YES
Time: 0.065527
TRS:
 {u21(ackout X, Y) -> u22 ackin(Y, X),
   ackin(s X, s Y) -> u21(ackin(s X, Y), X)}
 DP:
  DP:
   {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)}
  TRS:
  {u21(ackout X, Y) -> u22 ackin(Y, X),
    ackin(s X, s Y) -> u21(ackin(s X, Y), X)}
  UR:
   {u21(ackout X, Y) -> u22 ackin(Y, X),
     ackin(s X, s Y) -> u21(ackin(s X, Y), X),
             a(x, y) -> x,
             a(x, y) -> y}
   EDG:
    {(ackin#(s X, s Y) -> u21#(ackin(s X, Y), X), u21#(ackout X, Y) -> ackin#(Y, X))
     (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) -> 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))}
    STATUS:
     arrows: 0.444444
     SCCS (1):
      Scc:
       {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)}
      
      SCC (3):
       Strict:
        {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)}
       Weak:
       {u21(ackout X, Y) -> u22 ackin(Y, X),
         ackin(s X, s Y) -> u21(ackin(s X, Y), X)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [u21](x0, x1) = 0,
         
         [ackin](x0, x1) = 0,
         
         [s](x0) = x0 + 1,
         
         [u22](x0) = 0,
         
         [ackout](x0) = x0 + 1,
         
         [u21#](x0, x1) = x0,
         
         [ackin#](x0, x1) = x0 + 1
        Strict:
         ackin#(s X, s Y) -> ackin#(s X, Y)
         2 + 0X + 1Y >= 1 + 0X + 1Y
         ackin#(s X, s Y) -> u21#(ackin(s X, Y), X)
         2 + 0X + 1Y >= 0 + 0X + 0Y
         u21#(ackout X, Y) -> ackin#(Y, X)
         1 + 1X + 0Y >= 1 + 1X + 0Y
        Weak:
         ackin(s X, s Y) -> u21(ackin(s X, Y), X)
         0 + 0X + 0Y >= 0 + 0X + 0Y
         u21(ackout X, Y) -> u22 ackin(Y, X)
         0 + 0X + 0Y >= 0 + 0X + 0Y
       SCCS (0):