YES
Input TRS:
      1: minus(x,0()) -> x
      2: minus(s(x),s(y)) -> minus(x,y)
      3: f(0()) -> s(0())
      4: f(s(x)) -> minus(s(x),g(f(x)))
      5: g(0()) -> 0()
      6: g(s(x)) -> minus(s(x),f(g(x)))
      7: rand(x) ->= x
      8: rand(x) ->= rand(s(x))
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #minus(s(x),s(y)) -> #minus(x,y)
     #2: #g(s(x)) -> #minus(s(x),f(g(x)))
     #3: #g(s(x)) -> #f(g(x))
     #4: #g(s(x)) -> #g(x)
     #5: #f(s(x)) -> #minus(s(x),g(f(x)))
     #6: #f(s(x)) -> #g(f(x))
     #7: #f(s(x)) -> #f(x)
Number of SCCs: 2, DPs: 5
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 2	w: x1
      minus	s: []	p: 3	w: max(x1 + 8366)
      f 	s: []	p: 2	w: x1 + 8367
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 0	w: 34723
      #f 	s: []	p: 0	w: 1
      #g 	s: []	p: 0	w: 1
      #minus	s: [1]	p: 3	w: max(x1 + 19306)
      g 	s: [1]	p: 1	w: x1 + 20164
    Removed DPs: #1
Number of SCCs: 1, DPs: 4
  SCC { #3 #4 #6 #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 2	w: x1
      minus	s: [1]	p: 0	w: max(x1)
      f 	s: [1]	p: 2	w: x1
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 0	w: 1
      #f 	s: 1
      #g 	s: 1
      #minus	s: [1]	p: 3	w: max(x1 + 19306)
      g 	s: [1]	p: 1	w: x1
    Removed DPs: #3 #4 #7
Number of SCCs: 0, DPs: 0