YES
Input TRS:
      1: times(x,0()) -> 0()
      2: times(x,s(y)) -> plus(times(x,y),x)
      3: plus(x,0()) -> x
      4: plus(0(),x) -> x
      5: plus(x,s(y)) -> s(plus(x,y))
      6: plus(s(x),y) -> s(plus(x,y))
      7: rand(x) ->= x
      8: rand(x) ->= rand(s(x))
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #times(x,s(y)) -> #plus(times(x,y),x)
     #2: #times(x,s(y)) -> #times(x,y)
     #3: #plus(s(x),y) -> #plus(x,y)
     #4: #plus(x,s(y)) -> #plus(x,y)
Number of SCCs: 2, DPs: 3
  SCC { #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      #plus	s: []	p: 0	w: max(x2 + 1)
      rand	s: []	p: 0	w: x1 + 1
      #times	s: 2
      0 	s: []	p: 3	w: 1
      times	s: [1,2]	p: 2	w: x1 + x2 + 2
      plus	s: [1,2]	p: 1	w: max(x1, x2 + 1)
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
  SCC { #3 #4 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      #plus	s: 1
      rand	s: []	p: 0	w: x1 + 1
      #times	s: 2
      0 	s: []	p: 3	w: 1
      times	s: [1,2]	p: 2	w: x1 + x2 + 21240
      plus	s: [1,2]	p: 1	w: max(x1, x2 + 21239)
    Removed DPs: #3
Number of SCCs: 1, DPs: 1
  SCC { #4 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      #plus	s: 2
      rand	s: []	p: 0	w: x1 + 1
      #times	s: 2
      0 	s: []	p: 3	w: 1
      times	s: [1,2]	p: 2	w: x1 + x2 + 8857
      plus	s: [1,2]	p: 1	w: max(x1, x2 + 8856)
    Removed DPs: #4
Number of SCCs: 0, DPs: 0