0.00/0.29	YES
0.00/0.30	Input TRS:
0.00/0.30	    1: le(0(),y) -> true()
0.00/0.30	    2: le(s(x),0()) -> false()
0.00/0.30	    3: le(s(x),s(y)) -> le(x,y)
0.00/0.30	    4: minus(0(),y) -> 0()
0.00/0.30	    5: minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
0.00/0.30	    6: if_minus(true(),s(x),y) -> 0()
0.00/0.30	    7: if_minus(false(),s(x),y) -> s(minus(x,y))
0.00/0.30	    8: mod(0(),y) -> 0()
0.00/0.30	    9: mod(s(x),0()) -> 0()
0.00/0.30	    10: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
0.00/0.30	    11: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
0.00/0.30	    12: if_mod(false(),s(x),s(y)) -> s(x)
0.00/0.30	    13: rand(x) ->= x
0.00/0.30	    14: rand(x) ->= rand(s(x))
0.00/0.30	Number of strict rules: 12
0.00/0.30	Direct POLO(bPol) ... failed.
0.00/0.30	Uncurrying le
0.00/0.30	1: le^1_0(y) -> true()
0.00/0.30	2: le^1_s(x,0()) -> false()
0.00/0.30	3: le^1_s(x,s(y)) -> le(x,y)
0.00/0.30	4: minus(0(),y) -> 0()
0.00/0.30	5: minus(s(x),y) -> if_minus(le^1_s(x,y),s(x),y)
0.00/0.30	6: if_minus(true(),s(x),y) -> 0()
0.00/0.30	7: if_minus(false(),s(x),y) -> s(minus(x,y))
0.00/0.30	8: mod(0(),y) -> 0()
0.00/0.30	9: mod(s(x),0()) -> 0()
0.00/0.30	10: mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
0.00/0.30	11: if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
0.00/0.30	12: if_mod(false(),s(x),s(y)) -> s(x)
0.00/0.30	13: rand(x) ->= x
0.00/0.30	14: rand(x) ->= rand(s(x))
0.00/0.30	15: le(0(),_1) ->= le^1_0(_1)
0.00/0.30	16: le(s(_1),_2) ->= le^1_s(_1,_2)
0.00/0.30	Number of strict rules: 12
0.00/0.30	Direct POLO(bPol) ... failed.
0.00/0.30	Dependency Pairs:
0.00/0.30	   #1: #if_mod(true(),s(x),s(y)) -> #mod(minus(x,y),s(y))
0.00/0.30	   #2: #if_mod(true(),s(x),s(y)) -> #minus(x,y)
0.00/0.30	   #3: #if_minus(false(),s(x),y) -> #minus(x,y)
0.00/0.30	   #4: #mod(s(x),s(y)) -> #if_mod(le(y,x),s(x),s(y))
0.00/0.30	   #5: #mod(s(x),s(y)) -> #le(y,x)
0.00/0.30	   #6: #minus(s(x),y) -> #if_minus(le^1_s(x,y),s(x),y)
0.00/0.30	   #7: #minus(s(x),y) -> #le^1_s(x,y)
0.00/0.30	   #8: #le(s(_1),_2) ->? #le^1_s(_1,_2)
0.00/0.30	   #9: #le^1_s(x,s(y)) -> #le(x,y)
0.00/0.30	   #10: #le(0(),_1) ->? #le^1_0(_1)
0.00/0.30	Number of SCCs: 3, DPs: 6
0.00/0.30	  SCC { #8 #9 }
0.00/0.30	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.30	      #le^1_s	s: 2
0.00/0.30	      le	s: [1,2]	p: 2	w: max(x1 + 2, x2 + 4)
0.00/0.30	      le^1_s	s: [1,2]	p: 2	w: max(x1 + 2, x2 + 4)
0.00/0.30	      s 	s: [1]	p: 2	w: x1
0.00/0.30	      #le	s: 2
0.00/0.30	      #le^1_0	s: []	p: 0	w: 0
