0.00/0.09	MAYBE
0.00/0.09	Input TRS:
0.00/0.09	    AC symbols: + U *
0.00/0.09	    1: 0(\#()) -> \#()
0.00/0.09	    2: +(\#(),x) -> x
0.00/0.09	    3: +(0(x),0(y)) -> 0(+(x,y))
0.00/0.09	    4: +(0(x),1(y)) -> 1(+(x,y))
0.00/0.09	    5: +(1(x),1(y)) -> 0(+(1(\#()),+(x,y)))
0.00/0.09	    6: *(\#(),x) -> \#()
0.00/0.09	    7: *(0(x),y) -> 0(*(x,y))
0.00/0.09	    8: *(1(x),y) -> +(0(*(x,y)),y)
0.00/0.09	    9: U(empty(),b) -> b
0.00/0.09	    10: sum(empty()) -> 0(\#())
0.00/0.09	    11: sum(singl(x)) -> x
0.00/0.09	    12: sum(U(x,y)) -> +(sum(x),sum(y))
0.00/0.09	    13: prod(empty()) -> 1(\#())
0.00/0.09	    14: prod(singl(x)) -> x
0.00/0.09	    15: prod(U(x,y)) -> *(prod(x),prod(y))
0.00/0.09	Number of strict rules: 15
0.00/0.09	Direct POLO(bPol) ... failed.
0.00/0.09	Uncurrying ... failed.
0.00/0.09	Dependency Pairs:
0.00/0.09	   #1: #sum(U(x,y)) -> #+(sum(x),sum(y))
0.00/0.09	   #2: #sum(U(x,y)) -> #sum(x)
0.00/0.09	   #3: #sum(U(x,y)) -> #sum(y)
0.00/0.09	   #4: #*(0(x),y) -> #0(*(x,y))
0.00/0.09	   #5: #*(0(x),y) -> #*(x,y)
0.00/0.09	   #6: #sum(empty()) -> #0(\#())
0.00/0.09	   #7: #+(1(x),1(y)) -> #0(+(1(\#()),+(x,y)))
0.00/0.09	   #8: #+(1(x),1(y)) -> #+(1(\#()),+(x,y))
0.00/0.09	   #9: #+(1(x),1(y)) -> #+(x,y)
0.00/0.09	   #10: #U(x,U(y,z)) ->= #U(U(x,y),z)
0.00/0.09	   #11: #U(x,U(y,z)) ->= #U(x,y)
0.00/0.09	   #12: #+(x,+(y,z)) ->= #+(+(x,y),z)
0.00/0.09	   #13: #+(x,+(y,z)) ->= #+(x,y)
0.00/0.09	   #14: #+(0(x),0(y)) -> #0(+(x,y))
0.00/0.09	   #15: #+(0(x),0(y)) -> #+(x,y)
0.00/0.09	   #16: #*(1(x),y) -> #+(0(*(x,y)),y)
0.00/0.09	   #17: #*(1(x),y) -> #0(*(x,y))
0.00/0.09	   #18: #*(1(x),y) -> #*(x,y)
0.00/0.09	   #19: #prod(U(x,y)) -> #*(prod(x),prod(y))
0.00/0.09	   #20: #prod(U(x,y)) -> #prod(x)
0.00/0.09	   #21: #prod(U(x,y)) -> #prod(y)
0.00/0.09	   #22: #+(0(x),1(y)) -> #+(x,y)
0.00/0.09	   #23: #*(x,*(y,z)) ->= #*(*(x,y),z)
0.00/0.09	   #24: #*(x,*(y,z)) ->= #*(x,y)
0.00/0.09	Number of SCCs: 5, DPs: 16
0.00/0.09	  SCC { #2 #3 }
0.00/0.09	POLO(Sum)... succeeded.
0.00/0.09	      #0 	w: 0
0.00/0.09	      1 	w: 0
0.00/0.09	      prod	w: 0
0.00/0.09	      #prod	w: 0
0.00/0.09	      #* 	w: 0
0.00/0.09	      \#	w: 0
0.00/0.09	      #U 	w: 0
0.00/0.09	      sum	w: 0
0.00/0.09	      0 	w: 0
0.00/0.09	      singl	w: 0
0.00/0.09	      empty	w: 0
0.00/0.09	      + 	w: 0
0.00/0.09	      #sum	w: x1
0.00/0.09	      U 	w: x1 + x2 + 1
0.00/0.09	      #+ 	w: 0
0.00/0.09	      * 	w: 0
0.00/0.09	    USABLE RULES: { }
0.00/0.09	    Removed DPs: #2 #3
0.00/0.09	Number of SCCs: 4, DPs: 14
0.00/0.09	  SCC { #20 #21 }
0.00/0.09	POLO(Sum)... succeeded.
0.00/0.09	      #0 	w: 0
0.00/0.09	      1 	w: 0
0.00/0.09	      prod	w: 0
0.00/0.09	      #prod	w: x1
0.00/0.09	      #* 	w: 0
0.00/0.09	      \#	w: 0
0.00/0.09	      #U 	w: 0
0.00/0.09	      sum	w: 0
0.00/0.09	      0 	w: 0
0.00/0.09	      singl	w: 0
0.00/0.09	      empty	w: 0
0.00/0.09	      + 	w: 0
0.00/0.09	      #sum	w: 0
0.00/0.09	      U 	w: x1 + x2 + 1
0.00/0.09	      #+ 	w: 0
0.00/0.09	      * 	w: 0
0.00/0.09	    USABLE RULES: { }
0.00/0.09	    Removed DPs: #20 #21
0.00/0.09	Number of SCCs: 3, DPs: 12
0.00/0.09	  SCC { #10 #11 }
0.00/0.09	only weak rules.
0.00/0.09	Number of SCCs: 2, DPs: 10
0.00/0.09	  SCC { #5 #18 #23 #24 }
0.00/0.09	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
0.00/0.09	      #0 	w: max(x1 - 1, 0)
0.00/0.09	      1 	w: max(x1, 0)
0.00/0.09	      prod	w: 0
0.00/0.09	      #prod	w: max(x1 - 1, 0)
0.00/0.09	      #* 	w: max(x1 + x2 - 1, 0)
0.00/0.09	      \#	w: 0
0.00/0.09	      #U 	w: max(x1 + x2 - 1, 0)
0.00/0.09	      sum	w: 0
0.00/0.09	      0 	w: max(x1, 0)
0.00/0.09	      singl	w: max(x1 - 1, 0)
0.00/0.09	      empty	w: 0
0.00/0.09	      + 	w: max(x1, x2, 0)
0.00/0.09	      #sum	w: 0
0.00/0.09	      U 	w: 0
0.00/0.09	      #+ 	w: 0
0.00/0.09	      * 	w: max(x1 + x2 + 2, 0)
0.00/0.09	    USABLE RULES: { 1..8 16 18 }
0.00/0.09	    Removed DPs: #24
0.00/0.09	Number of SCCs: 2, DPs: 9
0.00/0.09	  SCC { #5 #18 #23 }
0.00/0.09	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
0.00/0.09	Finding a loop...  failed.
0.00/0.09	EOF