0.00/0.07	YES
0.00/0.07	Input TRS:
0.00/0.07	    AC symbols: plus times
0.00/0.07	    1: plus(x,0()) -> x
0.00/0.07	    2: plus(0(),y) -> y
0.00/0.07	    3: plus(s(x),y) -> s(plus(x,y))
0.00/0.07	    4: times(0(),y) -> 0()
0.00/0.07	    5: times(s(0()),y) -> y
0.00/0.07	    6: times(s(x),y) -> plus(y,times(x,y))
0.00/0.07	    7: div(0(),y) -> 0()
0.00/0.07	    8: div(x,y) -> quot(x,y,y)
0.00/0.07	    9: quot(0(),s(y),z) -> 0()
0.00/0.07	    10: quot(s(x),s(y),z) -> quot(x,y,z)
0.00/0.07	    11: quot(x,0(),s(z)) -> s(div(x,s(z)))
0.00/0.07	    12: div(div(x,y),z) -> div(x,times(y,z))
0.00/0.07	Number of strict rules: 12
0.00/0.07	Direct POLO(bPol) ... failed.
0.00/0.07	Uncurrying ... failed.
0.00/0.07	Dependency Pairs:
0.00/0.07	   #1: #times(s(x),y) -> #plus(y,times(x,y))
0.00/0.07	   #2: #times(s(x),y) -> #times(x,y)
0.00/0.07	   #3: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.07	   #4: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.07	   #5: #quot(x,0(),s(z)) -> #div(x,s(z))
0.00/0.07	   #6: #div(div(x,y),z) -> #div(x,times(y,z))
0.00/0.07	   #7: #div(div(x,y),z) -> #times(y,z)
0.00/0.07	   #8: #times(x,times(y,z)) ->= #times(times(x,y),z)
0.00/0.07	   #9: #times(x,times(y,z)) ->= #times(x,y)
0.00/0.07	   #10: #quot(s(x),s(y),z) -> #quot(x,y,z)
0.00/0.07	   #11: #plus(s(x),y) -> #plus(x,y)
0.00/0.07	   #12: #div(x,y) -> #quot(x,y,y)
0.00/0.07	Number of SCCs: 3, DPs: 10
0.00/0.07	  SCC { #2 #8 #9 }
0.00/0.07	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.07	      #div	s: []	p: 0
0.00/0.07	      s 	s: [1]	p: 0
0.00/0.07	      #plus	s: {}	p: 1
0.00/0.07	      div	s: []	p: 0
0.00/0.07	      #times	s: {1,2}	p: 2
0.00/0.07	      0 	s: []	p: 0
0.00/0.07	      quot	s: []	p: 0
0.00/0.07	      times	s: {1,2}	p: 2
0.00/0.07	      plus	s: {1,2}	p: 1
0.00/0.07	      #quot	s: []	p: 0
0.00/0.07	    USABLE RULES: { 1..6 13 14 }
0.00/0.07	    Removed DPs: #2 #9
0.00/0.07	Number of SCCs: 3, DPs: 8
0.00/0.07	  SCC { #8 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 2, DPs: 7
0.00/0.07	  SCC { #3 #4 #11 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      #div	w: 0
0.00/0.07	      s 	w: x1 + 1
0.00/0.07	      #plus	w: x1 + x2
0.00/0.07	      div	w: 0
0.00/0.07	      #times	w: 0
0.00/0.07	      0 	w: 2
0.00/0.07	      quot	w: 0
0.00/0.07	      times	w: 1
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      #quot	w: 0
0.00/0.07	    USABLE RULES: { 1..3 13 }
0.00/0.07	    Removed DPs: #4 #11
0.00/0.07	Number of SCCs: 2, DPs: 5
0.00/0.07	  SCC { #3 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 1, DPs: 4
0.00/0.07	  SCC { #5 #6 #10 #12 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      #div	w: x1
0.00/0.07	      s 	w: x1 + 1
0.00/0.07	      #plus	w: x1 + x2
0.00/0.07	      div	w: x1 + x2 + 1
0.00/0.07	      #times	w: 0
0.00/0.07	      0 	w: 2
0.00/0.07	      quot	w: 0
0.00/0.07	      times	w: 1
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      #quot	w: x1
0.00/0.07	    USABLE RULES: { 1..3 13 }
0.00/0.07	    Removed DPs: #6 #10
0.00/0.07	Number of SCCs: 1, DPs: 2
0.00/0.07	  SCC { #5 #12 }
0.00/0.07	POLO(Sum)... POLO(max)... succeeded.
0.00/0.07	      #div	w: max(x2 + 2)
0.00/0.07	      s 	w: 1
0.00/0.07	      #plus	w: 0
0.00/0.07	      div	w: 0
0.00/0.07	      #times	w: 0
0.00/0.07	      0 	w: 2
0.00/0.07	      quot	w: 0
0.00/0.07	      times	w: max(x1, x2)
0.00/0.07	      plus	w: max(x1, x2)
0.00/0.07	      #quot	w: max(x2 + 1)
0.00/0.07	    USABLE RULES: { }
0.00/0.07	    Removed DPs: #12
0.00/0.07	Number of SCCs: 0, DPs: 0
0.00/0.07	Next Dependency Pairs:
0.00/0.07	   #13: #plus(plus(0(),y),_1) -> #plus(y,_1)
0.00/0.07	   #14: #times(times(s(x),y),_1) -> #times(plus(y,times(x,y)),_1)
0.00/0.07	   #15: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.07	   #16: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.07	   #17: #times(x,times(y,z)) ->= #times(times(x,y),z)
0.00/0.07	   #18: #times(x,times(y,z)) ->= #times(x,y)
0.00/0.07	   #19: #times(times(s(0()),y),_1) -> #times(y,_1)
0.00/0.07	   #20: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
0.00/0.07	   #21: #plus(plus(x,0()),_1) -> #plus(x,_1)
0.00/0.07	   #22: #times(times(0(),y),_1) -> #times(0(),_1)
0.00/0.07	Number of SCCs: 2, DPs: 10
0.00/0.07	  SCC { #14 #17..19 #22 }
0.00/0.07	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.07	      #div	s: []	p: 0
0.00/0.07	      s 	s: [1]	p: 0
0.00/0.07	      #plus	s: {}	p: 1
0.00/0.07	      div	s: []	p: 0
0.00/0.07	      #times	s: {1,2}	p: 2
0.00/0.07	      0 	s: []	p: 0
0.00/0.07	      quot	s: []	p: 0
0.00/0.07	      times	s: {1,2}	p: 2
0.00/0.07	      plus	s: {1,2}	p: 1
0.00/0.07	      #quot	s: []	p: 0
0.00/0.07	    USABLE RULES: { 1..6 13 14 }
0.00/0.07	    Removed DPs: #14 #18 #19 #22
0.00/0.07	Number of SCCs: 2, DPs: 6
0.00/0.07	  SCC { #17 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 1, DPs: 5
0.00/0.07	  SCC { #13 #15 #16 #20 #21 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      #div	w: 0
0.00/0.07	      s 	w: 1
0.00/0.07	      #plus	w: x1 + x2
0.00/0.07	      div	w: 1
0.00/0.07	      #times	w: 0
0.00/0.07	      0 	w: 2
0.00/0.07	      quot	w: 0
0.00/0.07	      times	w: 1
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      #quot	w: 0
0.00/0.07	    USABLE RULES: { 1..3 13 }
0.00/0.07	    Removed DPs: #13 #16 #20 #21
0.00/0.07	Number of SCCs: 1, DPs: 1
0.00/0.07	  SCC { #15 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 0, DPs: 0
0.00/0.07	EOF