YES

Problem:
 min(x,0()) -> 0()
 min(0(),y) -> 0()
 min(s(x),s(y)) -> s(min(x,y))
 max(x,0()) -> x
 max(0(),y) -> y
 max(s(x),s(y)) -> s(max(x,y))
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)
 gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))
 gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))
 gcd(x,0(),0()) -> x
 gcd(0(),y,0()) -> y
 gcd(0(),0(),z) -> z

Proof:
 DP Processor:
  DPs:
   min#(s(x),s(y)) -> min#(x,y)
   max#(s(x),s(y)) -> max#(x,y)
   -#(s(x),s(y)) -> -#(x,y)
   gcd#(s(x),s(y),z) -> min#(x,y)
   gcd#(s(x),s(y),z) -> max#(x,y)
   gcd#(s(x),s(y),z) -> -#(max(x,y),min(x,y))
   gcd#(s(x),s(y),z) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y)),z)
   gcd#(x,s(y),s(z)) -> min#(y,z)
   gcd#(x,s(y),s(z)) -> max#(y,z)
   gcd#(x,s(y),s(z)) -> -#(max(y,z),min(y,z))
   gcd#(x,s(y),s(z)) -> gcd#(x,-(max(y,z),min(y,z)),s(min(y,z)))
   gcd#(s(x),y,s(z)) -> min#(x,z)
   gcd#(s(x),y,s(z)) -> max#(x,z)
   gcd#(s(x),y,s(z)) -> -#(max(x,z),min(x,z))
   gcd#(s(x),y,s(z)) -> gcd#(-(max(x,z),min(x,z)),y,s(min(x,z)))
  TRS:
   min(x,0()) -> 0()
   min(0(),y) -> 0()
   min(s(x),s(y)) -> s(min(x,y))
   max(x,0()) -> x
   max(0(),y) -> y
   max(s(x),s(y)) -> s(max(x,y))
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)
   gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))
   gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))
   gcd(x,0(),0()) -> x
   gcd(0(),y,0()) -> y
   gcd(0(),0(),z) -> z
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [gcd#](x0, x1, x2) = 6x0 + 4x1 + 3x2 + 2,
    
    [-#](x0, x1) = 2x0 + 4x1 + 6,
    
    [max#](x0, x1) = 2x0,
    
    [min#](x0, x1) = 2x0 + 1,
    
    [gcd](x0, x1, x2) = 4x0 + 3x1 + 2x2 + 1,
    
    [-](x0, x1) = x0,
    
    [max](x0, x1) = x0 + 2x1,
    
    [s](x0) = 4x0 + 1,
    
    [min](x0, x1) = x0,
    
    [0] = 0
   orientation:
    min#(s(x),s(y)) = 8x + 3 >= 2x + 1 = min#(x,y)
    
    max#(s(x),s(y)) = 8x + 2 >= 2x = max#(x,y)
    
    -#(s(x),s(y)) = 8x + 16y + 12 >= 2x + 4y + 6 = -#(x,y)
    
    gcd#(s(x),s(y),z) = 24x + 16y + 3z + 12 >= 2x + 1 = min#(x,y)
    
    gcd#(s(x),s(y),z) = 24x + 16y + 3z + 12 >= 2x = max#(x,y)
    
    gcd#(s(x),s(y),z) = 24x + 16y + 3z + 12 >= 6x + 4y + 6 = -#(max(x,y),min(x,y))
    
    gcd#(s(x),s(y),z) = 24x + 16y + 3z + 12 >= 22x + 12y + 3z + 6 = gcd#(-(max(x,y),min(x,y)),s(min(x,y)),z)
    
    gcd#(x,s(y),s(z)) = 6x + 16y + 12z + 9 >= 2y + 1 = min#(y,z)
    
    gcd#(x,s(y),s(z)) = 6x + 16y + 12z + 9 >= 2y = max#(y,z)
    
    gcd#(x,s(y),s(z)) = 6x + 16y + 12z + 9 >= 6y + 4z + 6 = -#(max(y,z),min(y,z))
    
    gcd#(x,s(y),s(z)) = 6x + 16y + 12z + 9 >= 6x + 16y + 8z + 5 = gcd#(x,-(max(y,z),min(y,z)),s(min(y,z)))
    
    gcd#(s(x),y,s(z)) = 24x + 4y + 12z + 11 >= 2x + 1 = min#(x,z)
    
    gcd#(s(x),y,s(z)) = 24x + 4y + 12z + 11 >= 2x = max#(x,z)
    
    gcd#(s(x),y,s(z)) = 24x + 4y + 12z + 11 >= 6x + 4z + 6 = -#(max(x,z),min(x,z))
    
    gcd#(s(x),y,s(z)) = 24x + 4y + 12z + 11 >= 18x + 4y + 12z + 5 = gcd#(-(max(x,z),min(x,z)),y,s(min(x,z)))
    
    min(x,0()) = x >= 0 = 0()
    
    min(0(),y) = 0 >= 0 = 0()
    
    min(s(x),s(y)) = 4x + 1 >= 4x + 1 = s(min(x,y))
    
    max(x,0()) = x >= x = x
    
    max(0(),y) = 2y >= y = y
    
    max(s(x),s(y)) = 4x + 8y + 3 >= 4x + 8y + 1 = s(max(x,y))
    
    -(x,0()) = x >= x = x
    
    -(s(x),s(y)) = 4x + 1 >= x = -(x,y)
    
    gcd(s(x),s(y),z) = 16x + 12y + 2z + 8 >= 16x + 8y + 2z + 4 = gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)
    
    gcd(x,s(y),s(z)) = 4x + 12y + 8z + 6 >= 4x + 11y + 6z + 3 = gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))
    
    gcd(s(x),y,s(z)) = 16x + 3y + 8z + 7 >= 12x + 3y + 8z + 3 = gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))
    
    gcd(x,0(),0()) = 4x + 1 >= x = x
    
    gcd(0(),y,0()) = 3y + 1 >= y = y
    
    gcd(0(),0(),z) = 2z + 1 >= z = z
   problem:
    DPs:
     
    TRS:
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     max(x,0()) -> x
     max(0(),y) -> y
     max(s(x),s(y)) -> s(max(x,y))
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z)
     gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z)))
     gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z)))
     gcd(x,0(),0()) -> x
     gcd(0(),y,0()) -> y
     gcd(0(),0(),z) -> z
   Qed