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))
  ADG 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)) -> ackin#(s(X),Y)
    u21#(ackout(X),Y) -> ackin#(Y,X) ->
    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)
    ackin#(s(X),s(Y)) -> ackin#(s(X),Y) -> ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X)
   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: 1
     #arcs: 4/9
     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