YES
Input TRS:
      1: app(app(lt(),app(s(),x)),app(s(),y)) -> app(app(lt(),x),y)
      2: app(app(lt(),0()),app(s(),y)) -> true()
      3: app(app(lt(),y),0()) -> false()
      4: app(app(eq(),x),x) -> true()
      5: app(app(eq(),app(s(),x)),0()) -> false()
      6: app(app(eq(),0()),app(s(),x)) -> false()
      7: app(app(member(),w),null()) -> false()
      8: app(app(member(),w),app(app(app(fork(),x),y),z)) -> app(app(app(if(),app(app(lt(),w),y)),app(app(member(),w),x)),app(app(app(if(),app(app(eq(),w),y)),true()),app(app(member(),w),z)))
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Uncurrying app
      1: app^2_lt(app^1_s(x),app^1_s(y)) -> app^2_lt(x,y)
      2: app^2_lt(0(),app^1_s(y)) -> true()
      3: app^2_lt(y,0()) -> false()
      4: app^2_eq(x,x) -> true()
      5: app^2_eq(app^1_s(x),0()) -> false()
      6: app^2_eq(0(),app^1_s(x)) -> false()
      7: app^2_member(w,null()) -> false()
      8: app^2_member(w,app^3_fork(x,y,z)) -> app^3_if(app^2_lt(w,y),app^2_member(w,x),app^3_if(app^2_eq(w,y),true(),app^2_member(w,z)))
      9: app(eq(),_1) ->= app^1_eq(_1)
      10: app(app^1_eq(_1),_2) ->= app^2_eq(_1,_2)
      11: app(if(),_1) ->= app^1_if(_1)
      12: app(app^1_if(_1),_2) ->= app^2_if(_1,_2)
      13: app(app^2_if(_1,_2),_3) ->= app^3_if(_1,_2,_3)
      14: app(s(),_1) ->= app^1_s(_1)
      15: app(fork(),_1) ->= app^1_fork(_1)
      16: app(app^1_fork(_1),_2) ->= app^2_fork(_1,_2)
      17: app(app^2_fork(_1,_2),_3) ->= app^3_fork(_1,_2,_3)
      18: app(member(),_1) ->= app^1_member(_1)
      19: app(app^1_member(_1),_2) ->= app^2_member(_1,_2)
      20: app(lt(),_1) ->= app^1_lt(_1)
      21: app(app^1_lt(_1),_2) ->= app^2_lt(_1,_2)
Number of strict rules: 8
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #app(app^1_eq(_1),_2) ->? #app^2_eq(_1,_2)
     #2: #app(app^1_member(_1),_2) ->? #app^2_member(_1,_2)
     #3: #app(app^1_lt(_1),_2) ->? #app^2_lt(_1,_2)
     #4: #app^2_lt(app^1_s(x),app^1_s(y)) -> #app^2_lt(x,y)
     #5: #app^2_member(w,app^3_fork(x,y,z)) -> #app^2_lt(w,y)
     #6: #app^2_member(w,app^3_fork(x,y,z)) -> #app^2_member(w,x)
     #7: #app^2_member(w,app^3_fork(x,y,z)) -> #app^2_eq(w,y)
     #8: #app^2_member(w,app^3_fork(x,y,z)) -> #app^2_member(w,z)
Number of SCCs: 2, DPs: 3
  SCC { #4 }
POLO(Sum)... succeeded.
      #app^2_member	w: 0
      app^1_lt	w: 0
      s 	w: 0
      app^1_fork	w: 0
      member	w: 0
      #app^2_lt	w: x1 + x2
      app^2_member	w: 0
      eq	w: 0
      false	w: 0
      fork	w: 0
      true	w: 0
      0 	w: 0
      if	w: 0
      null	w: 0
      #app	w: 0
      app^2_lt	w: 0
      #app^2_eq	w: 0
      app^2_if	w: 0
      app^3_if	w: 0
      app^2_eq	w: 0
      app^3_fork	w: 0
      app^1_member	w: 0
      app^2_fork	w: 0
      lt	w: 0
      app^1_eq	w: 0
      app^1_if	w: 0
      app^1_s	w: x1 + 1
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 2
  SCC { #6 #8 }
POLO(Sum)... succeeded.
      #app^2_member	w: x2
      app^1_lt	w: 0
      s 	w: 0
      app^1_fork	w: 0
      member	w: 0
      #app^2_lt	w: 0
      app^2_member	w: 0
      eq	w: 0
      false	w: 0
      fork	w: 0
      true	w: 0
      0 	w: 0
      if	w: 0
      null	w: 0
      #app	w: 0
      app^2_lt	w: 0
      #app^2_eq	w: 0
      app^2_if	w: 0
      app^3_if	w: 0
      app^2_eq	w: 0
      app^3_fork	w: x1 + x3 + 1
      app^1_member	w: 0
      app^2_fork	w: 0
      lt	w: 0
      app^1_eq	w: 0
      app^1_if	w: 0
      app^1_s	w: 1
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #6 #8
Number of SCCs: 0, DPs: 0