YES

Problem:
 ite(tt(),u,v) -> u
 ite(ff(),u,v) -> v
 find(u,v,nil()) -> ff()
 find(u,v,cons(cons(u,v),E)) -> tt()
 find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
 complete(u,nil(),E) -> tt()
 complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
 clique(nil(),E) -> tt()
 clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
 choice(nil(),K,E) -> ite(clique(K,E),K,nil())
 choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
 choice(cons(u,S),K,E) -> choice(S,K,E)

Proof:
 DP Processor:
  DPs:
   find#(u,v,cons(cons(u2,v2),E)) -> find#(u,v,E)
   complete#(u,cons(v,S),E) -> complete#(u,S,E)
   complete#(u,cons(v,S),E) -> find#(u,v,E)
   complete#(u,cons(v,S),E) -> ite#(find(u,v,E),complete(u,S,E),ff())
   clique#(cons(u,K),E) -> clique#(K,E)
   clique#(cons(u,K),E) -> complete#(u,K,E)
   clique#(cons(u,K),E) -> ite#(complete(u,K,E),clique(K,E),ff())
   choice#(nil(),K,E) -> clique#(K,E)
   choice#(nil(),K,E) -> ite#(clique(K,E),K,nil())
   choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E)
   choice#(cons(u,S),K,E) -> choice#(S,K,E)
  TRS:
   ite(tt(),u,v) -> u
   ite(ff(),u,v) -> v
   find(u,v,nil()) -> ff()
   find(u,v,cons(cons(u,v),E)) -> tt()
   find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
   complete(u,nil(),E) -> tt()
   complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
   clique(nil(),E) -> tt()
   clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
   choice(nil(),K,E) -> ite(clique(K,E),K,nil())
   choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
   choice(cons(u,S),K,E) -> choice(S,K,E)
  TDG Processor:
   DPs:
    find#(u,v,cons(cons(u2,v2),E)) -> find#(u,v,E)
    complete#(u,cons(v,S),E) -> complete#(u,S,E)
    complete#(u,cons(v,S),E) -> find#(u,v,E)
    complete#(u,cons(v,S),E) -> ite#(find(u,v,E),complete(u,S,E),ff())
    clique#(cons(u,K),E) -> clique#(K,E)
    clique#(cons(u,K),E) -> complete#(u,K,E)
    clique#(cons(u,K),E) -> ite#(complete(u,K,E),clique(K,E),ff())
    choice#(nil(),K,E) -> clique#(K,E)
    choice#(nil(),K,E) -> ite#(clique(K,E),K,nil())
    choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E)
    choice#(cons(u,S),K,E) -> choice#(S,K,E)
   TRS:
    ite(tt(),u,v) -> u
    ite(ff(),u,v) -> v
    find(u,v,nil()) -> ff()
    find(u,v,cons(cons(u,v),E)) -> tt()
    find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
    complete(u,nil(),E) -> tt()
    complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
    clique(nil(),E) -> tt()
    clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
    choice(nil(),K,E) -> ite(clique(K,E),K,nil())
    choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
    choice(cons(u,S),K,E) -> choice(S,K,E)
   graph:
    choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E) ->
    choice#(cons(u,S),K,E) -> choice#(S,K,E)
    choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E) ->
    choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E)
    choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E) ->
    choice#(nil(),K,E) -> ite#(clique(K,E),K,nil())
    choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E) ->
    choice#(nil(),K,E) -> clique#(K,E)
    choice#(cons(u,S),K,E) -> choice#(S,K,E) ->
    choice#(cons(u,S),K,E) -> choice#(S,K,E)
    choice#(cons(u,S),K,E) -> choice#(S,K,E) ->
    choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E)
    choice#(cons(u,S),K,E) -> choice#(S,K,E) ->
    choice#(nil(),K,E) -> ite#(clique(K,E),K,nil())
    choice#(cons(u,S),K,E) -> choice#(S,K,E) ->
    choice#(nil(),K,E) -> clique#(K,E)
    choice#(nil(),K,E) -> clique#(K,E) ->
    clique#(cons(u,K),E) -> ite#(complete(u,K,E),clique(K,E),ff())
    choice#(nil(),K,E) -> clique#(K,E) ->
    clique#(cons(u,K),E) -> complete#(u,K,E)
    choice#(nil(),K,E) -> clique#(K,E) ->
    clique#(cons(u,K),E) -> clique#(K,E)
    clique#(cons(u,K),E) -> clique#(K,E) ->
    clique#(cons(u,K),E) -> ite#(complete(u,K,E),clique(K,E),ff())
    clique#(cons(u,K),E) -> clique#(K,E) ->
    clique#(cons(u,K),E) -> complete#(u,K,E)
    clique#(cons(u,K),E) -> clique#(K,E) ->
    clique#(cons(u,K),E) -> clique#(K,E)
    clique#(cons(u,K),E) -> complete#(u,K,E) ->
    complete#(u,cons(v,S),E) -> ite#(find(u,v,E),complete(u,S,E),ff())
    clique#(cons(u,K),E) -> complete#(u,K,E) ->
    complete#(u,cons(v,S),E) -> find#(u,v,E)
    clique#(cons(u,K),E) -> complete#(u,K,E) ->
    complete#(u,cons(v,S),E) -> complete#(u,S,E)
    complete#(u,cons(v,S),E) -> complete#(u,S,E) ->
    complete#(u,cons(v,S),E) -> ite#(find(u,v,E),complete(u,S,E),ff())
    complete#(u,cons(v,S),E) -> complete#(u,S,E) ->
    complete#(u,cons(v,S),E) -> find#(u,v,E)
    complete#(u,cons(v,S),E) -> complete#(u,S,E) ->
    complete#(u,cons(v,S),E) -> complete#(u,S,E)
    complete#(u,cons(v,S),E) -> find#(u,v,E) ->
    find#(u,v,cons(cons(u2,v2),E)) -> find#(u,v,E)
    find#(u,v,cons(cons(u2,v2),E)) -> find#(u,v,E) ->
    find#(u,v,cons(cons(u2,v2),E)) -> find#(u,v,E)
   SCC Processor:
    #sccs: 4
    #rules: 5
    #arcs: 22/121
    DPs:
     choice#(cons(u,S),K,E) -> choice#(S,cons(u,K),E)
     choice#(cons(u,S),K,E) -> choice#(S,K,E)
    TRS:
     ite(tt(),u,v) -> u
     ite(ff(),u,v) -> v
     find(u,v,nil()) -> ff()
     find(u,v,cons(cons(u,v),E)) -> tt()
     find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
     complete(u,nil(),E) -> tt()
     complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
     clique(nil(),E) -> tt()
     clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
     choice(nil(),K,E) -> ite(clique(K,E),K,nil())
     choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
     choice(cons(u,S),K,E) -> choice(S,K,E)
    Subterm Criterion Processor:
     simple projection:
      pi(choice#) = 0
     problem:
      DPs:
       