0.00/0.30	      minus	s: [1]	p: 2	w: max(x1)
0.00/0.30	      mod	s: 1
0.00/0.30	      false	s: []	p: 1	w: 3
0.00/0.30	      true	s: []	p: 1	w: 1
0.00/0.30	      rand	s: []	p: 0	w: x1 + 1
0.00/0.30	      if_mod	s: 2
0.00/0.30	      0 	s: []	p: 2	w: 0
0.00/0.30	      #if_minus	s: [1,3,2]	p: 0	w: max(x1 + 1, x2, x3)
0.00/0.30	      #minus	s: []	p: 0	w: max(x2)
0.00/0.30	      #mod	s: []	p: 0	w: max(x2)
0.00/0.30	      #if_mod	s: []	p: 0	w: max(x1 + 1)
0.00/0.30	      le^1_0	s: []	p: 3	w: 1
0.00/0.30	      if_minus	s: [2]	p: 2	w: max(x2)
0.00/0.30	    Removed DPs: #9
0.00/0.30	Number of SCCs: 2, DPs: 4
0.00/0.30	  SCC { #3 #6 }
0.00/0.30	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.30	      #le^1_s	s: 2
0.00/0.30	      le	s: [1,2]	p: 2	w: max(x1 + 2, x2 + 4)
0.00/0.30	      le^1_s	s: [1,2]	p: 2	w: max(x1 + 2, x2 + 4)
0.00/0.30	      s 	s: [1]	p: 2	w: x1
0.00/0.30	      #le	s: 2
0.00/0.30	      #le^1_0	s: []	p: 0	w: 0
0.00/0.30	      minus	s: [1]	p: 2	w: max(x1)
0.00/0.30	      mod	s: 1
0.00/0.30	      false	s: []	p: 0	w: 3
0.00/0.30	      true	s: []	p: 1	w: 1
0.00/0.30	      rand	s: []	p: 0	w: x1 + 1
0.00/0.30	      if_mod	s: 2
0.00/0.30	      0 	s: []	p: 2	w: 0
0.00/0.30	      #if_minus	s: [3,2]	p: 1	w: max(x1 + 3, x2 + 5, x3 + 7)
0.00/0.30	      #minus	s: [2,1]	p: 1	w: max(x1 + 5, x2 + 7)
0.00/0.30	      #mod	s: []	p: 0	w: max(x2)
0.00/0.30	      #if_mod	s: []	p: 0	w: max(x1 + 1)
0.00/0.30	      le^1_0	s: []	p: 3	w: 1
0.00/0.30	      if_minus	s: [2]	p: 2	w: max(x2)
0.00/0.30	    Removed DPs: #3
0.00/0.30	Number of SCCs: 1, DPs: 2
0.00/0.30	  SCC { #1 #4 }
0.00/0.30	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.30	      #le^1_s	s: 2
0.00/0.30	      le	s: [2]	p: 4	w: max(x1 + 1, x2)
0.00/0.30	      le^1_s	s: [2]	p: 4	w: max(x1 + 1, x2)
0.00/0.30	      s 	s: [1]	p: 5	w: x1
0.00/0.30	      #le	s: 2
0.00/0.30	      #le^1_0	s: []	p: 0	w: 0
0.00/0.30	      minus	s: 1
0.00/0.30	      mod	s: []	p: 6	w: max(x1 + 3, x2 + 2)
0.00/0.30	      false	s: []	p: 1	w: 0
0.00/0.30	      true	s: []	p: 3	w: 0
0.00/0.30	      rand	s: []	p: 0	w: x1 + 1
0.00/0.30	      if_mod	s: []	p: 6	w: max(x1 + 1, x2 + 3, x3 + 2)
0.00/0.30	      0 	s: []	p: 2	w: 0
0.00/0.30	      #if_minus	s: [3,1]	p: 1	w: max(x1 + 3, x2 + 5, x3 + 7)
0.00/0.30	      #minus	s: [2]	p: 1	w: max(x2 + 7)
0.00/0.30	      #mod	s: [1]	p: 6	w: max(x1 + 2)
0.00/0.30	      #if_mod	s: [2]	p: 6	w: max(x2 + 2)
0.00/0.30	      le^1_0	s: []	p: 3	w: 0
0.00/0.30	      if_minus	s: 2
0.00/0.30	    Removed DPs: #1
0.00/0.30	Number of SCCs: 0, DPs: 0
0.00/0.30	EOF