YES
Input TRS:
      1: minus(x,0()) -> x
      2: minus(s(x),s(y)) -> minus(x,y)
      3: double(0()) -> 0()
      4: double(s(x)) -> s(s(double(x)))
      5: plus(0(),y) -> y
      6: plus(s(x),y) -> s(plus(x,y))
      7: plus(s(x),y) -> plus(x,s(y))
      8: plus(s(x),y) -> s(plus(minus(x,y),double(y)))
      9: plus(s(plus(x,y)),z) -> s(plus(plus(x,y),z))
      10: rand(x) ->= x
      11: rand(x) ->= rand(s(x))
Number of strict rules: 9
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #minus(s(x),s(y)) -> #minus(x,y)
     #2: #plus(s(x),y) -> #plus(x,y)
     #3: #plus(s(plus(x,y)),z) -> #plus(plus(x,y),z)
     #4: #plus(s(x),y) -> #plus(x,s(y))
     #5: #plus(s(x),y) -> #plus(minus(x,y),double(y))
     #6: #plus(s(x),y) -> #minus(x,y)
     #7: #plus(s(x),y) -> #double(y)
     #8: #double(s(x)) -> #double(x)
Number of SCCs: 3, DPs: 6
  SCC { #8 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #plus	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 1
      #double	s: 1
      double	s: [1]	p: 1	w: x1
      #minus	s: [1]	p: 0	w: max(x1 + 1)
      plus	s: [1]	p: 2	w: max(x1, x2 + 1)
    Removed DPs: #8
Number of SCCs: 2, DPs: 5
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #plus	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 1
      #double	s: 1
      double	s: [1]	p: 1	w: x1
      #minus	s: 1
      plus	s: [1]	p: 2	w: max(x1, x2 + 1)
    Removed DPs: #1
Number of SCCs: 1, DPs: 4
  SCC { #2..5 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #plus	s: [1,2]	p: 2	w: max(x1 + 21241, x2 + 21242)
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 1
      #double	s: 1
      double	s: [1]	p: 1	w: x1
      #minus	s: 1
      plus	s: [1]	p: 2	w: max(x1, x2 + 21240)
    Removed DPs: #4 #5
Number of SCCs: 1, DPs: 2
  SCC { #2 #3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #plus	s: [1,2]	p: 3	w: max(x1 + 8858, x2 + 8856)
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 1
      #double	s: 1
      double	s: [1]	p: 1	w: x1
      #minus	s: 1
      plus	s: [1]	p: 2	w: max(x1, x2 + 8857)
    Removed DPs: #2
Number of SCCs: 1, DPs: 1
  SCC { #3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #plus	s: [1,2]	p: 2	w: max(x1 + 32287, x2 + 64574)
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 1
      #double	s: 1
      double	s: [1]	p: 1	w: x1
      #minus	s: 1
      plus	s: [1]	p: 2	w: max(x1, x2 + 32286)
    Removed DPs: #3
Number of SCCs: 0, DPs: 0