YES
Input TRS:
      1: g(c(x,s(y))) -> g(c(s(x),y))
      2: f(c(s(x),y)) -> f(c(x,s(y)))
      3: f(f(x)) -> f(d(f(x)))
      4: f(x) -> x
      5: rand(x) ->= x
      6: rand(x) ->= rand(s(x))
Number of strict rules: 4
Direct POLO(bPol) ... removes: 4 5
      d 	w: x1
      s 	w: x1
      c 	w: 2 * x1 + x2 + 30613
      f 	w: x1 + 1
      rand	w: 2 * x1 + 5854
      g 	w: 2 * x1
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying g
      1: g^1_c(x,s(y)) -> g^1_c(s(x),y)
      2: f(c(s(x),y)) -> f(c(x,s(y)))
      3: f(f(x)) -> f(d(f(x)))
      6: rand(x) ->= rand(s(x))
      7: g(c(_1,_2)) ->= g^1_c(_1,_2)
Number of strict rules: 3
Direct POLO(bPol) ... removes: 7
      d 	w: x1
      s 	w: x1
      g^1_c	w: x1 + x2
      c 	w: x1 + x2 + 3
      f 	w: x1 + 5854
      rand	w: x1 + 28100
      g 	w: x1
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #f(c(s(x),y)) -> #f(c(x,s(y)))
     #2: #f(f(x)) -> #f(d(f(x)))
     #3: #g^1_c(x,s(y)) -> #g^1_c(s(x),y)
Number of SCCs: 2, DPs: 2
  SCC { #3 }
POLO(Sum)... succeeded.
      d 	w: 2438
      s 	w: x1 + 1
      g^1_c	w: 0
      c 	w: x1 + x2 + 8855
      #g^1_c	w: x2
      f 	w: x1 + 7720
      rand	w: 0
      #f 	w: 0
      g 	w: 0
    Removed DPs: #3
Number of SCCs: 1, DPs: 1
  SCC { #1 }
POLO(Sum)... succeeded.
      d 	w: 2731
      s 	w: x1 + 1
      g^1_c	w: 0
      c 	w: x1 + 8856
      #g^1_c	w: 0
      f 	w: x1 + 7720
      rand	w: 0
      #f 	w: x1
      g 	w: 0
    Removed DPs: #1
Number of SCCs: 0, DPs: 0