      TRS:
       ite(tt(),u,v) -> u
       ite(ff(),u,v) -> v
       find(u,v,nil()) -> ff()
       find(u,v,cons(cons(u,v),E)) -> tt()
       find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
       complete(u,nil(),E) -> tt()
       complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
       clique(nil(),E) -> tt()
       clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
       choice(nil(),K,E) -> ite(clique(K,E),K,nil())
       choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
       choice(cons(u,S),K,E) -> choice(S,K,E)
     Qed
    
    DPs:
     clique#(cons(u,K),E) -> clique#(K,E)
    TRS:
     ite(tt(),u,v) -> u
     ite(ff(),u,v) -> v
     find(u,v,nil()) -> ff()
     find(u,v,cons(cons(u,v),E)) -> tt()
     find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
     complete(u,nil(),E) -> tt()
     complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
     clique(nil(),E) -> tt()
     clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
     choice(nil(),K,E) -> ite(clique(K,E),K,nil())
     choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
     choice(cons(u,S),K,E) -> choice(S,K,E)
    Subterm Criterion Processor:
     simple projection:
      pi(clique#) = 0
     problem:
      DPs:
       
      TRS:
       ite(tt(),u,v) -> u
       ite(ff(),u,v) -> v
       find(u,v,nil()) -> ff()
       find(u,v,cons(cons(u,v),E)) -> tt()
       find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
       complete(u,nil(),E) -> tt()
       complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
       clique(nil(),E) -> tt()
       clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
       choice(nil(),K,E) -> ite(clique(K,E),K,nil())
       choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
       choice(cons(u,S),K,E) -> choice(S,K,E)
     Qed
    
    DPs:
     complete#(u,cons(v,S),E) -> complete#(u,S,E)
    TRS:
     ite(tt(),u,v) -> u
     ite(ff(),u,v) -> v
     find(u,v,nil()) -> ff()
     find(u,v,cons(cons(u,v),E)) -> tt()
     find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
     complete(u,nil(),E) -> tt()
     complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
     clique(nil(),E) -> tt()
     clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
     choice(nil(),K,E) -> ite(clique(K,E),K,nil())
     choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
     choice(cons(u,S),K,E) -> choice(S,K,E)
    Subterm Criterion Processor:
     simple projection:
      pi(complete#) = 1
     problem:
      DPs:
       
      TRS:
       ite(tt(),u,v) -> u
       ite(ff(),u,v) -> v
       find(u,v,nil()) -> ff()
       find(u,v,cons(cons(u,v),E)) -> tt()
       find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
       complete(u,nil(),E) -> tt()
       complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
       clique(nil(),E) -> tt()
       clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
       choice(nil(),K,E) -> ite(clique(K,E),K,nil())
       choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
       choice(cons(u,S),K,E) -> choice(S,K,E)
     Qed
    
    DPs:
     find#(u,v,cons(cons(u2,v2),E)) -> find#(u,v,E)
    TRS:
     ite(tt(),u,v) -> u
     ite(ff(),u,v) -> v
     find(u,v,nil()) -> ff()
     find(u,v,cons(cons(u,v),E)) -> tt()
     find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
     complete(u,nil(),E) -> tt()
     complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
     clique(nil(),E) -> tt()
     clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
     choice(nil(),K,E) -> ite(clique(K,E),K,nil())
     choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
     choice(cons(u,S),K,E) -> choice(S,K,E)
    Subterm Criterion Processor:
     simple projection:
      pi(find#) = 2
     problem:
      DPs:
       
      TRS:
       ite(tt(),u,v) -> u
       ite(ff(),u,v) -> v
       find(u,v,nil()) -> ff()
       find(u,v,cons(cons(u,v),E)) -> tt()
       find(u,v,cons(cons(u2,v2),E)) -> find(u,v,E)
       complete(u,nil(),E) -> tt()
       complete(u,cons(v,S),E) -> ite(find(u,v,E),complete(u,S,E),ff())
       clique(nil(),E) -> tt()
       clique(cons(u,K),E) -> ite(complete(u,K,E),clique(K,E),ff())
       choice(nil(),K,E) -> ite(clique(K,E),K,nil())
       choice(cons(u,S),K,E) -> choice(S,cons(u,K),E)
       choice(cons(u,S),K,E) -> choice(S,K,E)
     Qed