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)
   EDG 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)
    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))
     KBO Processor:
      argument filtering:
       pi(s) = [0]
       pi(ackin) = []
       pi(u21) = 0
       pi(ackout) = []
       pi(u22) = []
       pi(ackin#) = 1
      weight function:
       w0 = 1
       w(ackin#) = w(u22) = w(ackout) = w(ackin) = w(s) = 1
       w(u21) = 0
      precedence:
       ackin# ~ ackout ~ ackin ~ s > u22 ~ u21
      problem:
       DPs:
        
       TRS:
        ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
        u21(ackout(X),Y) -> u22(ackin(Y,X))
      Qed