YES

Problem:
 U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
 U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
 U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
 U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
 plus(N,0()) -> N
 plus(N,s(M)) -> U11(tt(),M,N)
 x(N,0()) -> 0()
 x(N,s(M)) -> U21(tt(),M,N)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   U11#(tt(),M,N) -> activate#(N)
   U11#(tt(),M,N) -> activate#(M)
   U11#(tt(),M,N) -> U12#(tt(),activate(M),activate(N))
   U12#(tt(),M,N) -> activate#(M)
   U12#(tt(),M,N) -> activate#(N)
   U12#(tt(),M,N) -> plus#(activate(N),activate(M))
   U21#(tt(),M,N) -> activate#(N)
   U21#(tt(),M,N) -> activate#(M)
   U21#(tt(),M,N) -> U22#(tt(),activate(M),activate(N))
   U22#(tt(),M,N) -> activate#(M)
   U22#(tt(),M,N) -> activate#(N)
   U22#(tt(),M,N) -> x#(activate(N),activate(M))
   U22#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N))
   plus#(N,s(M)) -> U11#(tt(),M,N)
   x#(N,s(M)) -> U21#(tt(),M,N)
  TRS:
   U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
   U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
   U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
   U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
   plus(N,0()) -> N
   plus(N,s(M)) -> U11(tt(),M,N)
   x(N,0()) -> 0()
   x(N,s(M)) -> U21(tt(),M,N)
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    activate(X) -> X
   interpretation:
    [x#](x0, x1) = 2x0 + 2x1 + 4,
    
    [U22#](x0, x1, x2) = 2x0 + 2x1 + 2x2 + 4,
    
    [U21#](x0, x1, x2) = 3x0 + 2x1 + 2x2 + 1,
    
    [plus#](x0, x1) = 2x1 + 7,
    
    [U12#](x0, x1, x2) = 2x0 + 2x1 + 1,
    
    [activate#](x0) = 0,
    
    [U11#](x0, x1, x2) = 4x0 + 2x1,
    
    [0] = 2,
    
    [x](x0, x1) = 3x0 + 5x1,
    
    [U22](x0, x1, x2) = 4x1,
    
    [U21](x0, x1, x2) = 0,
    
    [s](x0) = 4x0 + 5,
    
    [plus](x0, x1) = 2x0 + 2x1,
    
    [U12](x0, x1, x2) = 6x2,
    
    [activate](x0) = x0,
    
    [U11](x0, x1, x2) = 0,
    
    [tt] = 4
   orientation:
    U11#(tt(),M,N) = 2M + 16 >= 0 = activate#(N)
    
    U11#(tt(),M,N) = 2M + 16 >= 0 = activate#(M)
    
    U11#(tt(),M,N) = 2M + 16 >= 2M + 9 = U12#(tt(),activate(M),activate(N))
    
    U12#(tt(),M,N) = 2M + 9 >= 0 = activate#(M)
    
    U12#(tt(),M,N) = 2M + 9 >= 0 = activate#(N)
    
    U12#(tt(),M,N) = 2M + 9 >= 2M + 7 = plus#(activate(N),activate(M))
    
    U21#(tt(),M,N) = 2M + 2N + 13 >= 0 = activate#(N)
    
    U21#(tt(),M,N) = 2M + 2N + 13 >= 0 = activate#(M)
    
    U21#(tt(),M,N) = 2M + 2N + 13 >= 2M + 2N + 12 = U22#(tt(),activate(M),activate(N))
    
    U22#(tt(),M,N) = 2M + 2N + 12 >= 0 = activate#(M)
    
    U22#(tt(),M,N) = 2M + 2N + 12 >= 0 = activate#(N)
    
    U22#(tt(),M,N) = 2M + 2N + 12 >= 2M + 2N + 4 = x#(activate(N),activate(M))
    
    U22#(tt(),M,N) = 2M + 2N + 12 >= 2N + 7 = plus#(x(activate(N),activate(M)),activate(N))
    
    plus#(N,s(M)) = 8M + 17 >= 2M + 16 = U11#(tt(),M,N)
    
    x#(N,s(M)) = 8M + 2N + 14 >= 2M + 2N + 13 = U21#(tt(),M,N)
    
    U11(tt(),M,N) = 0 >= 6N = U12(tt(),activate(M),activate(N))
    
    U12(tt(),M,N) = 6N >= 8M + 8N + 5 = s(plus(activate(N),activate(M)))
    
    U21(tt(),M,N) = 0 >= 4M = U22(tt(),activate(M),activate(N))
    
    U22(tt(),M,N) = 4M >= 10M + 8N = plus(x(activate(N),activate(M)),activate(N))
    
    plus(N,0()) = 2N + 4 >= N = N
    
    plus(N,s(M)) = 8M + 2N + 10 >= 0 = U11(tt(),M,N)
    
    x(N,0()) = 3N + 10 >= 2 = 0()
    
    x(N,s(M)) = 20M + 3N + 25 >= 0 = U21(tt(),M,N)
    
    activate(X) = X >= X = X
   problem:
    DPs:
     
    TRS:
     U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
     U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
     U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
     U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
     plus(N,0()) -> N
     plus(N,s(M)) -> U11(tt(),M,N)
     x(N,0()) -> 0()
     x(N,s(M)) -> U21(tt(),M,N)
     activate(X) -> X
   Qed