MAYBE
Time: 0.002481
TRS:
 { ack_in(s m, s n) -> u21(ack_in(s m, n), m),
   ack_in(s m, 0()) -> u11 ack_in(m, s 0()),
     ack_in(0(), n) -> ack_out s n,
      u11 ack_out n -> ack_out n,
  u21(ack_out n, m) -> u22 ack_in(m, n),
      u22 ack_out n -> ack_out n}
 DP:
  DP:
   { ack_in#(s m, s n) -> ack_in#(s m, n),
     ack_in#(s m, s n) -> u21#(ack_in(s m, n), m),
     ack_in#(s m, 0()) -> ack_in#(m, s 0()),
     ack_in#(s m, 0()) -> u11# ack_in(m, s 0()),
    u21#(ack_out n, m) -> ack_in#(m, n),
    u21#(ack_out n, m) -> u22# ack_in(m, n)}
  TRS:
  { ack_in(s m, s n) -> u21(ack_in(s m, n), m),
    ack_in(s m, 0()) -> u11 ack_in(m, s 0()),
      ack_in(0(), n) -> ack_out s n,
       u11 ack_out n -> ack_out n,
   u21(ack_out n, m) -> u22 ack_in(m, n),
       u22 ack_out n -> ack_out n}
  UR:
   { ack_in(s m, s n) -> u21(ack_in(s m, n), m),
     ack_in(s m, 0()) -> u11 ack_in(m, s 0()),
       ack_in(0(), n) -> ack_out s n,
        u11 ack_out n -> ack_out n,
    u21(ack_out n, m) -> u22 ack_in(m, n),
        u22 ack_out n -> ack_out n,
              a(x, y) -> x,
              a(x, y) -> y}
   EDG:
    {(ack_in#(s m, 0()) -> ack_in#(m, s 0()), ack_in#(s m, s n) -> u21#(ack_in(s m, n), m))
     (ack_in#(s m, 0()) -> ack_in#(m, s 0()), ack_in#(s m, s n) -> ack_in#(s m, n))
     (ack_in#(s m, s n) -> u21#(ack_in(s m, n), m), u21#(ack_out n, m) -> u22# ack_in(m, n))
     (ack_in#(s m, s n) -> u21#(ack_in(s m, n), m), u21#(ack_out n, m) -> ack_in#(m, n))
     (ack_in#(s m, s n) -> ack_in#(s m, n), ack_in#(s m, 0()) -> u11# ack_in(m, s 0()))
     (ack_in#(s m, s n) -> ack_in#(s m, n), ack_in#(s m, 0()) -> ack_in#(m, s 0()))
     (ack_in#(s m, s n) -> ack_in#(s m, n), ack_in#(s m, s n) -> u21#(ack_in(s m, n), m))
     (ack_in#(s m, s n) -> ack_in#(s m, n), ack_in#(s m, s n) -> ack_in#(s m, n))
     (u21#(ack_out n, m) -> ack_in#(m, n), ack_in#(s m, s n) -> ack_in#(s m, n))
     (u21#(ack_out n, m) -> ack_in#(m, n), ack_in#(s m, s n) -> u21#(ack_in(s m, n), m))
     (u21#(ack_out n, m) -> ack_in#(m, n), ack_in#(s m, 0()) -> ack_in#(m, s 0()))
     (u21#(ack_out n, m) -> ack_in#(m, n), ack_in#(s m, 0()) -> u11# ack_in(m, s 0()))}
    STATUS:
     arrows: 0.666667
     SCCS (1):
      Scc:
       { ack_in#(s m, s n) -> ack_in#(s m, n),
         ack_in#(s m, s n) -> u21#(ack_in(s m, n), m),
         ack_in#(s m, 0()) -> ack_in#(m, s 0()),
        u21#(ack_out n, m) -> ack_in#(m, n)}
      
      SCC (4):
       Strict:
        { ack_in#(s m, s n) -> ack_in#(s m, n),
          ack_in#(s m, s n) -> u21#(ack_in(s m, n), m),
          ack_in#(s m, 0()) -> ack_in#(m, s 0()),
         u21#(ack_out n, m) -> ack_in#(m, n)}
       Weak:
       { ack_in(s m, s n) -> u21(ack_in(s m, n), m),
         ack_in(s m, 0()) -> u11 ack_in(m, s 0()),
           ack_in(0(), n) -> ack_out s n,
            u11 ack_out n -> ack_out n,
        u21(ack_out n, m) -> u22 ack_in(m, n),
            u22 ack_out n -> ack_out n}
       Open