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