- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] and(false,false) -> false
[2] and(true,false) -> false
[3] and(false,true) -> false
[4] and(true,true) -> true
[5] eq(nil,nil) -> true
[6] eq(cons(T,L),nil) -> false
[7] eq(nil,cons(T,L)) -> false
[8] eq(cons(T,L),cons(Tp,Lp)) -> and(eq(T,Tp),eq(L,Lp))
[9] eq(var(L),var(Lp)) -> eq(L,Lp)
[10] eq(var(L),apply(T,S)) -> false
[11] eq(var(L),lambda(X,T)) -> false
[12] eq(apply(T,S),var(L)) -> false
[13] eq(apply(T,S),apply(Tp,Sp)) -> and(eq(T,Tp),eq(S,Sp))
[14] eq(apply(T,S),lambda(X,Tp)) -> false
[15] eq(lambda(X,T),var(L)) -> false
[16] eq(lambda(X,T),apply(Tp,Sp)) -> false
[17] eq(lambda(X,T),lambda(Xp,Tp)) -> and(eq(T,Tp),eq(X,Xp))
[18] if(true,var(K),var(L)) -> var(K)
[19] if(false,var(K),var(L)) -> var(L)
[20] ren(var(L),var(K),var(Lp)) -> if(eq(L,Lp),var(K),var(Lp))
[21] ren(X,Y,apply(T,S)) -> apply(ren(X,Y,T),ren(X,Y,S))
[22] ren(X,Y,lambda(Z,T)) ->
 lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
  ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))


Sub problem: 
guided: 

DP termination of:
<Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_and(eq(T,Tp),eq(L,Lp))>
<Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)>
<Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)>
<Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)>
<Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_and(eq(T,Tp),eq(S,Sp))>
<Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)>
<Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)>
<Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_and(eq(T,Tp),eq(X,Xp))>
<Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)>
<Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)>
<Marked_ren(var(L),var(K),var(Lp)) , Marked_if(eq(L,Lp),var(K),var(Lp))>
<Marked_ren(var(L),var(K),var(Lp)) , Marked_eq(L,Lp)>
<Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)>
<Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)>
<Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                ren(Z,
                                 var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                 T))>
<Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                T)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                   var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                   T)> 
      --> <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                          var(cons(X,
                                               cons(Y,cons(lambda(Z,T),nil)))),
                                          T)>
  <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                  var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                  T)> 
     --> <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                         ren(Z,
                                          var(cons(X,
                                               cons(Y,cons(lambda(Z,T),nil)))),
                                          T))>
  <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                  var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                  T)> 
     --> <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)>
  <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                  var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                  T)> 
     --> <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)>
  <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                  ren(Z,
                                   var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                   T))> 
     --> <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                         var(cons(X,
                                              cons(Y,cons(lambda(Z,T),nil)))),
                                         T)>
  <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                  ren(Z,
                                   var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                   T))> 
     --> <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                         ren(Z,
                                          var(cons(X,
                                               cons(Y,cons(lambda(Z,T),nil)))),
                                          T))>
  <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                  ren(Z,
