MAYBE

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())

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())
  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())
  EDG 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())
   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())
   graph:
    clique#(cons(u,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) -> complete#(u,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) -> complete#(u,K,E) ->
    complete#(u,cons(v,S),E) -> complete#(u,S,E)
    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) -> 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) -> complete#(u,S,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) -> 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) -> 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: 3
    #rules: 3
    #arcs: 11/49
    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())
    Open
    
    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())
    Open
    
    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())
    Open