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: quot(0(),s(y)) -> 0()
      9: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      10: log(s(0())) -> 0()
      11: log(s(s(x))) -> s(log(s(quot(x,s(s(0()))))))
      12: rand(x) ->= x
      13: rand(x) ->= rand(s(x))
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying log 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: quot(0(),s(y)) -> 0()
      9: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      10: log^1_s(0()) -> 0()
      11: log^1_s(s(x)) -> s(log^1_s(quot(x,s(s(0())))))
      12: rand(x) ->= x
      13: rand(x) ->= rand(s(x))
      14: le(0(),_1) ->= le^1_0(_1)
      15: le(s(_1),_2) ->= le^1_s(_1,_2)
      16: log(s(_1)) ->= log^1_s(_1)
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
     #2: #quot(s(x),s(y)) -> #minus(x,y)
     #3: #log^1_s(s(x)) -> #log^1_s(quot(x,s(s(0()))))
     #4: #log^1_s(s(x)) -> #quot(x,s(s(0())))
     #5: #le(0(),_1) ->? #le^1_0(_1)
     #6: #if_minus(false(),s(x),y) -> #minus(x,y)
     #7: #minus(s(x),y) -> #if_minus(le^1_s(x,y),s(x),y)
     #8: #minus(s(x),y) -> #le^1_s(x,y)
     #9: #log(s(_1)) ->? #log^1_s(_1)
     #10: #le^1_s(x,s(y)) -> #le(x,y)
     #11: #le(s(_1),_2) ->? #le^1_s(_1,_2)
Number of SCCs: 4, DPs: 6
  SCC { #3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: [2]	p: 0	w: max(x2 + 1)
      le	s: [2]	p: 1	w: max(x2)
      le^1_s	s: 2
      s 	s: [1]	p: 1	w: x1
      #le	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
      #le^1_0	s: 1
      minus	s: 1
      false	s: []	p: 0	w: 0
      #log^1_s	s: [1]	p: 0	w: x1 + 1
      #log	s: []	p: 0	w: 1
      true	s: []	p: 0	w: 0
      rand	s: []	p: 0	w: x1 + 1
      log	s: []	p: 3	w: x1 + 1
      0 	s: []	p: 0	w: 0
      quot	s: 1
      #if_minus	s: []	p: 0	w: max(x2 + 1)
      #minus	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
      le^1_0	s: []	p: 1	w: 0
      if_minus	s: 2
      #quot	s: [1]	p: 0	w: max(x1 + 1)
      log^1_s	s: 1
    Removed DPs: #3
Number of SCCs: 3, DPs: 5
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: [2]	p: 0	w: max(x2 + 1)
      le	s: [2]	p: 1	w: max(x2)
      le^1_s	s: 2
      s 	s: [1]	p: 1	w: x1
      #le	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
      #le^1_0	s: 1
      minus	s: 1
      false	s: []	p: 0	w: 0
      #log^1_s	s: [1]	p: 0	w: x1 + 1
      #log	s: []	p: 0	w: 1
      true	s: []	p: 0	w: 0
      rand	s: []	p: 0	w: x1 + 1
      log	s: []	p: 3	w: x1 + 1
      0 	s: []	p: 0	w: 0
      quot	s: 1
      #if_minus	s: []	p: 0	w: max(x2 + 1)
      #minus	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
      le^1_0	s: []	p: 1	w: 0
      if_minus	s: 2
      #quot	s: [2,1]	p: 0	w: max(x1 + 2439, x2 + 1)
      log^1_s	s: 1
    Removed DPs: #1
Number of SCCs: 2, DPs: 4
  SCC { #10 #11 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: 2
      le	s: [2]	p: 1	w: max(x2)
      le^1_s	s: 2
      s 	s: [1]	p: 1	w: x1
      #le	s: 2
      #le^1_0	s: 1
      minus	s: 1
      false	s: []	p: 0	w: 0
      #log^1_s	s: [1]	p: 0	w: x1 + 1
      #log	s: []	p: 0	w: 1
      true	s: []	p: 0	w: 0
      rand	s: []	p: 0	w: x1 + 1
      log	s: []	p: 3	w: x1 + 1
      0 	s: []	p: 0	w: 0
      quot	s: 1
      #if_minus	s: []	p: 0	w: max(x2 + 1)
      #minus	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
      le^1_0	s: []	p: 1	w: 0
      if_minus	s: 2
      #quot	s: [2,1]	p: 0	w: max(x1 + 2439, x2 + 1)
      log^1_s	s: 1
    Removed DPs: #10
Number of SCCs: 1, DPs: 2
  SCC { #6 #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: 2
      le	s: [2]	p: 1	w: max(x2)
      le^1_s	s: 2
      s 	s: [1]	p: 1	w: x1
      #le	s: 2
      #le^1_0	s: 1
      minus	s: 1
      false	s: []	p: 0	w: 0
      #log^1_s	s: [1]	p: 0	w: x1 + 1
      #log	s: []	p: 0	w: 1
      true	s: []	p: 0	w: 0
      rand	s: []	p: 0	w: x1 + 1
      log	s: []	p: 3	w: x1 + 1
      0 	s: []	p: 0	w: 0
      quot	s: 1
      #if_minus	s: 2
      #minus	s: 1
      le^1_0	s: []	p: 1	w: 0
      if_minus	s: 2
      #quot	s: [2,1]	p: 0	w: max(x1 + 2439, x2 + 1)
      log^1_s	s: 1
    Removed DPs: #6
Number of SCCs: 0, DPs: 0