YES

Problem:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))

Proof:
 DP Processor:
  DPs:
   ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
   ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X)
   u21#(ackout(X),Y) -> ackin#(Y,X)
  TRS:
   ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
   u21(ackout(X),Y) -> u22(ackin(Y,X))
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
    u21(ackout(X),Y) -> u22(ackin(Y,X))
   interpretation:
    [u21#](x0, x1) = x0 + 2,
    
    [ackin#](x0, x1) = 3x1,
    
    [u22](x0) = 0,
    
    [ackout](x0) = 3x0 + 7,
    
    [u21](x0, x1) = 0,
    
    [ackin](x0, x1) = 3x1,
    
    [s](x0) = x0 + 1
   orientation:
    ackin#(s(X),s(Y)) = 3Y + 3 >= 3Y = ackin#(s(X),Y)
    
    ackin#(s(X),s(Y)) = 3Y + 3 >= 3Y + 2 = u21#(ackin(s(X),Y),X)
    
    u21#(ackout(X),Y) = 3X + 9 >= 3X = ackin#(Y,X)
    
    ackin(s(X),s(Y)) = 3Y + 3 >= 0 = u21(ackin(s(X),Y),X)
    
    u21(ackout(X),Y) = 0 >= 0 = u22(ackin(Y,X))
   problem:
    DPs:
     
    TRS:
     ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
     u21(ackout(X),Y) -> u22(ackin(Y,X))
   Qed