0.00/0.16	YES
0.00/0.16	Input TRS:
0.00/0.16	    1: le(0(),y) -> true()
0.00/0.16	    2: le(s(x),0()) -> false()
0.00/0.16	    3: le(s(x),s(y)) -> le(x,y)
0.00/0.16	    4: minus(x,0()) -> x
0.00/0.16	    5: minus(s(x),s(y)) -> minus(x,y)
0.00/0.16	    6: mod(0(),y) -> 0()
0.00/0.16	    7: mod(s(x),0()) -> 0()
0.00/0.16	    8: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
0.00/0.16	    9: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
0.00/0.16	    10: if_mod(false(),s(x),s(y)) -> s(x)
0.00/0.16	    11: rand(x) ->= x
0.00/0.16	    12: rand(x) ->= rand(s(x))
0.00/0.16	Number of strict rules: 10
0.00/0.16	Direct POLO(bPol) ... failed.
0.00/0.16	Uncurrying ... failed.
0.00/0.16	Dependency Pairs:
0.00/0.16	   #1: #if_mod(true(),s(x),s(y)) -> #mod(minus(x,y),s(y))
0.00/0.16	   #2: #if_mod(true(),s(x),s(y)) -> #minus(x,y)
0.00/0.16	   #3: #minus(s(x),s(y)) -> #minus(x,y)
0.00/0.16	   #4: #le(s(x),s(y)) -> #le(x,y)
0.00/0.16	   #5: #mod(s(x),s(y)) -> #if_mod(le(y,x),s(x),s(y))
0.00/0.16	   #6: #mod(s(x),s(y)) -> #le(y,x)
0.00/0.16	Number of SCCs: 3, DPs: 4
0.00/0.16	  SCC { #4 }
0.00/0.16	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.16	      le	s: []	p: 4	w: 0
0.00/0.16	      s 	s: [1]	p: 5	w: x1
0.00/0.16	      #le	s: [2]	p: 6	w: max(x1 + 2, x2 + 1)
0.00/0.16	      minus	s: [1]	p: 1	w: max(x1)
0.00/0.16	      mod	s: [1]	p: 2	w: max(x1)
0.00/0.16	      false	s: []	p: 4	w: 0
0.00/0.16	      true	s: []	p: 0	w: 0
0.00/0.16	      rand	s: []	p: 0	w: x1 + 1
0.00/0.16	      if_mod	s: [2,1]	p: 1	w: max(x1, x2)
0.00/0.16	      0 	s: []	p: 3	w: 0
0.00/0.16	      #minus	s: [2,1]	p: 0	w: max(x1 + 1, x2)
0.00/0.16	      #mod	s: [1]	p: 0	w: max(x1)
0.00/0.16	      #if_mod	s: [1,3,2]	p: 0	w: max(x1 + 1, x2, x3)
0.00/0.16	    Removed DPs: #4
0.00/0.16	Number of SCCs: 2, DPs: 3
0.00/0.16	  SCC { #3 }
0.00/0.16	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.16	      le	s: []	p: 4	w: 0
0.00/0.16	      s 	s: [1]	p: 5	w: x1
0.00/0.16	      #le	s: [2]	p: 6	w: max(x1 + 2, x2 + 1)
0.00/0.16	      minus	s: [1]	p: 1	w: max(x1)
0.00/0.16	      mod	s: [1]	p: 2	w: max(x1)
0.00/0.16	      false	s: []	p: 4	w: 0
0.00/0.16	      true	s: []	p: 0	w: 0
0.00/0.16	      rand	s: []	p: 0	w: x1 + 1
0.00/0.16	      if_mod	s: [2,1]	p: 1	w: max(x1, x2)
0.00/0.16	      0 	s: []	p: 3	w: 0
0.00/0.16	      #minus	s: [2]	p: 0	w: max(x1 + 1, x2)
0.00/0.16	      #mod	s: [1]	p: 0	w: max(x1)
0.00/0.16	      #if_mod	s: [1,3,2]	p: 0	w: max(x1 + 1, x2, x3)
0.00/0.16	    Removed DPs: #3
0.00/0.16	Number of SCCs: 1, DPs: 2
0.00/0.16	  SCC { #1 #5 }
0.00/0.16	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.16	      le	s: []	p: 4	w: 0
0.00/0.16	      s 	s: [1]	p: 5	w: x1
0.00/0.16	      #le	s: [2]	p: 6	w: max(x1 + 2, x2 + 1)
0.00/0.16	      minus	s: [1]	p: 1	w: max(x1)
0.00/0.16	      mod	s: [1]	p: 2	w: max(x1)
0.00/0.16	      false	s: []	p: 4	w: 0
0.00/0.16	      true	s: []	p: 0	w: 0
0.00/0.16	      rand	s: []	p: 0	w: x1 + 1
0.00/0.16	      if_mod	s: [2,1]	p: 1	w: max(x1, x2)
0.00/0.16	      0 	s: []	p: 3	w: 0
0.00/0.16	      #minus	s: [2]	p: 0	w: max(x1 + 1, x2)
0.00/0.16	      #mod	s: [1]	p: 6	w: max(x1 + 1, x2 + 3)
0.00/0.16	      #if_mod	s: [2]	p: 6	w: max(x1 + 2, x2 + 1, x3 + 3)
0.00/0.16	    Removed DPs: #1
0.00/0.16	Number of SCCs: 0, DPs: 0
0.00/0.16	EOF