0.00/0.06	YES
0.00/0.07	Input TRS:
0.00/0.07	    AC symbols: + U *
0.00/0.07	    1: +(0(),x) -> x
0.00/0.07	    2: +(s(x),s(y)) -> s(s(+(x,y)))
0.00/0.07	    3: *(0(),x) -> 0()
0.00/0.07	    4: *(s(x),s(y)) -> s(+(+(x,y),*(x,y)))
0.00/0.07	    5: U(empty(),b) -> b
0.00/0.07	    6: sum(empty()) -> 0()
0.00/0.07	    7: sum(singl(x)) -> x
0.00/0.07	    8: sum(U(x,y)) -> +(sum(x),sum(y))
0.00/0.07	    9: prod(empty()) -> s(0())
0.00/0.07	    10: prod(singl(x)) -> x
0.00/0.07	    11: prod(U(x,y)) -> *(prod(x),prod(y))
0.00/0.07	Number of strict rules: 11
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: #+(s(x),s(y)) -> #+(x,y)
0.00/0.07	   #2: #U(x,U(y,z)) ->= #U(U(x,y),z)
0.00/0.07	   #3: #U(x,U(y,z)) ->= #U(x,y)
0.00/0.07	   #4: #prod(U(x,y)) -> #*(prod(x),prod(y))
0.00/0.07	   #5: #prod(U(x,y)) -> #prod(x)
0.00/0.07	   #6: #prod(U(x,y)) -> #prod(y)
0.00/0.07	   #7: #+(x,+(y,z)) ->= #+(+(x,y),z)
0.00/0.07	   #8: #+(x,+(y,z)) ->= #+(x,y)
0.00/0.07	   #9: #*(x,*(y,z)) ->= #*(*(x,y),z)
0.00/0.07	   #10: #*(x,*(y,z)) ->= #*(x,y)
0.00/0.07	   #11: #sum(U(x,y)) -> #+(sum(x),sum(y))
0.00/0.07	   #12: #sum(U(x,y)) -> #sum(x)
0.00/0.07	   #13: #sum(U(x,y)) -> #sum(y)
0.00/0.07	   #14: #*(s(x),s(y)) -> #+(+(x,y),*(x,y))
0.00/0.07	   #15: #*(s(x),s(y)) -> #+(x,y)
0.00/0.07	   #16: #*(s(x),s(y)) -> #*(x,y)
0.00/0.07	Number of SCCs: 5, DPs: 12
0.00/0.07	  SCC { #12 #13 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      prod	w: 0
0.00/0.07	      s 	w: 0
0.00/0.07	      #prod	w: 0
0.00/0.07	      #* 	w: 0
0.00/0.07	      #U 	w: 0
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 0
0.00/0.07	      singl	w: 0
0.00/0.07	      empty	w: 0
0.00/0.07	      + 	w: 0
0.00/0.07	      #sum	w: x1
0.00/0.07	      U 	w: x1 + x2 + 1
0.00/0.07	      #+ 	w: 0
0.00/0.07	      * 	w: 0
0.00/0.07	    USABLE RULES: { }
0.00/0.07	    Removed DPs: #12 #13
0.00/0.07	Number of SCCs: 4, DPs: 10
0.00/0.07	  SCC { #5 #6 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      prod	w: 0
0.00/0.07	      s 	w: 0
0.00/0.07	      #prod	w: x1
0.00/0.07	      #* 	w: 0
0.00/0.07	      #U 	w: 0
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 0
0.00/0.07	      singl	w: 0
0.00/0.07	      empty	w: 0
0.00/0.07	      + 	w: 0
0.00/0.07	      #sum	w: 0
0.00/0.07	      U 	w: x1 + x2 + 1
0.00/0.07	      #+ 	w: 0
0.00/0.07	      * 	w: 0
0.00/0.07	    USABLE RULES: { }
0.00/0.07	    Removed DPs: #5 #6
0.00/0.07	Number of SCCs: 3, DPs: 8
0.00/0.07	  SCC { #2 #3 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 2, DPs: 6
0.00/0.07	  SCC { #9 #10 #16 }
0.00/0.07	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.07	      prod	s: []	p: 0
0.00/0.07	      s 	s: [1]	p: 0
0.00/0.07	      #prod	s: []	p: 0
0.00/0.07	      #* 	s: {1,2}	p: 2
0.00/0.07	      #U 	s: {}	p: 0
0.00/0.07	      sum	s: []	p: 0
0.00/0.07	      0 	s: []	p: 0
0.00/0.07	      singl	s: []	p: 0
0.00/0.07	      empty	s: []	p: 0
0.00/0.07	      + 	s: {1,2}	p: 1
0.00/0.07	      #sum	s: []	p: 0
0.00/0.07	      U 	s: {}	p: 0
0.00/0.07	      #+ 	s: {}	p: 1
0.00/0.07	      * 	s: {1,2}	p: 2
0.00/0.07	    USABLE RULES: { 1..4 12 14 }
0.00/0.07	    Removed DPs: #10 #16
0.00/0.07	Number of SCCs: 2, DPs: 4
0.00/0.07	  SCC { #9 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 1, DPs: 3
