 + 4V2 + 3 >= V2 + 1 = activate#(V2)
    
    isNat#(n__plus(V1,V2)) = 4V1 + 4V2 + 3 >= V1 + 1 = activate#(V1)
    
    isNat#(n__plus(V1,V2)) = 4V1 + 4V2 + 3 >= V1 = isNat#(activate(V1))
    
    isNat#(n__plus(V1,V2)) = 4V1 + 4V2 + 3 >= 4V2 + 2 = and#(isNat(activate(V1)),n__isNat(activate(V2)))
    
    isNat#(n__s(V1)) = V1 + 2 >= V1 + 1 = activate#(V1)
    
    isNat#(n__s(V1)) = V1 + 2 >= V1 = isNat#(activate(V1))
    
    plus#(N,0()) = 4N + 7 >= N = isNat#(N)
    
    plus#(N,0()) = 4N + 7 >= N + 5 = U11#(isNat(N),N)
    
    plus#(N,s(M)) = 4M + 4N + 11 >= M = isNat#(M)
    
    plus#(N,s(M)) = 4M + 4N + 11 >= 4N + 2 = and#(isNat(M),n__isNat(N))
    
    plus#(N,s(M)) = 4M + 4N + 11 >= 4M + 4N + 4 = U21#(and(isNat(M),n__isNat(N)),M,N)
    
    activate#(n__0()) = 2 >= 0 = 0#()
    
    activate#(n__plus(X1,X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 3 = plus#(X1,X2)
    
    activate#(n__isNat(X)) = 4X + 1 >= X = isNat#(X)
    
    activate#(n__s(X)) = X + 3 >= X = s#(X)
    
    U11(tt(),N) = 4N + 7 >= N = activate(N)
    
    U21(tt(),M,N) = 4M + 4N + 5 >= 4M + 4N + 5 = s(plus(activate(N),activate(M)))
    
    and(tt(),X) = 4X + 1 >= X = activate(X)
    
    isNat(n__0()) = 4 >= 0 = tt()
    
    isNat(n__plus(V1,V2)) = 16V1 + 16V2 + 12 >= 16V1 + 16V2 + 1 = and(isNat(activate(V1)),n__isNat(activate(V2)))
    
    isNat(n__s(V1)) = 4V1 + 8 >= 4V1 = isNat(activate(V1))
    
    plus(N,0()) = 4N + 7 >= 4N + 7 = U11(isNat(N),N)
    
    plus(N,s(M)) = 4M + 4N + 11 >= 4M + 4N + 5 = U21(and(isNat(M),n__isNat(N)),M,N)
    
    0() = 1 >= 1 = n__0()
    
    plus(X1,X2) = 4X1 + 4X2 + 3 >= 4X1 + 4X2 + 3 = n__plus(X1,X2)
    
    isNat(X) = 4X >= 4X = n__isNat(X)
    
    s(X) = X + 2 >= X + 2 = n__s(X)
    
    activate(n__0()) = 1 >= 1 = 0()
    
    activate(n__plus(X1,X2)) = 4X1 + 4X2 + 3 >= 4X1 + 4X2 + 3 = plus(X1,X2)
    
    activate(n__isNat(X)) = 4X >= 4X = isNat(X)
    
    activate(n__s(X)) = X + 2 >= X + 2 = s(X)
    
    activate(X) = X >= X = X
   problem:
    DPs:
     
    TRS:
     U11(tt(),N) -> activate(N)
     U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
     and(tt(),X) -> activate(X)
     isNat(n__0()) -> tt()
     isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
     isNat(n__s(V1)) -> isNat(activate(V1))
     plus(N,0()) -> U11(isNat(N),N)
     plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
     0() -> n__0()
     plus(X1,X2) -> n__plus(X1,X2)
     isNat(X) -> n__isNat(X)
     s(X) -> n__s(X)
     activate(n__0()) -> 0()
     activate(n__plus(X1,X2)) -> plus(X1,X2)
     activate(n__isNat(X)) -> isNat(X)
     activate(n__s(X)) -> s(X)
     activate(X) -> X
   Qed