                                   var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                   T))> 
     --> <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)>
  <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                  ren(Z,
                                   var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                   T))> 
     --> <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)>
  <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)> 
     --> <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                         var(cons(X,
                                              cons(Y,cons(lambda(Z,T),nil)))),
                                         T)>
  <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)> 
     --> <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                         ren(Z,
                                          var(cons(X,
                                               cons(Y,cons(lambda(Z,T),nil)))),
                                          T))>
  <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)> 
     --> <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)>
  <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)> 
     --> <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)>
  <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)> 
     --> <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(Z,
                                         var(cons(X,
                                              cons(Y,cons(lambda(Z,T),nil)))),
                                         T)>
  <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)> 
     --> <Marked_ren(X,Y,lambda(Z,T)) , Marked_ren(X,Y,
                                         ren(Z,
                                          var(cons(X,
                                               cons(Y,cons(lambda(Z,T),nil)))),
                                          T))>
  <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)> 
     --> <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,S)>
  <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)> 
     --> <Marked_ren(X,Y,apply(T,S)) , Marked_ren(X,Y,T)>
}

{  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)> 
      --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)> 
     --> <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)> 
     --> <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)>
  <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)>
  <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)>
  <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)>
  <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)>
  <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(X,Xp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(lambda(X,T),lambda(Xp,Tp)) , Marked_eq(T,Tp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(S,Sp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(apply(T,S),apply(Tp,Sp)) , Marked_eq(T,Tp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(var(L),var(Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(L,Lp)>
  <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)> 
     --> <Marked_eq(cons(T,L),cons(Tp,Lp)) , Marked_eq(T,Tp)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(false,false) >= false ;
  and(false,true) >= false ;
  and(true,false) >= false ;
  and(true,true) >= true ;
  eq(nil,nil) >= true ;
  eq(nil,cons(T,L)) >= false ;
  eq(cons(T,L),nil) >= false ;
  eq(cons(T,L),cons(Tp,Lp)) >= and(eq(T,Tp),eq(L,Lp)) ;
  eq(var(L),var(Lp)) >= eq(L,Lp) ;
  eq(var(L),apply(T,S)) >= false ;
  eq(var(L),lambda(X,T)) >= false ;
  eq(apply(T,S),var(L)) >= false ;
  eq(apply(T,S),apply(Tp,Sp)) >= and(eq(T,Tp),eq(S,Sp)) ;
  eq(apply(T,S),lambda(X,Tp)) >= false ;
  eq(lambda(X,T),var(L)) >= false ;
  eq(lambda(X,T),apply(Tp,Sp)) >= false ;
  eq(lambda(X,T),lambda(Xp,Tp)) >= and(eq(T,Tp),eq(X,Xp)) ;
  if(false,var(K),var(L)) >= var(L) ;
  if(true,var(K),var(L)) >= var(K) ;
  ren(var(L),var(K),var(Lp)) >= if(eq(L,Lp),var(K),var(Lp)) ;
  ren(X,Y,apply(T,S)) >= apply(ren(X,Y,T),ren(X,Y,S)) ;
  ren(X,Y,lambda(Z,T)) >= lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                           ren(X,Y,
                            ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))
                            ;
  Marked_ren(X,Y,apply(T,S)) >= Marked_ren(X,Y,T) ;
