MAYBE
Input TRS:
AC symbols: plus times
      1: zero(0()) -> 0()
      2: plus(x,0()) -> x
      3: plus(zero(x),zero(y)) -> zero(plus(x,y))
      4: plus(zero(x),un(y)) -> un(plus(x,y))
      5: plus(zero(x),j(y)) -> j(plus(x,y))
      6: plus(un(x),j(y)) -> zero(plus(x,y))
      7: plus(un(x),un(y)) -> j(plus(x,plus(y,un(0()))))
      8: plus(j(x),j(y)) -> un(plus(x,plus(y,j(0()))))
      9: minus(x,y) -> plus(x,neg(y))
      10: neg(0()) -> 0()
      11: neg(zero(x)) -> zero(neg(x))
      12: neg(un(x)) -> j(neg(x))
      13: neg(j(x)) -> un(neg(x))
      14: times(x,0()) -> 0()
      15: times(x,times(0(),z)) -> times(0(),z)
      16: times(x,zero(y)) -> zero(times(x,y))
      17: times(x,times(zero(y),z)) -> times(zero(times(x,y)),z)
      18: times(x,un(y)) -> plus(x,zero(times(x,y)))
      19: times(x,times(un(y),z)) -> times(plus(x,zero(times(x,y))),z)
      20: times(x,j(y)) -> plus(zero(times(x,y)),neg(x))
      21: times(x,times(j(y),z)) -> times(plus(zero(times(x,y)),neg(x)),z)
Number of strict rules: 21
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #plus(un(x),j(y)) -> #zero(plus(x,y))
     #2: #plus(un(x),j(y)) -> #plus(x,y)
     #3: #neg(j(x)) -> #neg(x)
     #4: #minus(x,y) -> #plus(x,neg(y))
     #5: #minus(x,y) -> #neg(y)
     #6: #neg(zero(x)) -> #zero(neg(x))
     #7: #neg(zero(x)) -> #neg(x)
     #8: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #9: #times(x,times(y,z)) ->= #times(x,y)
     #10: #neg(un(x)) -> #neg(x)
     #11: #times(x,j(y)) -> #plus(zero(times(x,y)),neg(x))
     #12: #times(x,j(y)) -> #zero(times(x,y))
     #13: #times(x,j(y)) -> #times(x,y)
     #14: #times(x,j(y)) -> #neg(x)
     #15: #plus(un(x),un(y)) -> #plus(x,plus(y,un(0())))
     #16: #plus(un(x),un(y)) -> #plus(y,un(0()))
     #17: #plus(zero(x),j(y)) -> #plus(x,y)
     #18: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #19: #plus(x,plus(y,z)) ->= #plus(x,y)
     #20: #times(x,times(zero(y),z)) -> #times(zero(times(x,y)),z)
     #21: #times(x,times(zero(y),z)) -> #zero(times(x,y))
     #22: #times(x,times(zero(y),z)) -> #times(x,y)
     #23: #times(x,times(un(y),z)) -> #times(plus(x,zero(times(x,y))),z)
     #24: #times(x,times(un(y),z)) -> #plus(x,zero(times(x,y)))
     #25: #times(x,times(un(y),z)) -> #zero(times(x,y))
     #26: #times(x,times(un(y),z)) -> #times(x,y)
     #27: #times(x,times(j(y),z)) -> #times(plus(zero(times(x,y)),neg(x)),z)
     #28: #times(x,times(j(y),z)) -> #plus(zero(times(x,y)),neg(x))
     #29: #times(x,times(j(y),z)) -> #zero(times(x,y))
     #30: #times(x,times(j(y),z)) -> #times(x,y)
     #31: #times(x,times(j(y),z)) -> #neg(x)
     #32: #times(x,zero(y)) -> #zero(times(x,y))
     #33: #times(x,zero(y)) -> #times(x,y)
     #34: #plus(zero(x),zero(y)) -> #zero(plus(x,y))
     #35: #plus(zero(x),zero(y)) -> #plus(x,y)
     #36: #plus(j(x),j(y)) -> #plus(x,plus(y,j(0())))
     #37: #plus(j(x),j(y)) -> #plus(y,j(0()))
     #38: #plus(zero(x),un(y)) -> #plus(x,y)
     #39: #times(x,un(y)) -> #plus(x,zero(times(x,y)))
     #40: #times(x,un(y)) -> #zero(times(x,y))
     #41: #times(x,un(y)) -> #times(x,y)
Number of SCCs: 3, DPs: 24
  SCC { #3 #7 #10 }
POLO(Sum)... succeeded.
      zero	w: x1 + 1
      minus	w: 0
      #plus	w: 0
      #times	w: 0
      0 	w: 0
      times	w: 0
      neg	w: 0
      j 	w: x1 + 1
      #minus	w: 0
      plus	w: 0
      #neg	w: x1
      #zero	w: 0
      un	w: x1 + 1
    USABLE RULES: { }
    Removed DPs: #3 #7 #10
Number of SCCs: 2, DPs: 21
  SCC { #2 #15..19 #35..38 }
POLO(Sum)... succeeded.
      zero	w: x1 + 10451
      minus	w: 0
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 0
      times	w: 0
      neg	w: 0
      j 	w: x1 + 32286
      #minus	w: 0
      plus	w: x1 + x2
      #neg	w: 0
      #zero	w: 0
      un	w: x1 + 32286
    USABLE RULES: { 1..8 22 }
    Removed DPs: #2 #15..17 #35..38
Number of SCCs: 2, DPs: 13
  SCC { #18 #19 }
only weak rules.
Number of SCCs: 1, DPs: 11
  SCC { #8 #9 #13 #20 #22 #23 #26 #27 #30 #33 #41 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      zero	w: max(x1, 0)
      minus	w: 0
      #plus	w: 0
      #times	w: max(x1 + x2 + 2, 0)
      0 	w: 0
      times	w: max(x1 + x2 + 7721, 0)
      neg	w: max(x1 - 1, 0)
      j 	w: max(x1, 0)
      #minus	w: max(x1 - 1, 0)
      plus	w: max(x1, x2, 0)
      #neg	w: 0
      #zero	w: max(x1 - 1, 0)
      un	w: max(x1, 0)
    USABLE RULES: { 1..8 10..23 }
    Removed DPs: #9 #22 #26 #30
Number of SCCs: 1, DPs: 7
  SCC { #8 #13 #20 #23 #27 #33 #41 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.