YES
Input TRS:
AC symbols: plus
      1: minus(x,0()) -> x
      2: minus(s(x),s(y)) -> minus(x,y)
      3: minus(minus(x,y),z) -> minus(x,plus(y,z))
      4: quot(0(),s(y)) -> 0()
      5: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      6: plus(0(),y) -> y
      7: plus(s(x),y) -> s(plus(x,y))
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #minus(s(x),s(y)) -> #minus(x,y)
     #2: #plus(s(x),y) -> #plus(x,y)
     #3: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
     #4: #quot(s(x),s(y)) -> #minus(x,y)
     #5: #minus(minus(x,y),z) -> #minus(x,plus(y,z))
     #6: #minus(minus(x,y),z) -> #plus(y,z)
     #7: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #8: #plus(x,plus(y,z)) ->= #plus(x,y)
Number of SCCs: 3, DPs: 6
  SCC { #3 }
POLO(Sum)... succeeded.
      s 	w: x1 + 2
      minus	w: x1 + 1
      #plus	w: 0
      0 	w: 1
      quot	w: 0
      #minus	w: 0
      plus	w: 7720
      #quot	w: x1
    USABLE RULES: { 1..3 }
    Removed DPs: #3
Number of SCCs: 2, DPs: 5
  SCC { #1 #5 }
POLO(Sum)... succeeded.
      s 	w: x1 + 2
      minus	w: x1 + x2 + 8367
      #plus	w: 0
      0 	w: 0
      quot	w: 0
      #minus	w: x1 + x2
      plus	w: x1 + x2 + 8366
      #quot	w: x1
    USABLE RULES: { 1..3 6..8 }
    Removed DPs: #1 #5
Number of SCCs: 1, DPs: 3
  SCC { #2 #7 #8 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      minus	w: x1 + x2 + 32286
      #plus	w: x1 + x2
      0 	w: 0
      quot	w: 0
      #minus	w: x2
      plus	w: x1 + x2 + 1
      #quot	w: x1
    USABLE RULES: { 1..3 6..8 }
    Removed DPs: #2 #8
Number of SCCs: 1, DPs: 1
  SCC { #7 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #9: #plus(plus(0(),y),_1) -> #plus(y,_1)
     #10: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
     #11: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #12: #plus(x,plus(y,z)) ->= #plus(x,y)
Number of SCCs: 1, DPs: 4
  SCC { #9..12 }
POLO(Sum)... succeeded.
      s 	w: 28101
      minus	w: x1 + x2 + 1
      #plus	w: x1 + x2
      0 	w: 0
      quot	w: 0
      #minus	w: x2
      plus	w: x1 + x2 + 1
      #quot	w: 0
    USABLE RULES: { 1 6..8 }
    Removed DPs: #9 #10 #12
Number of SCCs: 1, DPs: 1
  SCC { #11 }
only weak rules.
Number of SCCs: 0, DPs: 0