0.00/0.06	YES
0.00/0.06	Input TRS:
0.00/0.06	    AC symbols: plus
0.00/0.06	    1: minus(x,0()) -> x
0.00/0.06	    2: minus(s(x),s(y)) -> minus(x,y)
0.00/0.06	    3: minus(minus(x,y),z) -> minus(x,plus(y,z))
0.00/0.06	    4: quot(0(),s(y)) -> 0()
0.00/0.06	    5: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
0.00/0.06	    6: plus(0(),y) -> y
0.00/0.06	    7: plus(s(x),y) -> s(plus(x,y))
0.00/0.06	    8: app(nil(),k) -> k
0.00/0.06	    9: app(l,nil()) -> l
0.00/0.06	    10: app(cons(x,l),k) -> cons(x,app(l,k))
0.00/0.06	    11: sum(cons(x,nil())) -> cons(x,nil())
0.00/0.06	    12: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
0.00/0.06	    13: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
0.00/0.06	Number of strict rules: 13
0.00/0.06	Direct POLO(bPol) ... failed.
0.00/0.06	Uncurrying ... failed.
0.00/0.06	Dependency Pairs:
0.00/0.06	   #1: #minus(s(x),s(y)) -> #minus(x,y)
0.00/0.06	   #2: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k)))))
0.00/0.06	   #3: #sum(app(l,cons(x,cons(y,k)))) -> #app(l,sum(cons(x,cons(y,k))))
0.00/0.06	   #4: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k)))
0.00/0.06	   #5: #sum(cons(x,cons(y,l))) -> #sum(cons(plus(x,y),l))
0.00/0.06	   #6: #sum(cons(x,cons(y,l))) -> #plus(x,y)
0.00/0.06	   #7: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.06	   #8: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.06	   #9: #plus(s(x),y) -> #plus(x,y)
0.00/0.06	   #10: #app(cons(x,l),k) -> #app(l,k)
0.00/0.06	   #11: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
0.00/0.06	   #12: #quot(s(x),s(y)) -> #minus(x,y)
0.00/0.06	   #13: #minus(minus(x,y),z) -> #minus(x,plus(y,z))
0.00/0.06	   #14: #minus(minus(x,y),z) -> #plus(y,z)
0.00/0.06	Number of SCCs: 6, DPs: 9
0.00/0.06	  SCC { #10 }
0.00/0.06	POLO(Sum)... succeeded.
0.00/0.06	      s 	w: 0
0.00/0.06	      minus	w: 0
0.00/0.06	      #plus	w: 0
0.00/0.06	      sum	w: 0
0.00/0.06	      0 	w: 0
0.00/0.06	      quot	w: 0
0.00/0.06	      nil	w: 0
0.00/0.06	      #app	w: x1
0.00/0.06	      #minus	w: 0
0.00/0.06	      plus	w: 0
0.00/0.06	      cons	w: x2 + 1
0.00/0.06	      #quot	w: 0
0.00/0.06	      #sum	w: 0
0.00/0.06	      app	w: 0
0.00/0.06	    USABLE RULES: { }
0.00/0.06	    Removed DPs: #10
0.00/0.06	Number of SCCs: 5, DPs: 8
0.00/0.06	  SCC { #11 }
0.00/0.06	POLO(Sum)... succeeded.
0.00/0.06	      s 	w: x1 + 2
0.00/0.06	      minus	w: x1 + 1
0.00/0.06	      #plus	w: 0
0.00/0.06	      sum	w: 0
0.00/0.06	      0 	w: 1
0.00/0.06	      quot	w: 0
0.00/0.06	      nil	w: 0
0.00/0.06	      #app	w: 0
0.00/0.06	      #minus	w: 0
0.00/0.06	      plus	w: x1 + x2 + 1
0.00/0.06	      cons	w: 1
0.00/0.06	      #quot	w: x1
0.00/0.06	      #sum	w: 0
0.00/0.06	      app	w: 0
0.00/0.06	    USABLE RULES: { 1..3 6 7 14 }
0.00/0.06	    Removed DPs: #11
0.00/0.06	Number of SCCs: 4, DPs: 7
0.00/0.06	  SCC { #5 }
0.00/0.06	POLO(Sum)... succeeded.
0.00/0.06	      s 	w: x1 + 2
0.00/0.06	      minus	w: x1 + 1
0.00/0.06	      #plus	w: 0
0.00/0.06	      sum	w: 0
0.00/0.06	      0 	w: 1
0.00/0.06	      quot	w: 0
0.00/0.06	      nil	w: 0
0.00/0.06	      #app	w: 0
0.00/0.06	      #minus	w: 0
0.00/0.06	      plus	w: x1 + x2 + 1
0.00/0.06	      cons	w: x1 + x2 + 2
0.00/0.06	      #quot	w: x1
0.00/0.06	      #sum	w: x1
0.00/0.06	      app	w: 0
0.00/0.06	    USABLE RULES: { 1..3 6 7 14 }
0.00/0.06	    Removed DPs: #5
0.00/0.06	Number of SCCs: 3, DPs: 6
0.00/0.06	  SCC { #2 }
0.00/0.06	POLO(Sum)... succeeded.