0.00/0.07	  SCC { #1 #7 #8 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      prod	w: 0
0.00/0.07	      s 	w: x1 + 1
0.00/0.07	      #prod	w: 0
0.00/0.07	      #* 	w: 0
0.00/0.07	      #U 	w: 0
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 1
0.00/0.07	      singl	w: 0
0.00/0.07	      empty	w: 0
0.00/0.07	      + 	w: x1 + x2 + 1
0.00/0.07	      #sum	w: 0
0.00/0.07	      U 	w: 1
0.00/0.07	      #+ 	w: x1 + x2
0.00/0.07	      * 	w: x1 + x2
0.00/0.07	    USABLE RULES: { 1 2 12 }
0.00/0.07	    Removed DPs: #1 #8
0.00/0.07	Number of SCCs: 1, DPs: 1
0.00/0.07	  SCC { #7 }
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	   #17: #+(+(s(x),s(y)),_1) -> #+(s(s(+(x,y))),_1)
0.00/0.07	   #18: #U(x,U(y,z)) ->= #U(U(x,y),z)
0.00/0.07	   #19: #U(x,U(y,z)) ->= #U(x,y)
0.00/0.07	   #20: #+(x,+(y,z)) ->= #+(+(x,y),z)
0.00/0.07	   #21: #+(x,+(y,z)) ->= #+(x,y)
0.00/0.07	   #22: #*(x,*(y,z)) ->= #*(*(x,y),z)
0.00/0.07	   #23: #*(x,*(y,z)) ->= #*(x,y)
0.00/0.07	   #24: #U(U(empty(),b),_1) -> #U(b,_1)
0.00/0.07	   #25: #*(*(0(),x),_1) -> #*(0(),_1)
0.00/0.07	   #26: #+(+(0(),x),_1) -> #+(x,_1)
0.00/0.07	   #27: #*(*(s(x),s(y)),_1) -> #*(s(+(+(x,y),*(x,y))),_1)
0.00/0.07	Number of SCCs: 3, DPs: 11
0.00/0.07	  SCC { #18 #19 #24 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      prod	w: 0
0.00/0.07	      s 	w: x1 + 1
0.00/0.07	      #prod	w: 0
0.00/0.07	      #* 	w: 0
0.00/0.07	      #U 	w: x1 + x2
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 1
0.00/0.07	      singl	w: 0
0.00/0.07	      empty	w: 1
0.00/0.07	      + 	w: x1 + x2 + 1
0.00/0.07	      #sum	w: 0
0.00/0.07	      U 	w: x1 + x2 + 1
0.00/0.07	      #+ 	w: x1 + x2
0.00/0.07	      * 	w: x1 + x2
0.00/0.07	    USABLE RULES: { 1 2 5 12 13 }
0.00/0.07	    Removed DPs: #19 #24
0.00/0.07	Number of SCCs: 3, DPs: 9
0.00/0.07	  SCC { #18 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 2, DPs: 8
0.00/0.07	  SCC { #22 #23 #25 #27 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      prod	w: 0
0.00/0.07	      s 	w: 1
0.00/0.07	      #prod	w: 0
0.00/0.07	      #* 	w: x1 + x2
0.00/0.07	      #U 	w: x1 + x2
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 1
0.00/0.07	      singl	w: 0
0.00/0.07	      empty	w: 1
0.00/0.07	      + 	w: x1 + x2 + 1
0.00/0.07	      #sum	w: 0
0.00/0.07	      U 	w: x1 + x2 + 1
0.00/0.07	      #+ 	w: 0
0.00/0.07	      * 	w: x1 + x2 + 1
0.00/0.07	    USABLE RULES: { 3..5 13 14 }
0.00/0.07	    Removed DPs: #23 #25 #27
0.00/0.07	Number of SCCs: 2, DPs: 5
0.00/0.07	  SCC { #22 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 1, DPs: 4
0.00/0.07	  SCC { #17 #20 #21 #26 }
0.00/0.07	POLO(Sum)... succeeded.
0.00/0.07	      prod	w: 0
0.00/0.07	      s 	w: 1
0.00/0.07	      #prod	w: 0
0.00/0.07	      #* 	w: x1 + x2
0.00/0.07	      #U 	w: x1 + x2
0.00/0.07	      sum	w: 0
0.00/0.07	      0 	w: 1
0.00/0.07	      singl	w: 0
0.00/0.07	      empty	w: 1
0.00/0.07	      + 	w: x1 + x2 + 1
0.00/0.07	      #sum	w: 0
0.00/0.07	      U 	w: x1 + x2 + 1
0.00/0.07	      #+ 	w: x1 + x2
0.00/0.07	      * 	w: x1 + x2 + 1
0.00/0.07	    USABLE RULES: { 1..5 12..14 }
0.00/0.07	    Removed DPs: #17 #21 #26
0.00/0.07	Number of SCCs: 1, DPs: 1
0.00/0.07	  SCC { #20 }
0.00/0.07	only weak rules.
0.00/0.07	Number of SCCs: 0, DPs: 0
0.00/0.07	EOF