YES
Input TRS:
      1: f(0()) -> true()
      2: f(1()) -> false()
      3: f(s(x)) -> f(x)
      4: if(true(),s(x),s(y)) -> s(x)
      5: if(false(),s(x),s(y)) -> s(y)
      6: g(x,c(y)) -> c(g(x,y))
      7: g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
      8: rand(x) ->= x
      9: rand(x) ->= rand(s(x))
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #g(x,c(y)) -> #g(x,y)
     #2: #g(x,c(y)) -> #g(x,if(f(x),c(g(s(x),y)),c(y)))
     #3: #g(x,c(y)) -> #if(f(x),c(g(s(x),y)),c(y))
     #4: #g(x,c(y)) -> #f(x)
     #5: #g(x,c(y)) -> #g(s(x),y)
     #6: #f(s(x)) -> #f(x)
Number of SCCs: 2, DPs: 3
  SCC { #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      1 	s: []	p: 0	w: 0
      s 	s: [1]	p: 0	w: x1
      false	s: []	p: 3	w: 1
      c 	s: []	p: 2	w: 1
      true	s: []	p: 3	w: 1
      f 	s: []	p: 2	w: 2
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 0	w: 0
      if	s: [1]	p: 1	w: max(x1 + 1, x2 + 1, x3 + 1)
      #f 	s: [1]	p: 0	w: x1 + 1
      #g 	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
      #if	s: 2
      g 	s: []	p: 2	w: max(x1 + 32289)
    Removed DPs: #6
Number of SCCs: 1, DPs: 2
  SCC { #1 #5 }
POLO(Sum)... succeeded.
      1 	w: 1
      s 	w: 0
      false	w: 1
      c 	w: x1 + 1
      true	w: 1
      f 	w: 1
      rand	w: x1
      0 	w: 1
      if	w: 1
      #f 	w: 0
      #g 	w: x2
      #if	w: 0
      g 	w: x2 + 11293
    Removed DPs: #1 #5
Number of SCCs: 0, DPs: 0