YES
Input TRS:
      1: le(0(),y) -> true()
      2: le(s(x),0()) -> false()
      3: le(s(x),s(y)) -> le(x,y)
      4: pred(s(x)) -> x
      5: minus(x,0()) -> x
      6: minus(x,s(y)) -> pred(minus(x,y))
      7: mod(0(),y) -> 0()
      8: mod(s(x),0()) -> 0()
      9: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
      10: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
      11: if_mod(false(),s(x),s(y)) -> s(x)
      12: rand(x) ->= x
      13: rand(x) ->= rand(s(x))
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #minus(x,s(y)) -> #pred(minus(x,y))
     #2: #minus(x,s(y)) -> #minus(x,y)
     #3: #mod(s(x),s(y)) -> #if_mod(le(y,x),s(x),s(y))
     #4: #mod(s(x),s(y)) -> #le(y,x)
     #5: #if_mod(true(),s(x),s(y)) -> #mod(minus(x,y),s(y))
     #6: #if_mod(true(),s(x),s(y)) -> #minus(x,y)
     #7: #le(s(x),s(y)) -> #le(x,y)
Number of SCCs: 3, DPs: 4
  SCC { #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      le	s: [2,1]	p: 3	w: max(x1 + 5, x2 + 4)
      s 	s: [1]	p: 0	w: x1
      #le	s: []	p: 0	w: 0
      minus	s: [1]	p: 0	w: max(x1, x2 + 1)
      mod	s: []	p: 1	w: max(x1 + 2, x2 + 3)
      false	s: []	p: 0	w: 0
      true	s: []	p: 2	w: 5
      pred	s: 1
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: []	p: 1	w: max(x2 + 2, x3 + 3)
      0 	s: []	p: 0	w: 4
      #minus	s: 2
      #mod	s: []	p: 0	w: max(x2 + 1)
      #if_mod	s: []	p: 0	w: max(x2 + 1)
      #pred	s: []	p: 0	w: 1
    Removed DPs: #2
Number of SCCs: 2, DPs: 3
  SCC { #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      le	s: [2,1]	p: 3	w: max(x1 + 5, x2 + 4)
      s 	s: [1]	p: 0	w: x1
      #le	s: 1
      minus	s: [1]	p: 0	w: max(x1, x2 + 1)
      mod	s: []	p: 1	w: max(x1 + 2, x2 + 3)
      false	s: []	p: 0	w: 0
      true	s: []	p: 2	w: 5
      pred	s: 1
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: []	p: 1	w: max(x2 + 2, x3 + 3)
      0 	s: []	p: 0	w: 4
      #minus	s: 2
      #mod	s: []	p: 0	w: max(x2 + 1)
      #if_mod	s: []	p: 0	w: max(x2 + 1)
      #pred	s: []	p: 0	w: 1
    Removed DPs: #7
Number of SCCs: 1, DPs: 2
  SCC { #3 #5 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      le	s: 1
      s 	s: [1]	p: 0	w: x1
      #le	s: 1
      minus	s: 1
      mod	s: []	p: 4	w: max(x1 + 30616)
      false	s: []	p: 0	w: 0
      true	s: []	p: 5	w: 30614
      pred	s: 1
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: []	p: 4	w: max(x2 + 30616)
      0 	s: []	p: 0	w: 30615
      #minus	s: 2
      #mod	s: [1,2]	p: 2	w: max(x1 + 61228, x2 + 30615)
      #if_mod	s: [2,1,3]	p: 2	w: max(x1 + 30615, x2 + 61228, x3 + 30615)
      #pred	s: []	p: 0	w: 1
    Removed DPs: #3 #5
Number of SCCs: 0, DPs: 0