0.00/0.06	      s 	w: x1 + 2
0.00/0.06	      minus	w: x1 + 1
0.00/0.06	      #plus	w: 0
0.00/0.06	      sum	w: 3
0.00/0.06	      0 	w: 1
0.00/0.06	      quot	w: 0
0.00/0.06	      nil	w: 1
0.00/0.06	      #app	w: 0
0.00/0.06	      #minus	w: 0
0.00/0.06	      plus	w: x1 + x2 + 1
0.00/0.06	      cons	w: x2 + 2
0.00/0.06	      #quot	w: x1
0.00/0.06	      #sum	w: x1
0.00/0.06	      app	w: x1 + x2 + 1
0.00/0.06	    USABLE RULES: { 1..3 6..12 14 }
0.00/0.06	    Removed DPs: #2
0.00/0.06	Number of SCCs: 2, DPs: 5
0.00/0.06	  SCC { #1 #13 }
0.00/0.06	POLO(Sum)... succeeded.
0.00/0.06	      s 	w: x1 + 2
0.00/0.06	      minus	w: x1 + x2 + 2
0.00/0.06	      #plus	w: 0
0.00/0.06	      sum	w: 3
0.00/0.06	      0 	w: 0
0.00/0.06	      quot	w: 0
0.00/0.06	      nil	w: 1
0.00/0.06	      #app	w: 0
0.00/0.06	      #minus	w: x1 + x2
0.00/0.06	      plus	w: x1 + x2 + 1
0.00/0.06	      cons	w: x2 + 2
0.00/0.06	      #quot	w: x1
0.00/0.06	      #sum	w: x1
0.00/0.06	      app	w: x1 + x2 + 1
0.00/0.06	    USABLE RULES: { 1..3 6..12 14 }
0.00/0.06	    Removed DPs: #1 #13
0.00/0.06	Number of SCCs: 1, DPs: 3
0.00/0.06	  SCC { #7..9 }
0.00/0.06	POLO(Sum)... succeeded.
0.00/0.06	      s 	w: x1 + 2
0.00/0.06	      minus	w: x1 + x2 + 1
0.00/0.06	      #plus	w: x1 + x2
0.00/0.06	      sum	w: 3
0.00/0.06	      0 	w: 1
0.00/0.06	      quot	w: 0
0.00/0.06	      nil	w: 1
0.00/0.06	      #app	w: 0
0.00/0.06	      #minus	w: 0
0.00/0.06	      plus	w: x1 + x2 + 1
0.00/0.06	      cons	w: x2 + 2
0.00/0.06	      #quot	w: x1
0.00/0.06	      #sum	w: x1
0.00/0.06	      app	w: x1 + x2 + 1
0.00/0.06	    USABLE RULES: { 1..3 6..12 14 }
0.00/0.06	    Removed DPs: #8 #9
0.00/0.06	Number of SCCs: 1, DPs: 1
0.00/0.06	  SCC { #7 }
0.00/0.06	only weak rules.
0.00/0.06	Number of SCCs: 0, DPs: 0
0.00/0.06	Next Dependency Pairs:
0.00/0.06	   #15: #plus(plus(0(),y),_1) -> #plus(y,_1)
0.00/0.06	   #16: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.06	   #17: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.06	   #18: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
0.00/0.06	Number of SCCs: 1, DPs: 4
0.00/0.06	  SCC { #15..18 }
0.00/0.06	POLO(Sum)... succeeded.
0.00/0.06	      s 	w: x1 + 2
0.00/0.06	      minus	w: x1 + x2 + 1
0.00/0.06	      #plus	w: x1 + x2
0.00/0.06	      sum	w: 3
0.00/0.06	      0 	w: 1
0.00/0.06	      quot	w: 0
0.00/0.06	      nil	w: 1
0.00/0.06	      #app	w: 0
0.00/0.06	      #minus	w: 0
0.00/0.06	      plus	w: x1 + x2 + 1
0.00/0.06	      cons	w: x2 + 2
0.00/0.06	      #quot	w: x1
0.00/0.06	      #sum	w: x1
0.00/0.06	      app	w: x1 + x2 + 1
0.00/0.06	    USABLE RULES: { 1..3 6..12 14 }
0.00/0.06	    Removed DPs: #15 #17
0.00/0.06	Number of SCCs: 1, DPs: 2
0.00/0.06	  SCC { #16 #18 }
0.00/0.06	POLO(Sum)... succeeded.
0.00/0.06	      s 	w: 1
0.00/0.06	      minus	w: x1 + x2 + 1
0.00/0.06	      #plus	w: x1 + x2
0.00/0.06	      sum	w: 3
0.00/0.06	      0 	w: 1
0.00/0.06	      quot	w: 0
0.00/0.06	      nil	w: 1
0.00/0.06	      #app	w: 0
0.00/0.06	      #minus	w: 0
0.00/0.06	      plus	w: x1 + x2 + 1
0.00/0.06	      cons	w: x2 + 2
0.00/0.06	      #quot	w: 0
0.00/0.06	      #sum	w: x1
0.00/0.06	      app	w: x1 + x2 + 1
0.00/0.06	    USABLE RULES: { 6..12 14 }
0.00/0.06	    Removed DPs: #18
0.00/0.06	Number of SCCs: 1, DPs: 1
0.00/0.06	  SCC { #16 }
0.00/0.06	only weak rules.
0.00/0.06	Number of SCCs: 0, DPs: 0
0.00/0.06	EOF