0.00/0.12	YES
0.00/0.12	Input TRS:
0.00/0.12	    AC symbols: inter union
0.00/0.12	    C symbols: eq
0.00/0.12	    1: if(true(),x,y) -> x
0.00/0.12	    2: if(false(),x,y) -> y
0.00/0.12	    3: eq(0(),0()) -> true()
0.00/0.12	    4: eq(0(),s(x)) -> false()
0.00/0.12	    5: eq(s(x),s(y)) -> eq(x,y)
0.00/0.12	    6: union(empty(),x) -> x
0.00/0.12	    7: inter(empty(),x) -> empty()
0.00/0.12	    8: inter(union(y,z),x) -> union(inter(x,y),inter(x,z))
0.00/0.12	    9: inter(singl(x),singl(y)) -> if(eq(x,y),singl(x),empty())
0.00/0.12	Number of strict rules: 9
0.00/0.12	Direct POLO(bPol) ... failed.
0.00/0.12	Uncurrying ... failed.
0.00/0.12	Dependency Pairs:
0.00/0.12	   #1: #inter(singl(x),singl(y)) -> #if(eq(x,y),singl(x),empty())
0.00/0.12	   #2: #inter(singl(x),singl(y)) -> #eq(x,y)
0.00/0.12	   #3: #union(x,union(y,z)) ->= #union(union(x,y),z)
0.00/0.12	   #4: #union(x,union(y,z)) ->= #union(x,y)
0.00/0.12	   #5: #inter(x,inter(y,z)) ->= #inter(inter(x,y),z)
0.00/0.12	   #6: #inter(x,inter(y,z)) ->= #inter(x,y)
0.00/0.12	   #7: #eq(s(x),s(y)) -> #eq(x,y)
0.00/0.12	   #8: #inter(union(y,z),x) -> #union(inter(x,y),inter(x,z))
0.00/0.12	   #9: #inter(union(y,z),x) -> #inter(x,y)
0.00/0.12	   #10: #inter(union(y,z),x) -> #inter(x,z)
0.00/0.12	Number of SCCs: 3, DPs: 7
0.00/0.12	  SCC { #7 }
0.00/0.12	POLO(Sum)... succeeded.
0.00/0.12	      s 	w: x1 + 1
0.00/0.12	      eq	w: 0
0.00/0.12	      false	w: 0
0.00/0.12	      true	w: 0
0.00/0.12	      #eq	w: x1 + x2
0.00/0.12	      if	w: 0
0.00/0.12	      0 	w: 0
0.00/0.12	      union	w: 0
0.00/0.12	      singl	w: 0
0.00/0.12	      #if	w: 0
0.00/0.12	      inter	w: 0
0.00/0.12	      empty	w: 0
0.00/0.12	      #inter	w: 0
0.00/0.12	      #union	w: 0
0.00/0.12	    USABLE RULES: { }
0.00/0.12	    Removed DPs: #7
0.00/0.12	Number of SCCs: 2, DPs: 6
0.00/0.12	  SCC { #3 #4 }
0.00/0.12	only weak rules.
0.00/0.12	Number of SCCs: 1, DPs: 4
0.00/0.12	  SCC { #5 #6 #9 #10 }
0.00/0.12	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.12	      s 	s: [1]	p: 2
0.00/0.12	      eq	s: {1,2}	p: 1
0.00/0.12	      false	s: []	p: 0
0.00/0.12	      true	s: []	p: 0
0.00/0.12	      #eq	s: {}	p: 0
0.00/0.12	      if	s: [2,3]	p: 3
0.00/0.12	      0 	s: []	p: 0
0.00/0.12	      union	s: {1,2}	p: 0
0.00/0.12	      singl	s: 1
0.00/0.12	      #if	s: []	p: 0
0.00/0.12	      inter	s: {1,2}	p: 4
0.00/0.12	      empty	s: []	p: 2
0.00/0.12	      #inter	s: {1,2}	p: 4
0.00/0.12	      #union	s: {}	p: 0
0.00/0.12	    USABLE RULES: { 1 2 6..11 }
0.00/0.12	    Removed DPs: #6 #9 #10
0.00/0.12	Number of SCCs: 1, DPs: 1
0.00/0.12	  SCC { #5 }
0.00/0.12	only weak rules.
0.00/0.12	Number of SCCs: 0, DPs: 0
0.00/0.12	Next Dependency Pairs:
0.00/0.12	   #11: #union(union(empty(),x),_1) -> #union(x,_1)
0.00/0.12	   #12: #inter(inter(singl(x),singl(y)),_1) -> #inter(if(eq(x,y),singl(x),empty()),_1)
0.00/0.12	   #13: #union(x,union(y,z)) ->= #union(union(x,y),z)
0.00/0.12	   #14: #union(x,union(y,z)) ->= #union(x,y)
0.00/0.12	   #15: #inter(inter(empty(),x),_1) -> #inter(empty(),_1)
0.00/0.12	   #16: #inter(x,inter(y,z)) ->= #inter(inter(x,y),z)
0.00/0.12	   #17: #inter(x,inter(y,z)) ->= #inter(x,y)
0.00/0.12	   #18: #inter(inter(union(y,z),x),_1) -> #inter(union(inter(x,y),inter(x,z)),_1)
0.00/0.12	Number of SCCs: 2, DPs: 8
0.00/0.12	  SCC { #11 #13 #14 }
0.00/0.12	POLO(Sum)... succeeded.
0.00/0.12	      s 	w: 1
0.00/0.12	      eq	w: x1 + x2 + 1
0.00/0.12	      false	w: 4
0.00/0.12	      true	w: 4
0.00/0.12	      #eq	w: 0
0.00/0.12	      if	w: x2 + x3
0.00/0.12	      0 	w: 1
0.00/0.12	      union	w: x1 + x2 + 1
0.00/0.12	      singl	w: x1 + 1
0.00/0.12	      #if	w: 0
0.00/0.12	      inter	w: x1 + x2 + 1
0.00/0.12	      empty	w: 1
0.00/0.12	      #inter	w: 0
0.00/0.12	      #union	w: x1 + x2
0.00/0.12	    USABLE RULES: { 1 2 6 11 }
0.00/0.12	    Removed DPs: #11 #14
0.00/0.12	Number of SCCs: 2, DPs: 6
0.00/0.12	  SCC { #13 }
0.00/0.12	only weak rules.
0.00/0.12	Number of SCCs: 1, DPs: 5
0.00/0.12	  SCC { #12 #15..18 }
0.00/0.12	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.12	      s 	s: [1]	p: 2
0.00/0.12	      eq	s: {1,2}	p: 1
0.00/0.12	      false	s: []	p: 0
0.00/0.12	      true	s: []	p: 0
0.00/0.12	      #eq	s: {}	p: 0
0.00/0.12	      if	s: [2,3]	p: 3
0.00/0.12	      0 	s: []	p: 0
0.00/0.12	      union	s: {1,2}	p: 0
0.00/0.12	      singl	s: 1
0.00/0.12	      #if	s: []	p: 0
0.00/0.12	      inter	s: {1,2}	p: 4
0.00/0.12	      empty	s: []	p: 2
0.00/0.12	      #inter	s: {1,2}	p: 4
0.00/0.12	      #union	s: {}	p: 0
0.00/0.12	    USABLE RULES: { 1 2 6..11 }
0.00/0.12	    Removed DPs: #12 #15 #17 #18
0.00/0.12	Number of SCCs: 1, DPs: 1
0.00/0.12	  SCC { #16 }
0.00/0.12	only weak rules.
0.00/0.12	Number of SCCs: 0, DPs: 0
0.00/0.12	EOF