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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [choice#](x0, x1, x2) = 2x0 + x1 + 5/2x2,
    
    [clique#](x0, x1) = x0 + 2x1,
    
    [complete#](x0, x1, x2) = 1/2x0 + x1 + 2x2,
    
    [find#](x0, x1, x2) = x1 + 2x2,
    
    [ite#](x0, x1, x2) = x2,
    
    [choice](x0, x1, x2) = 3x0 + 2x1 + 1/2x2 + 7/2,
    
    [clique](x0, x1) = 0,
    
    [complete](x0, x1, x2) = 0,
    
    [cons](x0, x1) = x0 + x1 + 1/2,
    
    [find](x0, x1, x2) = x2 + 2,
    
    [nil] = 1,
    
    [ff] = 0,
    
    [ite](x0, x1, x2) = 2x1 + 2x2,
    
    [tt] = 0
   orientation:
    find#(u,v,cons(cons(u2,v2),E)) = 2E + 2u2 + v + 2v2 + 2 >= 2E + v = find#(u,v,E)
    
    complete#(u,cons(v,S),E) = 2E + S + 1/2u + v + 1/2 >= 2E + S + 1/2u = complete#(u,S,E)
    
    complete#(u,cons(v,S),E) = 2E + S + 1/2u + v + 1/2 >= 2E + v = find#(u,v,E)
    
    complete#(u,cons(v,S),E) = 2E + S + 1/2u + v + 1/2 >= 0 = ite#(find(u,v,E),complete(u,S,E),ff())
    
    clique#(cons(u,K),E) = 2E + K + u + 1/2 >= 2E + K = clique#(K,E)
    
    clique#(cons(u,K),E) = 2E + K + u + 1/2 >= 2E + K + 1/2u = complete#(u,K,E)
    
    clique#(cons(u,K),E) = 2E + K + u + 1/2 >= 0 = ite#(complete(u,K,E),clique(K,E),ff())
    
    choice#(nil(),K,E) = 5/2E + K + 2 >= 2E + K = clique#(K,E)
    
    choice#(nil(),K,E) = 5/2E + K + 2 >= 1 = ite#(clique(K,E),K,nil())
    
    choice#(cons(u,S),K,E) = 5/2E + K + 2S + 2u + 1 >= 5/2E + K + 2S + u + 1/2 = choice#(S,cons(u,K),E)
    
    choice#(cons(u,S),K,E) = 5/2E + K + 2S + 2u + 1 >= 5/2E + K + 2S = choice#(S,K,E)
    
    ite(tt(),u,v) = 2u + 2v >= u = u
    
    ite(ff(),u,v) = 2u + 2v >= v = v
    
    find(u,v,nil()) = 3 >= 0 = ff()
    
    find(u,v,cons(cons(u,v),E)) = E + u + v + 3 >= 0 = tt()
    
    find(u,v,cons(cons(u2,v2),E)) = E + u2 + v2 + 3 >= E + 2 = find(u,v,E)
    
    complete(u,nil(),E) = 0 >= 0 = tt()
    
    complete(u,cons(v,S),E) = 0 >= 0 = ite(find(u,v,E),complete(u,S,E),ff())
    
    clique(nil(),E) = 0 >= 0 = tt()
    
    clique(cons(u,K),E) = 0 >= 0 = ite(complete(u,K,E),clique(K,E),ff())
    
    choice(nil(),K,E) = 1/2E + 2K + 13/2 >= 2K + 2 = ite(clique(K,E),K,nil())
    
    choice(cons(u,S),K,E) = 1/2E + 2K + 3S + 3u + 5 >= 1/2E + 2K + 3S + 2u + 9/2 = choice(S,cons(u,K),E)
    
    choice(cons(u,S),K,E) = 1/2E + 2K + 3S + 3u + 5 >= 1/2E + 2K + 3S + 7/2 = choice(S,K,E)
   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