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))
  TDG 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))
   graph:
    u21#(ackout(X),Y) -> ackin#(Y,X) ->
    ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X)
    u21#(ackout(X),Y) -> ackin#(Y,X) ->
    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)
    ackin#(s(X),s(Y)) -> ackin#(s(X),Y) ->
    ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X)
    ackin#(s(X),s(Y)) -> ackin#(s(X),Y) -> ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
   Restore Modifier:
    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))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 5/9
     DPs:
      u21#(ackout(X),Y) -> ackin#(Y,X)
      ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
      ackin#(s(X),s(Y)) -> u21#(ackin(s(X),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:
      dimension: 1
      interpretation:
       [u21#](x0, x1) = x0,
       
       [ackin#](x0, x1) = 1,
       
       [u22](x0) = 0,
       
       [ackout](x0) = 1,
       
       [u21](x0, x1) = 0,
       
       [ackin](x0, x1) = 0,
       
       [s](x0) = 0
      orientation:
       u21#(ackout(X),Y) = 1 >= 1 = ackin#(Y,X)
       
       ackin#(s(X),s(Y)) = 1 >= 1 = ackin#(s(X),Y)
       
       ackin#(s(X),s(Y)) = 1 >= 0 = u21#(ackin(s(X),Y),X)
       
       ackin(s(X),s(Y)) = 0 >= 0 = u21(ackin(s(X),Y),X)
       
       u21(ackout(X),Y) = 0 >= 0 = u22(ackin(Y,X))
      problem:
       DPs:
        u21#(ackout(X),Y) -> ackin#(Y,X)
        ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
       TRS:
        ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
        u21(ackout(X),Y) -> u22(ackin(Y,X))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [u21#](x0, x1) = x0 + 1,
        
        [ackin#](x0, x1) = 0,
        
        [u22](x0) = 0,
        
        [ackout](x0) = 1,
        
        [u21](x0, x1) = 0,
        
        [ackin](x0, x1) = 0,
        
        [s](x0) = 0
       orientation:
        u21#(ackout(X),Y) = 2 >= 0 = ackin#(Y,X)
        
        ackin#(s(X),s(Y)) = 0 >= 0 = ackin#(s(X),Y)
        
        ackin(s(X),s(Y)) = 0 >= 0 = u21(ackin(s(X),Y),X)
        
        u21(ackout(X),Y) = 0 >= 0 = u22(ackin(Y,X))
       problem:
        DPs:
         ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
        TRS:
         ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
         u21(ackout(X),Y) -> u22(ackin(Y,X))
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [ackin#](x0, x1) = x1,
         
         [u22](x0) = 0,
         
         [ackout](x0) = 0,
         
         [u21](x0, x1) = 0,
         
         [ackin](x0, x1) = 0,
         
         [s](x0) = x0 + 1
        orientation:
         ackin#(s(X),s(Y)) = Y + 1 >= Y = ackin#(s(X),Y)
         
         ackin(s(X),s(Y)) = 0 >= 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