YES

Problem:
 f(x,y,z) -> g(<=(x,y),x,y,z)
 g(true(),x,y,z) -> z
 g(false(),x,y,z) -> f(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   f#(x,y,z) -> g#(<=(x,y),x,y,z)
   g#(false(),x,y,z) -> p#(z)
   g#(false(),x,y,z) -> f#(p(z),x,y)
   g#(false(),x,y,z) -> p#(y)
   g#(false(),x,y,z) -> f#(p(y),z,x)
   g#(false(),x,y,z) -> p#(x)
   g#(false(),x,y,z) -> f#(p(x),y,z)
   g#(false(),x,y,z) -> f#(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
  TRS:
   f(x,y,z) -> g(<=(x,y),x,y,z)
   g(true(),x,y,z) -> z
   g(false(),x,y,z) -> f(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
   p(0()) -> 0()
   p(s(x)) -> x
  Usable Rule Processor:
   DPs:
    f#(x,y,z) -> g#(<=(x,y),x,y,z)
    g#(false(),x,y,z) -> p#(z)
    g#(false(),x,y,z) -> f#(p(z),x,y)
    g#(false(),x,y,z) -> p#(y)
    g#(false(),x,y,z) -> f#(p(y),z,x)
    g#(false(),x,y,z) -> p#(x)
    g#(false(),x,y,z) -> f#(p(x),y,z)
    g#(false(),x,y,z) -> f#(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
   TRS:
    p(0()) -> 0()
    p(s(x)) -> x
    f(x,y,z) -> g(<=(x,y),x,y,z)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [p#](x0) = 1,
     
     [g#](x0, x1, x2, x3) = x0 + 0,
     
     [f#](x0, x1, x2) = 1,
     
     [s](x0) = 2x0 + 4,
     
     [0] = 2,
     
     [p](x0) = 3x0 + 1,
     
     [false] = 4,
     
     [g](x0, x1, x2, x3) = 5x0 + 13x1 + 1x2 + x3 + 8,
     
     [<=](x0, x1) = 0,
     
     [f](x0, x1, x2) = x1 + 2x2 + 1
    orientation:
     f#(x,y,z) = 1 >= 0 = g#(<=(x,y),x,y,z)
     
     g#(false(),x,y,z) = 4 >= 1 = p#(z)
     
     g#(false(),x,y,z) = 4 >= 1 = f#(p(z),x,y)
     
     g#(false(),x,y,z) = 4 >= 1 = p#(y)
     
     g#(false(),x,y,z) = 4 >= 1 = f#(p(y),z,x)
     
     g#(false(),x,y,z) = 4 >= 1 = p#(x)
     
     g#(false(),x,y,z) = 4 >= 1 = f#(p(x),y,z)
     
     g#(false(),x,y,z) = 4 >= 1 = f#(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
     
     p(0()) = 5 >= 2 = 0()
     
     p(s(x)) = 5x + 7 >= x = x
     
     f(x,y,z) = y + 2z + 1 >= 13x + 1y + z + 8 = g(<=(x,y),x,y,z)
    problem:
     DPs:
      
     TRS:
      p(0()) -> 0()
      p(s(x)) -> x
      f(x,y,z) -> g(<=(x,y),x,y,z)
    Qed