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