YES

Problem:
 U11(tt(),V2) -> U12(isNat(activate(V2)))
 U12(tt()) -> tt()
 U21(tt()) -> tt()
 U31(tt(),N) -> activate(N)
 U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
 U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
 isNat(n__0()) -> tt()
 isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
 isNat(n__s(V1)) -> U21(isNat(activate(V1)))
 plus(N,0()) -> U31(isNat(N),N)
 plus(N,s(M)) -> U41(isNat(M),M,N)
 0() -> n__0()
 plus(X1,X2) -> n__plus(X1,X2)
 s(X) -> n__s(X)
 activate(n__0()) -> 0()
 activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   U11#(tt(),V2) -> activate#(V2)
   U11#(tt(),V2) -> isNat#(activate(V2))
   U11#(tt(),V2) -> U12#(isNat(activate(V2)))
   U31#(tt(),N) -> activate#(N)
   U41#(tt(),M,N) -> activate#(M)
   U41#(tt(),M,N) -> activate#(N)
   U41#(tt(),M,N) -> isNat#(activate(N))
   U41#(tt(),M,N) -> U42#(isNat(activate(N)),activate(M),activate(N))
   U42#(tt(),M,N) -> activate#(M)
   U42#(tt(),M,N) -> activate#(N)
   U42#(tt(),M,N) -> plus#(activate(N),activate(M))
   U42#(tt(),M,N) -> s#(plus(activate(N),activate(M)))
   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)) -> U11#(isNat(activate(V1)),activate(V2))
   isNat#(n__s(V1)) -> activate#(V1)
   isNat#(n__s(V1)) -> isNat#(activate(V1))
   isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
   plus#(N,0()) -> isNat#(N)
   plus#(N,0()) -> U31#(isNat(N),N)
   plus#(N,s(M)) -> isNat#(M)
   plus#(N,s(M)) -> U41#(isNat(M),M,N)
   activate#(n__0()) -> 0#()
   activate#(n__plus(X1,X2)) -> activate#(X2)
   activate#(n__plus(X1,X2)) -> activate#(X1)
   activate#(n__plus(X1,X2)) -> plus#(activate(X1),activate(X2))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
  TRS:
   U11(tt(),V2) -> U12(isNat(activate(V2)))
   U12(tt()) -> tt()
   U21(tt()) -> tt()
   U31(tt(),N) -> activate(N)
   U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
   U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
   isNat(n__0()) -> tt()
   isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
   isNat(n__s(V1)) -> U21(isNat(activate(V1)))
   plus(N,0()) -> U31(isNat(N),N)
   plus(N,s(M)) -> U41(isNat(M),M,N)
   0() -> n__0()
   plus(X1,X2) -> n__plus(X1,X2)
   s(X) -> n__s(X)
   activate(n__0()) -> 0()
   activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    U31(tt(),N) -> activate(N)
    U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
    U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
    plus(N,0()) -> U31(isNat(N),N)
    plus(N,s(M)) -> U41(isNat(M),M,N)
    0() -> n__0()
    plus(X1,X2) -> n__plus(X1,X2)
    s(X) -> n__s(X)
    activate(n__0()) -> 0()
    activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
    activate(n__s(X)) -> s(activate(X))
    activate(X) -> X
   interpretation:
    [0#] = 0,
    
    [s#](x0) = 2x0 + 2,
    
    [plus#](x0, x1) = 2x0 + 4x1 + 4,
    
    [U42#](x0, x1, x2) = 4x1 + 2x2 + 6,
    
    [U41#](x0, x1, x2) = 4x1 + 2x2 + 7,
    
    [U31#](x0, x1) = 2x1 + 7,
    
    [U21#](x0) = 0,
    
    [U12#](x0) = 4,
    
    [isNat#](x0) = 2x0 + 4,
    
    [activate#](x0) = 2x0 + 4,
    
    [U11#](x0, x1) = 4x1 + 5,
    
    [0] = 2,
    
    [n__s](x0) = x0 + 4,
    
    [n__plus](x0, x1) = x0 + 2x1 + 1,
    
    [n__0] = 2,
    
    [s](x0) = x0 + 4,
    
    [plus](x0, x1) = x0 + 2x1 + 1,
    
    [U42](x0, x1, x2) = 2x1 + x2 + 6,
    
    [U41](x0, x1, x2) = 2x1 + x2 + 7,
    
    [U31](x0, x1) = x1 + 1,
    
    [U21](x0) = 6x0 + 2,
    
    [U12](x0) = 0,
    
    [isNat](x0) = 0,
    
    [activate](x0) = x0,
    
    [U11](x0, x1) = 6x0,
    
    [tt] = 3
   orientation:
    U11#(tt(),V2) = 4V2 + 5 >= 2V2 + 4 = activate#(V2)
    
    U11#(tt(),V2) = 4V2 + 5 >= 2V2 + 4 = isNat#(activate(V2))
    
    U11#(tt(),V2) = 4V2 + 5 >= 4 = U12#(isNat(activate(V2)))
    
    U31#(tt(),N) = 2N + 7 >= 2N + 4 = activate#(N)
    
    U41#(tt(),M,N) = 4M + 2N + 7 >= 2M + 4 = activate#(M)
    
