YES
Input TRS:
      1: le(0(),y) -> true()
      2: le(s(x),0()) -> false()
      3: le(s(x),s(y)) -> le(x,y)
      4: minus(0(),y) -> 0()
      5: minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
      6: if_minus(true(),s(x),y) -> 0()
      7: if_minus(false(),s(x),y) -> s(minus(x,y))
      8: mod(0(),y) -> 0()
      9: mod(s(x),0()) -> 0()
      10: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
      11: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
      12: if_mod(false(),s(x),s(y)) -> s(x)
      13: rand(x) ->= x
      14: rand(x) ->= rand(s(x))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying le
      1: le^1_0(y) -> true()
      2: le^1_s(x,0()) -> false()
      3: le^1_s(x,s(y)) -> le(x,y)
      4: minus(0(),y) -> 0()
      5: minus(s(x),y) -> if_minus(le^1_s(x,y),s(x),y)
      6: if_minus(true(),s(x),y) -> 0()
      7: if_minus(false(),s(x),y) -> s(minus(x,y))
      8: mod(0(),y) -> 0()
      9: mod(s(x),0()) -> 0()
      10: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
      11: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
      12: if_mod(false(),s(x),s(y)) -> s(x)
      13: rand(x) ->= x
      14: rand(x) ->= rand(s(x))
      15: le(0(),_1) ->= le^1_0(_1)
      16: le(s(_1),_2) ->= le^1_s(_1,_2)
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #if_mod(true(),s(x),s(y)) -> #mod(minus(x,y),s(y))
     #2: #if_mod(true(),s(x),s(y)) -> #minus(x,y)
     #3: #if_minus(false(),s(x),y) -> #minus(x,y)
     #4: #mod(s(x),s(y)) -> #if_mod(le(y,x),s(x),s(y))
     #5: #mod(s(x),s(y)) -> #le(y,x)
     #6: #minus(s(x),y) -> #if_minus(le^1_s(x,y),s(x),y)
     #7: #minus(s(x),y) -> #le^1_s(x,y)
     #8: #le(s(_1),_2) ->? #le^1_s(_1,_2)
     #9: #le^1_s(x,s(y)) -> #le(x,y)
     #10: #le(0(),_1) ->? #le^1_0(_1)
Number of SCCs: 3, DPs: 6
  SCC { #8 #9 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: [1]	p: 1	w: max(x1)
      le	s: []	p: 5	w: max(x1 + 33957, x2 + 33959)
      le^1_s	s: []	p: 5	w: max(x1 + 33957, x2 + 33959)
      s 	s: [1]	p: 3	w: x1
      #le	s: [1]	p: 0	w: max(x1)
      #le^1_0	s: 1
      minus	s: 1
      mod	s: []	p: 5	w: max(x1 + 33956, x2 + 33954)
      false	s: []	p: 4	w: 33958
      true	s: []	p: 5	w: 33955
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: []	p: 5	w: max(x2 + 33956, x3 + 33954)
      0 	s: []	p: 0	w: 0
      #if_minus	s: 3
      #minus	s: [2]	p: 0	w: max(x2 + 1)
      #mod	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
      #if_mod	s: [3,2,1]	p: 0	w: max(x1 + 1, x2 + 1, x3 + 1)
      le^1_0	s: []	p: 4	w: 33958
      if_minus	s: 2
    Removed DPs: #8 #9
Number of SCCs: 2, DPs: 4
  SCC { #3 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: [1]	p: 1	w: max(x1)
      le	s: []	p: 3	w: 0
      le^1_s	s: []	p: 3	w: 0
      s 	s: [1]	p: 4	w: x1
      #le	s: [1]	p: 0	w: max(x1)
      #le^1_0	s: 1
      minus	s: 1
      mod	s: []	p: 5	w: max(x1 + 8946)
      false	s: []	p: 2	w: 0
      true	s: []	p: 0	w: 0
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: []	p: 5	w: max(x2 + 8946)
      0 	s: []	p: 0	w: 0
      #if_minus	s: 2
      #minus	s: [1]	p: 3	w: max(x1)
      #mod	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
      #if_mod	s: [3,2,1]	p: 0	w: max(x1 + 1, x2 + 1, x3 + 1)
      le^1_0	s: []	p: 1	w: 0
      if_minus	s: 2
    Removed DPs: #3 #6
Number of SCCs: 1, DPs: 2
  SCC { #1 #4 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: [1]	p: 1	w: max(x1)
      le	s: []	p: 4	w: max(x1 + 13326)
      le^1_s	s: []	p: 4	w: max(x1 + 13326)
      s 	s: [1]	p: 5	w: x1
      #le	s: [1]	p: 0	w: max(x1)
      #le^1_0	s: 1
      minus	s: 1
      mod	s: []	p: 6	w: max(x1 + 13327, x2 + 868)
      false	s: []	p: 1	w: 1
      true	s: []	p: 3	w: 868
      rand	s: []	p: 0	w: x1 + 1
      if_mod	s: []	p: 6	w: max(x2 + 13327, x3 + 868)
      0 	s: []	p: 0	w: 0
      #if_minus	s: 3
      #minus	s: [1]	p: 3	w: max(x1)
      #mod	s: 1
      #if_mod	s: 2
      le^1_0	s: []	p: 4	w: 869
      if_minus	s: 2
    Removed DPs: #1
Number of SCCs: 0, DPs: 0