MAYBE
Input TRS:
      1: le(0(),y) -> true()
      2: le(s(x),0()) -> false()
      3: le(s(x),s(y)) -> le(x,y)
      4: minus(x,0()) -> x
      5: minus(s(x),s(y)) -> minus(x,y)
      6: gcd(0(),y) -> y
      7: gcd(s(x),0()) -> s(x)
      8: gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
      9: if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
      10: if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))
      11: rand(x) ->= x
      12: rand(x) ->= rand(s(x))
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #if_gcd(true(),s(x),s(y)) -> #gcd(minus(x,y),s(y))
     #2: #if_gcd(true(),s(x),s(y)) -> #minus(x,y)
     #3: #if_gcd(false(),s(x),s(y)) -> #gcd(minus(y,x),s(x))
     #4: #if_gcd(false(),s(x),s(y)) -> #minus(y,x)
     #5: #minus(s(x),s(y)) -> #minus(x,y)
     #6: #le(s(x),s(y)) -> #le(x,y)
     #7: #gcd(s(x),s(y)) -> #if_gcd(le(y,x),s(x),s(y))
     #8: #gcd(s(x),s(y)) -> #le(y,x)
Number of SCCs: 3, DPs: 5
  SCC { #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      le	s: [2]	p: 2	w: max(x1 + 8858, x2 + 1)
      s 	s: [1]	p: 1	w: x1
      #le	s: 2
      minus	s: [1]	p: 1	w: max(x1)
      gcd	s: []	p: 3	w: max(x1 + 8859, x2 + 8859)
      false	s: []	p: 1	w: 0
      true	s: []	p: 0	w: 8857
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 0
      #minus	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
      if_gcd	s: []	p: 3	w: max(x2 + 8859, x3 + 8859)
      #if_gcd	s: [3]	p: 0	w: max(x3 + 1)
      #gcd	s: [2]	p: 0	w: max(x2 + 1)
    Removed DPs: #6
Number of SCCs: 2, DPs: 4
  SCC { #5 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      le	s: [2]	p: 2	w: max(x1 + 3, x2 + 1)
      s 	s: [1]	p: 1	w: x1
      #le	s: 2
      minus	s: [1]	p: 1	w: max(x1)
      gcd	s: []	p: 3	w: max(x1 + 4, x2 + 4)
      false	s: []	p: 1	w: 0
      true	s: []	p: 0	w: 2
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 0
      #minus	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 2)
      if_gcd	s: []	p: 3	w: max(x2 + 4, x3 + 4)
      #if_gcd	s: [3]	p: 0	w: max(x3 + 1)
      #gcd	s: [2]	p: 0	w: max(x2 + 1)
    Removed DPs: #5
Number of SCCs: 1, DPs: 3
  SCC { #1 #3 #7 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.