    U41#(tt(),M,N) = 4M + 2N + 7 >= 2N + 4 = activate#(N)
    
    U41#(tt(),M,N) = 4M + 2N + 7 >= 2N + 4 = isNat#(activate(N))
    
    U41#(tt(),M,N) = 4M + 2N + 7 >= 4M + 2N + 6 = U42#(isNat(activate(N)),activate(M),activate(N))
    
    U42#(tt(),M,N) = 4M + 2N + 6 >= 2M + 4 = activate#(M)
    
    U42#(tt(),M,N) = 4M + 2N + 6 >= 2N + 4 = activate#(N)
    
    U42#(tt(),M,N) = 4M + 2N + 6 >= 4M + 2N + 4 = plus#(activate(N),activate(M))
    
    U42#(tt(),M,N) = 4M + 2N + 6 >= 4M + 2N + 4 = s#(plus(activate(N),activate(M)))
    
    isNat#(n__plus(V1,V2)) = 2V1 + 4V2 + 6 >= 2V2 + 4 = activate#(V2)
    
    isNat#(n__plus(V1,V2)) = 2V1 + 4V2 + 6 >= 2V1 + 4 = activate#(V1)
    
    isNat#(n__plus(V1,V2)) = 2V1 + 4V2 + 6 >= 2V1 + 4 = isNat#(activate(V1))
    
    isNat#(n__plus(V1,V2)) = 2V1 + 4V2 + 6 >= 4V2 + 5 = U11#(isNat(activate(V1)),activate(V2))
    
    isNat#(n__s(V1)) = 2V1 + 12 >= 2V1 + 4 = activate#(V1)
    
    isNat#(n__s(V1)) = 2V1 + 12 >= 2V1 + 4 = isNat#(activate(V1))
    
    isNat#(n__s(V1)) = 2V1 + 12 >= 0 = U21#(isNat(activate(V1)))
    
    plus#(N,0()) = 2N + 12 >= 2N + 4 = isNat#(N)
    
    plus#(N,0()) = 2N + 12 >= 2N + 7 = U31#(isNat(N),N)
    
    plus#(N,s(M)) = 4M + 2N + 20 >= 2M + 4 = isNat#(M)
    
    plus#(N,s(M)) = 4M + 2N + 20 >= 4M + 2N + 7 = U41#(isNat(M),M,N)
    
    activate#(n__0()) = 8 >= 0 = 0#()
    
    activate#(n__plus(X1,X2)) = 2X1 + 4X2 + 6 >= 2X2 + 4 = activate#(X2)
    
    activate#(n__plus(X1,X2)) = 2X1 + 4X2 + 6 >= 2X1 + 4 = activate#(X1)
    
    activate#(n__plus(X1,X2)) = 2X1 + 4X2 + 6 >= 2X1 + 4X2 + 4 = plus#(activate(X1),activate(X2))
    
    activate#(n__s(X)) = 2X + 12 >= 2X + 4 = activate#(X)
    
    activate#(n__s(X)) = 2X + 12 >= 2X + 2 = s#(activate(X))
    
    U11(tt(),V2) = 18 >= 0 = U12(isNat(activate(V2)))
    
    U12(tt()) = 0 >= 3 = tt()
    
    U21(tt()) = 20 >= 3 = tt()
    
    U31(tt(),N) = N + 1 >= N = activate(N)
    
    U41(tt(),M,N) = 2M + N + 7 >= 2M + N + 6 = U42(isNat(activate(N)),activate(M),activate(N))
    
    U42(tt(),M,N) = 2M + N + 6 >= 2M + N + 5 = s(plus(activate(N),activate(M)))
    
    isNat(n__0()) = 0 >= 3 = tt()
    
    isNat(n__plus(V1,V2)) = 0 >= 0 = U11(isNat(activate(V1)),activate(V2))
    
    isNat(n__s(V1)) = 0 >= 2 = U21(isNat(activate(V1)))
    
    plus(N,0()) = N + 5 >= N + 1 = U31(isNat(N),N)
    
    plus(N,s(M)) = 2M + N + 9 >= 2M + N + 7 = U41(isNat(M),M,N)
    
    0() = 2 >= 2 = n__0()
    
    plus(X1,X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = n__plus(X1,X2)
    
    s(X) = X + 4 >= X + 4 = n__s(X)
    
    activate(n__0()) = 2 >= 2 = 0()
    
    activate(n__plus(X1,X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = plus(activate(X1),activate(X2))
    
    activate(n__s(X)) = X + 4 >= X + 4 = s(activate(X))
    
    activate(X) = X >= X = X
   problem:
    DPs:
     
    TRS:
     U11(tt(),V2) -> U12(isNat(activate(V2)))
     U12(tt()) -> tt()
     U21(tt()) -> tt()
     U31(tt(),N) -> activate(N)
     U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
     U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
     isNat(n__0()) -> tt()
     isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
     isNat(n__s(V1)) -> U21(isNat(activate(V1)))
     plus(N,0()) -> U31(isNat(N),N)
     plus(N,s(M)) -> U41(isNat(M),M,N)
     0() -> n__0()
     plus(X1,X2) -> n__plus(X1,X2)
     s(X) -> n__s(X)
     activate(n__0()) -> 0()
     activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
   Qed