0.00/0.07	YES
0.00/0.07	Input TRS:
0.00/0.07	    AC symbols: plus
0.00/0.07	    1: app(nil(),k) -> k
0.00/0.07	    2: app(l,nil()) -> l
0.00/0.07	    3: app(cons(x,l),k) -> cons(x,app(l,k))
0.00/0.07	    4: sum(cons(x,nil())) -> cons(x,nil())
0.00/0.07	    5: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
0.00/0.07	    6: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
0.00/0.07	    7: plus(0(),y) -> y
0.00/0.07	    8: plus(s(x),y) -> s(plus(x,y))
0.00/0.07	Number of strict rules: 8
0.00/0.07	Direct POLO(bPol) ... removes: 1 7 2
0.00/0.07	      s 	w: x1
0.00/0.07	      sum	w: x1
0.00/0.07	      0 	w: 1
0.00/0.07	      nil	w: 1
0.00/0.07	      plus	w: x1 + x2
0.00/0.07	      cons	w: x1 + x2
0.00/0.07	      app	w: 2 * x1 + x2
0.00/0.07	Number of strict rules: 5
0.00/0.07	Direct POLO(bPol) ... removes: 5
0.00/0.07	      s 	w: x1
0.00/0.07	      sum	w: x1
0.00/0.07	      0 	w: 0
0.00/0.07	      nil	w: 1
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      cons	w: 2 * x1 + x2 + 3
0.00/0.07	      app	w: x1 + 2 * x2
0.00/0.07	Number of strict rules: 4
0.00/0.07	Direct POLO(bPol) ... removes: 3
0.00/0.07	      s 	w: x1
0.00/0.07	      sum	w: x1
0.00/0.07	      0 	w: 0
0.00/0.07	      nil	w: 1
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      cons	w: 2 * x1 + x2 + 2
0.00/0.07	      app	w: 2 * x1 + x2 + 1
0.00/0.07	Number of strict rules: 3
0.00/0.07	Direct POLO(bPol) ... failed.
0.00/0.07	Uncurrying sum
0.00/0.07	AC symbols: plus
0.00/0.07	4: sum^1_cons(x,nil()) -> cons(x,nil())
0.00/0.07	6: sum^1_app(l,cons(x,cons(y,k))) -> sum^1_app(l,sum^1_cons(x,cons(y,k)))
0.00/0.07	8: plus(s(x),y) -> s(plus(x,y))
0.00/0.07	9: sum(cons(_1,_2)) ->= sum^1_cons(_1,_2)
0.00/0.07	10: sum(app(_1,_2)) ->= sum^1_app(_1,_2)
0.00/0.07	Number of strict rules: 3
0.00/0.07	Direct POLO(bPol) ... removes: 4 10 9 6
0.00/0.07	      sum^1_app	w: 2 * x1 + 2 * x2
0.00/0.07	      s 	w: x1
0.00/0.07	      sum^1_cons	w: 2 * x1 + x2 + 5
0.00/0.07	      sum	w: x1 + 3
0.00/0.07	      0 	w: 0
0.00/0.07	      nil	w: 1
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      cons	w: 2 * x1 + 2 * x2 + 3
0.00/0.07	      app	w: 2 * x1 + 2 * x2 + 1
0.00/0.07	Number of strict rules: 1
0.00/0.07	Direct POLO(bPol) ... failed.
0.00/0.07	Dependency Pairs:
0.00/0.07	   #1: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.07	   #2: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.07	   #3: #plus(s(x),y) -> #plus(x,y)
0.00/0.07	Number of SCCs: 1, DPs: 3
0.00/0.07	  SCC { #1..3 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      sum^1_app	w: 0
0.00/0.07	      s 	w: x1 + 1
0.00/0.07	      sum^1_cons	w: 0
0.00/0.07	      #plus	w: x1 + x2
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 0
0.00/0.07	      nil	w: 0
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      cons	w: 0
0.00/0.07	      app	w: 0
0.00/0.07	    USABLE RULES: { 8 11 }
0.00/0.07	    Removed DPs: #2 #3
0.00/0.07	Number of SCCs: 1, DPs: 1
0.00/0.07	  SCC { #1 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 0, DPs: 0
0.00/0.07	Next Dependency Pairs:
0.00/0.07	   #4: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.07	   #5: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.07	   #6: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
0.00/0.07	Number of SCCs: 1, DPs: 3
0.00/0.07	  SCC { #4..6 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      sum^1_app	w: 0
0.00/0.07	      s 	w: x1 + 1
0.00/0.07	      sum^1_cons	w: 0
0.00/0.07	      #plus	w: x1 + x2
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 0
0.00/0.07	      nil	w: 0
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      cons	w: 0
0.00/0.07	      app	w: 0
0.00/0.07	    USABLE RULES: { 8 11 }
0.00/0.07	    Removed DPs: #5
0.00/0.07	Number of SCCs: 1, DPs: 2
0.00/0.07	  SCC { #4 #6 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      sum^1_app	w: 0
0.00/0.07	      s 	w: 1
0.00/0.07	      sum^1_cons	w: 0
0.00/0.07	      #plus	w: x1 + x2
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 0
0.00/0.07	      nil	w: 0
0.00/0.07	      plus	w: x1 + x2 + 1
0.00/0.07	      cons	w: 0
0.00/0.07	      app	w: 0
0.00/0.07	    USABLE RULES: { 8 11 }
0.00/0.07	    Removed DPs: #6
0.00/0.07	Number of SCCs: 1, DPs: 1
0.00/0.07	  SCC { #4 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 0, DPs: 0
0.00/0.07	EOF