YES
Input TRS:
C symbols: gcd
      1: le(0(),y) -> true()
      2: le(s(x),0()) -> false()
      3: le(s(x),s(y)) -> le(x,y)
      4: minus(0(),y) -> 0()
      5: minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
      6: if_minus(true(),s(x),y) -> 0()
      7: if_minus(false(),s(x),y) -> s(minus(x,y))
      8: gcd(0(),y) -> y
      9: gcd(s(x),0()) -> s(x)
      10: gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
      11: if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
      12: if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying le
C symbols: gcd
      1: le^1_0(y) -> true()
      2: le^1_s(x,0()) -> false()
      3: le^1_s(x,s(y)) -> le(x,y)
      4: minus(0(),y) -> 0()
      5: minus(s(x),y) -> if_minus(le^1_s(x,y),s(x),y)
      6: if_minus(true(),s(x),y) -> 0()
      7: if_minus(false(),s(x),y) -> s(minus(x,y))
      8: gcd(0(),y) -> y
      9: gcd(s(x),0()) -> s(x)
      10: gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
      11: if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
      12: if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))
      13: le(0(),_1) ->= le^1_0(_1)
      14: le(s(_1),_2) ->= le^1_s(_1,_2)
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #le(0(),_1) ->? #le^1_0(_1)
     #2: #if_gcd(true(),s(x),s(y)) -> #gcd(minus(x,y),s(y))
     #3: #if_gcd(true(),s(x),s(y)) -> #minus(x,y)
     #4: #if_gcd(false(),s(x),s(y)) -> #gcd(minus(y,x),s(x))
     #5: #if_gcd(false(),s(x),s(y)) -> #minus(y,x)
     #6: #le(s(_1),_2) ->? #le^1_s(_1,_2)
     #7: #if_minus(false(),s(x),y) -> #minus(x,y)
     #8: #gcd(s(x),s(y)) -> #if_gcd(le(y,x),s(x),s(y))
     #9: #gcd(s(x),s(y)) -> #le(y,x)
     #10: #minus(s(x),y) -> #if_minus(le^1_s(x,y),s(x),y)
     #11: #minus(s(x),y) -> #le^1_s(x,y)
     #12: #le^1_s(x,s(y)) -> #le(x,y)
Number of SCCs: 3, DPs: 7
  SCC { #6 #12 }
POLO(Sum)... succeeded.
      #le^1_s	w: x1 + x2
      le	w: 0
      le^1_s	w: 0
      s 	w: x1 + 1
      #le	w: x1 + x2
      #le^1_0	w: 0
      minus	w: 0
      gcd	w: 0
      false	w: 0
      true	w: 0
      0 	w: 0
      #if_minus	w: 0
      #minus	w: 0
      le^1_0	w: 0
      if_minus	w: 0
      if_gcd	w: 0
      #if_gcd	w: 0
      #gcd	w: 0
    USABLE RULES: { }
    Removed DPs: #6 #12
Number of SCCs: 2, DPs: 5
  SCC { #7 #10 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: x1
      le^1_s	w: x2 + 3
      s 	w: x1 + 2
      #le	w: 0
      #le^1_0	w: 0
      minus	w: 0
      gcd	w: 0
      false	w: 5
      true	w: 3
      0 	w: 1
      #if_minus	w: x2 + x3
      #minus	w: x1 + x2 + 1
      le^1_0	w: x1 + 2
      if_minus	w: 0
      if_gcd	w: 0
      #if_gcd	w: 0
      #gcd	w: 0
    USABLE RULES: { }
    Removed DPs: #7 #10
Number of SCCs: 1, DPs: 3
  SCC { #2 #4 #8 }
POLO(Sum)... succeeded.
      #le^1_s	w: 0
      le	w: x1 + x2 + 1
      le^1_s	w: 5
      s 	w: x1 + 3
      #le	w: 0
      #le^1_0	w: 0
      minus	w: x1 + 1
      gcd	w: 0
      false	w: 1
      true	w: 1
      0 	w: 1
      #if_minus	w: 0
      #minus	w: 1
      le^1_0	w: 2
      if_minus	w: x2 + 1
      if_gcd	w: 0
      #if_gcd	w: x2 + x3
      #gcd	w: x1 + x2 + 1
    USABLE RULES: { 4..7 }
    Removed DPs: #2 #4 #8
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
Number of SCCs: 0, DPs: 0