MAYBE
Input TRS:
      1: min(x,0()) -> 0()
      2: min(0(),y) -> 0()
      3: min(s(x),s(y)) -> s(min(x,y))
      4: max(x,0()) -> x
      5: max(0(),y) -> y
      6: max(s(x),s(y)) -> s(max(x,y))
      7: -(x,0()) -> x
      8: -(s(x),s(y)) -> -(x,y)
      9: gcd(nil()) -> 0()
      10: gcd(cons(x,nil())) -> x
      11: gcd(cons(0(),y)) -> gcd(y)
      12: gcd(cons(x,cons(0(),y))) -> gcd(cons(x,y))
      13: gcd(cons(s(x),cons(s(y),z))) -> gcd(cons(-(max(x,y),min(x,y)),cons(s(min(x,y)),z)))
      14: cons(x,cons(y,z)) ->= cons(y,cons(x,z))
Number of strict rules: 13
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #max(s(x),s(y)) -> #max(x,y)
     #2: #gcd(cons(s(x),cons(s(y),z))) -> #gcd(cons(-(max(x,y),min(x,y)),cons(s(min(x,y)),z)))
     #3: #gcd(cons(s(x),cons(s(y),z))) -> #-(max(x,y),min(x,y))
     #4: #gcd(cons(s(x),cons(s(y),z))) -> #max(x,y)
     #5: #gcd(cons(s(x),cons(s(y),z))) -> #min(x,y)
     #6: #gcd(cons(s(x),cons(s(y),z))) -> #min(x,y)
     #7: #gcd(cons(0(),y)) -> #gcd(y)
     #8: #gcd(cons(x,cons(0(),y))) -> #gcd(cons(x,y))
     #9: #min(s(x),s(y)) -> #min(x,y)
     #10: #-(s(x),s(y)) -> #-(x,y)
Number of SCCs: 4, DPs: 6
  SCC { #10 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      gcd	w: 0
      #min	w: 0
      0 	w: 0
      max	w: 0
      nil	w: 0
      #max	w: 0
      - 	w: 0
      min	w: 0
      #- 	w: x2
      cons	w: 0
      #gcd	w: 0
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 3, DPs: 5
  SCC { #1 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      gcd	w: 0
      #min	w: 0
      0 	w: 0
      max	w: 0
      nil	w: 0
      #max	w: x2
      - 	w: 0
      min	w: 0
      #- 	w: 0
      cons	w: 0
      #gcd	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 4
  SCC { #9 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      gcd	w: 0
      #min	w: x2
      0 	w: 0
      max	w: 0
      nil	w: 0
      #max	w: 0
      - 	w: 0
      min	w: 0
      #- 	w: 0
      cons	w: 0
      #gcd	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 1, DPs: 3
  SCC { #2 #7 #8 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      gcd	w: 0
      #min	w: 0
      0 	w: 1
      max	w: 1
      nil	w: 0
      #max	w: 0
      - 	w: x2
      min	w: x1 + x2 + 1
      #- 	w: 0
      cons	w: x2 + 33954
      #gcd	w: x1
    USABLE RULES: { 1 2 14 }
    Removed DPs: #7 #8
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.