YES
Input TRS:
AC symbols: inter union
C symbols: eq
      1: if(true(),x,y) -> x
      2: if(false(),x,y) -> y
      3: eq(0(),0()) -> true()
      4: eq(0(),s(x)) -> false()
      5: eq(s(x),s(y)) -> eq(x,y)
      6: union(empty(),x) -> x
      7: inter(empty(),x) -> empty()
      8: inter(union(y,z),x) -> union(inter(x,y),inter(x,z))
      9: inter(singl(x),singl(y)) -> if(eq(x,y),singl(x),empty())
Number of strict rules: 9
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #inter(singl(x),singl(y)) -> #if(eq(x,y),singl(x),empty())
     #2: #inter(singl(x),singl(y)) -> #eq(x,y)
     #3: #union(x,union(y,z)) ->= #union(union(x,y),z)
     #4: #union(x,union(y,z)) ->= #union(x,y)
     #5: #inter(x,inter(y,z)) ->= #inter(inter(x,y),z)
     #6: #inter(x,inter(y,z)) ->= #inter(x,y)
     #7: #eq(s(x),s(y)) -> #eq(x,y)
     #8: #inter(union(y,z),x) -> #union(inter(x,y),inter(x,z))
     #9: #inter(union(y,z),x) -> #inter(x,y)
     #10: #inter(union(y,z),x) -> #inter(x,z)
Number of SCCs: 3, DPs: 7
  SCC { #7 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      eq	w: 0
      false	w: 0
      true	w: 0
      #eq	w: x1 + x2
      if	w: 0
      0 	w: 0
      union	w: 0
      singl	w: 0
      #if	w: 0
      inter	w: 0
      empty	w: 0
      #inter	w: 0
      #union	w: 0
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 2, DPs: 6
  SCC { #3 #4 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #5 #6 #9 #10 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      eq	s: {}	p: 2
      false	s: []	p: 1
      true	s: []	p: 1
      #eq	s: {}	p: 0
      if	s: [3,2]	p: 4
      0 	s: []	p: 0
      union	s: {1,2}	p: 0
      singl	s: [1]	p: 3
      #if	s: [1,3,2]	p: 0
      inter	s: {1,2}	p: 5
      empty	s: []	p: 3
      #inter	s: {1,2}	p: 5
      #union	s: {}	p: 0
    USABLE RULES: { 1 2 6..11 }
    Removed DPs: #6 #9 #10
Number of SCCs: 1, DPs: 1
  SCC { #5 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #11: #union(union(empty(),x),_1) -> #union(x,_1)
     #12: #inter(inter(singl(x),singl(y)),_1) -> #inter(if(eq(x,y),singl(x),empty()),_1)
     #13: #union(x,union(y,z)) ->= #union(union(x,y),z)
     #14: #union(x,union(y,z)) ->= #union(x,y)
     #15: #inter(inter(empty(),x),_1) -> #inter(empty(),_1)
     #16: #inter(x,inter(y,z)) ->= #inter(inter(x,y),z)
     #17: #inter(x,inter(y,z)) ->= #inter(x,y)
     #18: #inter(inter(union(y,z),x),_1) -> #inter(union(inter(x,y),inter(x,z)),_1)
Number of SCCs: 2, DPs: 8
  SCC { #11 #13 #14 }
POLO(Sum)... succeeded.
      s 	w: 0
      eq	w: x1 + x2 + 1
      false	w: 3
      true	w: 4
      #eq	w: 0
      if	w: x1 + x2 + x3 + 1
      0 	w: 1
      union	w: x1 + x2 + 8366
      singl	w: 1
      #if	w: 0
      inter	w: x1 + x2 + 1
      empty	w: 1
      #inter	w: 0
      #union	w: x1 + x2
    USABLE RULES: { 6 11 }
    Removed DPs: #11 #14
Number of SCCs: 2, DPs: 6
  SCC { #13 }
only weak rules.
Number of SCCs: 1, DPs: 5
  SCC { #12 #15..18 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      eq	s: {}	p: 2
      false	s: []	p: 1
      true	s: []	p: 1
      #eq	s: {}	p: 0
      if	s: [3,2]	p: 2
      0 	s: []	p: 0
      union	s: {1,2}	p: 0
      singl	s: [1]	p: 4
      #if	s: [1,3,2]	p: 0
      inter	s: {1,2}	p: 3
      empty	s: []	p: 4
      #inter	s: {1,2}	p: 3
      #union	s: {}	p: 0
    USABLE RULES: { 1 2 6..11 }
    Removed DPs: #12 #15 #17 #18
Number of SCCs: 1, DPs: 1
  SCC { #16 }
only weak rules.
Number of SCCs: 0, DPs: 0