NO
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(y,z))) -> gcd(cons(-(x,y),cons(y,z)))
      13: gcd(cons(x,cons(y,z))) ->= gcd(cons(max(x,y),cons(min(x,y),z)))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying gcd
      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^1_nil() -> 0()
      10: gcd^1_cons(x,nil()) -> x
      11: gcd^1_cons(0(),y) -> gcd(y)
      12: gcd^1_cons(x,cons(y,z)) -> gcd^1_cons(-(x,y),cons(y,z))
      13: gcd^1_cons(x,cons(y,z)) ->= gcd^1_cons(max(x,y),cons(min(x,y),z))
      14: gcd(cons(_1,_2)) ->= gcd^1_cons(_1,_2)
      15: gcd(nil()) ->= gcd^1_nil()
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #max(s(x),s(y)) -> #max(x,y)
     #2: #gcd^1_cons(x,cons(y,z)) ->? #gcd^1_cons(max(x,y),cons(min(x,y),z))
     #3: #gcd^1_cons(x,cons(y,z)) ->? #max(x,y)
     #4: #gcd^1_cons(x,cons(y,z)) ->? #min(x,y)
     #5: #gcd^1_cons(0(),y) -> #gcd(y)
     #6: #gcd^1_cons(x,cons(y,z)) -> #gcd^1_cons(-(x,y),cons(y,z))
     #7: #gcd^1_cons(x,cons(y,z)) -> #-(x,y)
     #8: #gcd(cons(_1,_2)) ->? #gcd^1_cons(_1,_2)
     #9: #min(s(x),s(y)) -> #min(x,y)
     #10: #-(s(x),s(y)) -> #-(x,y)
     #11: #gcd(nil()) ->? #gcd^1_nil()
Number of SCCs: 4, DPs: 7
  SCC { #1 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      gcd	w: 0
      gcd^1_nil	w: 0
      #min	w: 0
      #gcd^1_nil	w: 0
      0 	w: 0
      max	w: 0
      nil	w: 0
      #max	w: x2
      - 	w: 0
      gcd^1_cons	w: 0
      min	w: 0
      #gcd^1_cons	w: 0
      #- 	w: 0
      cons	w: 0
      #gcd	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 3, DPs: 6
  SCC { #9 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      gcd	w: 0
      gcd^1_nil	w: 0
      #min	w: x2
      #gcd^1_nil	w: 0
      0 	w: 0
      max	w: 0
      nil	w: 0
      #max	w: 0
      - 	w: 0
      gcd^1_cons	w: 0
      min	w: 0
      #gcd^1_cons	w: 0
      #- 	w: 0
      cons	w: 0
      #gcd	w: 0
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 2, DPs: 5
  SCC { #10 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      gcd	w: 0
      gcd^1_nil	w: 0
      #min	w: 0
      #gcd^1_nil	w: 0
      0 	w: 0
      max	w: 0
      nil	w: 0
      #max	w: 0
      - 	w: 0
      gcd^1_cons	w: 0
      min	w: 0
      #gcd^1_cons	w: 0
      #- 	w: x2
      cons	w: 0
      #gcd	w: 0
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 1, DPs: 4
  SCC { #2 #5 #6 #8 }
POLO(Sum)... succeeded.
      s 	w: 1
      gcd	w: 0
      gcd^1_nil	w: 0
      #min	w: 0
      #gcd^1_nil	w: 0
      0 	w: 5854
      max	w: x2 + 1
      nil	w: 0
      #max	w: 0
      - 	w: x2 + 1
      gcd^1_cons	w: 0
      min	w: x1 + x2 + 1
      #gcd^1_cons	w: x2 + 28101
      #- 	w: 0
      cons	w: x2 + 28102
      #gcd	w: x1
    USABLE RULES: { 1..3 }
    Removed DPs: #5 #8
Number of SCCs: 1, DPs: 2
  SCC { #2 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #gcd^1_cons(x,cons(y_{1},z_{1}))	-#6->
  #gcd^1_cons(-(x,y_{1}),cons(y_{1},z_{1}))	--->*
  #gcd^1_cons(-(x,y_{1}),cons(y_{1},z_{1}))
  Looping with: [ x := -(x,y_{1}); y_{1} := y_{1}; z_{1} := z_{1}; ]