YES
Time: 0.017707
TRS:
 {               le(0(), y) -> true(),
               le(s x, 0()) -> false(),
               le(s x, s y) -> le(x, y),
                   pred s x -> x,
              minus(x, 0()) -> x,
              minus(x, s y) -> pred minus(x, y),
                gcd(0(), y) -> y,
              gcd(s x, 0()) -> s x,
              gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
   if_gcd(true(), s x, s y) -> gcd(minus(x, y), s y),
  if_gcd(false(), s x, s y) -> gcd(minus(y, x), s x)}
 DP:
  DP:
   {             le#(s x, s y) -> le#(x, y),
                minus#(x, s y) -> pred# minus(x, y),
                minus#(x, s y) -> minus#(x, y),
                gcd#(s x, s y) -> le#(y, x),
                gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y),
     if_gcd#(true(), s x, s y) -> minus#(x, y),
     if_gcd#(true(), s x, s y) -> gcd#(minus(x, y), s y),
    if_gcd#(false(), s x, s y) -> minus#(y, x),
    if_gcd#(false(), s x, s y) -> gcd#(minus(y, x), s x)}
  TRS:
  {               le(0(), y) -> true(),
                le(s x, 0()) -> false(),
                le(s x, s y) -> le(x, y),
                    pred s x -> x,
               minus(x, 0()) -> x,
               minus(x, s y) -> pred minus(x, y),
                 gcd(0(), y) -> y,
               gcd(s x, 0()) -> s x,
               gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
    if_gcd(true(), s x, s y) -> gcd(minus(x, y), s y),
   if_gcd(false(), s x, s y) -> gcd(minus(y, x), s x)}
  EDG:
   {(if_gcd#(false(), s x, s y) -> minus#(y, x), minus#(x, s y) -> minus#(x, y))
    (if_gcd#(false(), s x, s y) -> minus#(y, x), minus#(x, s y) -> pred# minus(x, y))
    (minus#(x, s y) -> minus#(x, y), minus#(x, s y) -> minus#(x, y))
    (minus#(x, s y) -> minus#(x, y), minus#(x, s y) -> pred# minus(x, y))
    (if_gcd#(true(), s x, s y) -> gcd#(minus(x, y), s y), gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y))
    (if_gcd#(true(), s x, s y) -> gcd#(minus(x, y), s y), gcd#(s x, s y) -> le#(y, x))
    (if_gcd#(false(), s x, s y) -> gcd#(minus(y, x), s x), gcd#(s x, s y) -> le#(y, x))
    (if_gcd#(false(), s x, s y) -> gcd#(minus(y, x), s x), gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y))
    (gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y), if_gcd#(true(), s x, s y) -> minus#(x, y))
    (gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y), if_gcd#(true(), s x, s y) -> gcd#(minus(x, y), s y))
    (gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y), if_gcd#(false(), s x, s y) -> minus#(y, x))
    (gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y), if_gcd#(false(), s x, s y) -> gcd#(minus(y, x), s x))
    (if_gcd#(true(), s x, s y) -> minus#(x, y), minus#(x, s y) -> pred# minus(x, y))
    (if_gcd#(true(), s x, s y) -> minus#(x, y), minus#(x, s y) -> minus#(x, y))
    (le#(s x, s y) -> le#(x, y), le#(s x, s y) -> le#(x, y))
    (gcd#(s x, s y) -> le#(y, x), le#(s x, s y) -> le#(x, y))}
   SCCS (3):
    Scc:
     {            gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y),
       if_gcd#(true(), s x, s y) -> gcd#(minus(x, y), s y),
      if_gcd#(false(), s x, s y) -> gcd#(minus(y, x), s x)}
    Scc:
     {minus#(x, s y) -> minus#(x, y)}
    Scc:
     {le#(s x, s y) -> le#(x, y)}
    SCC (3):
     Strict:
      {            gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y),
        if_gcd#(true(), s x, s y) -> gcd#(minus(x, y), s y),
       if_gcd#(false(), s x, s y) -> gcd#(minus(y, x), s x)}
     Weak:
     {               le(0(), y) -> true(),
                   le(s x, 0()) -> false(),
                   le(s x, s y) -> le(x, y),
                       pred s x -> x,
                  minus(x, 0()) -> x,
                  minus(x, s y) -> pred minus(x, y),
                    gcd(0(), y) -> y,
                  gcd(s x, 0()) -> s x,
                  gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
       if_gcd(true(), s x, s y) -> gcd(minus(x, y), s y),
      if_gcd(false(), s x, s y) -> gcd(minus(y, x), s x)}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [if_gcd](x0, x1, x2) = x0 + 1,
       
       [le](x0, x1) = 0,
       
       [minus](x0, x1) = x0,
       
       [gcd](x0, x1) = x0 + 1,
       
       [s](x0) = x0 + 1,
       
       [pred](x0) = x0,
       
       [true] = 0,
       
       [0] = 1,
       
       [false] = 0,
       
       [if_gcd#](x0, x1, x2) = x0 + x1,
       
       [gcd#](x0, x1) = x0 + x1 + 1
      Strict:
       if_gcd#(false(), s x, s y) -> gcd#(minus(y, x), s x)
       2 + 1y + 1x >= 2 + 1y + 1x
       if_gcd#(true(), s x, s y) -> gcd#(minus(x, y), s y)
       2 + 1y + 1x >= 2 + 1y + 1x
       gcd#(s x, s y) -> if_gcd#(le(y, x), s x, s y)
       3 + 1y + 1x >= 2 + 1y + 1x
      Weak:
       
     EDG:
      {}
      SCCS (0):
       
       Qed
   SCC (1):
    Strict:
     {minus#(x, s y) -> minus#(x, y)}
    Weak:
    {               le(0(), y) -> true(),
                  le(s x, 0()) -> false(),
                  le(s x, s y) -> le(x, y),
                      pred s x -> x,
                 minus(x, 0()) -> x,
                 minus(x, s y) -> pred minus(x, y),
                   gcd(0(), y) -> y,
                 gcd(s x, 0()) -> s x,
                 gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
      if_gcd(true(), s x, s y) -> gcd(minus(x, y), s y),
     if_gcd(false(), s x, s y) -> gcd(minus(y, x), s x)}
    SPSC:
     Simple Projection:
      pi(minus#) = 1
     Strict:
      {}
     Qed
   SCC (1):
    Strict:
     {le#(s x, s y) -> le#(x, y)}
    Weak:
    {               le(0(), y) -> true(),
                  le(s x, 0()) -> false(),
                  le(s x, s y) -> le(x, y),
                      pred s x -> x,
                 minus(x, 0()) -> x,
                 minus(x, s y) -> pred minus(x, y),
                   gcd(0(), y) -> y,
                 gcd(s x, 0()) -> s x,
                 gcd(s x, s y) -> if_gcd(le(y, x), s x, s y),
      if_gcd(true(), s x, s y) -> gcd(minus(x, y), s y),
     if_gcd(false(), s x, s y) -> gcd(minus(y, x), s x)}
    SPSC:
     Simple Projection:
      pi(le#) = 1
     Strict:
      {}
     Qed