  Marked_ren(X,Y,apply(T,S)) >= Marked_ren(X,Y,S) ;
  Marked_ren(X,Y,lambda(Z,T)) >= Marked_ren(X,Y,
                                  ren(Z,
                                   var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                   T)) ;
  Marked_ren(X,Y,lambda(Z,T)) >= Marked_ren(Z,
                                  var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                  T) ;
 }
 + Disjunctions:{ 
{
  Marked_ren(X,Y,apply(T,S)) > Marked_ren(X,Y,T) ;
 }
{
  Marked_ren(X,Y,apply(T,S)) > Marked_ren(X,Y,S) ;
 }
{
  Marked_ren(X,Y,lambda(Z,T)) > Marked_ren(X,Y,
                                 ren(Z,
                                  var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                  T)) ;
 }
{
  Marked_ren(X,Y,lambda(Z,T)) > Marked_ren(Z,
                                 var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                                 T) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: and(false,false) >= false
constraint: and(false,true) >= false
constraint: and(true,false) >= false
constraint: and(true,true) >= true
constraint: eq(nil,nil) >= true
constraint: eq(nil,cons(T,L)) >= false
constraint: eq(cons(T,L),nil) >= false
constraint: eq(cons(T,L),cons(Tp,Lp)) >= and(eq(T,Tp),eq(L,Lp))
constraint: eq(var(L),var(Lp)) >= eq(L,Lp)
constraint: eq(var(L),apply(T,S)) >= false
constraint: eq(var(L),lambda(X,T)) >= false
constraint: eq(apply(T,S),var(L)) >= false
constraint: eq(apply(T,S),apply(Tp,Sp)) >= and(eq(T,Tp),eq(S,Sp))
constraint: eq(apply(T,S),lambda(X,Tp)) >= false
constraint: eq(lambda(X,T),var(L)) >= false
constraint: eq(lambda(X,T),apply(Tp,Sp)) >= false
constraint: eq(lambda(X,T),lambda(Xp,Tp)) >= and(eq(T,Tp),eq(X,Xp))
constraint: if(false,var(K),var(L)) >= var(L)
constraint: if(true,var(K),var(L)) >= var(K)
constraint: ren(var(L),var(K),var(Lp)) >= if(eq(L,Lp),var(K),var(Lp))
constraint: ren(X,Y,apply(T,S)) >= apply(ren(X,Y,T),ren(X,Y,S))
constraint: ren(X,Y,lambda(Z,T)) >= lambda(var(cons(X,
                                                cons(Y,cons(lambda(Z,T),nil)))),
                                     ren(X,Y,
                                      ren(Z,
                                       var(cons(X,
                                            cons(Y,cons(lambda(Z,T),nil)))),
                                       T)))
constraint: Marked_ren(X,Y,apply(T,S)) >= Marked_ren(X,Y,T)
constraint: Marked_ren(X,Y,apply(T,S)) >= Marked_ren(X,Y,S)
constraint: Marked_ren(X,Y,lambda(Z,T)) >= Marked_ren(X,Y,
                                            ren(Z,
                                             var(cons(X,
                                                  cons(Y,cons(lambda(Z,T),nil))))
                                              ,T))
constraint: Marked_ren(X,Y,lambda(Z,T)) >= Marked_ren(Z,
                                            var(cons(X,
                                                 cons(Y,cons(lambda(Z,T),nil)))),
                                            T)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(false,false) >= false ;
  and(false,true) >= false ;
  and(true,false) >= false ;
  and(true,true) >= true ;
  eq(nil,nil) >= true ;
  eq(nil,cons(T,L)) >= false ;
  eq(cons(T,L),nil) >= false ;
  eq(cons(T,L),cons(Tp,Lp)) >= and(eq(T,Tp),eq(L,Lp)) ;
  eq(var(L),var(Lp)) >= eq(L,Lp) ;
  eq(var(L),apply(T,S)) >= false ;
  eq(var(L),lambda(X,T)) >= false ;
  eq(apply(T,S),var(L)) >= false ;
  eq(apply(T,S),apply(Tp,Sp)) >= and(eq(T,Tp),eq(S,Sp)) ;
  eq(apply(T,S),lambda(X,Tp)) >= false ;
  eq(lambda(X,T),var(L)) >= false ;
  eq(lambda(X,T),apply(Tp,Sp)) >= false ;
  eq(lambda(X,T),lambda(Xp,Tp)) >= and(eq(T,Tp),eq(X,Xp)) ;
  if(false,var(K),var(L)) >= var(L) ;
  if(true,var(K),var(L)) >= var(K) ;
  ren(var(L),var(K),var(Lp)) >= if(eq(L,Lp),var(K),var(Lp)) ;
  ren(X,Y,apply(T,S)) >= apply(ren(X,Y,T),ren(X,Y,S)) ;
  ren(X,Y,lambda(Z,T)) >= lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),
                           ren(X,Y,
                            ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil)))),T)))
                            ;
  Marked_eq(cons(T,L),cons(Tp,Lp)) >= Marked_eq(T,Tp) ;
  Marked_eq(cons(T,L),cons(Tp,Lp)) >= Marked_eq(L,Lp) ;
  Marked_eq(var(L),var(Lp)) >= Marked_eq(L,Lp) ;
  Marked_eq(apply(T,S),apply(Tp,Sp)) >= Marked_eq(T,Tp) ;
  Marked_eq(apply(T,S),apply(Tp,Sp)) >= Marked_eq(S,Sp) ;
  Marked_eq(lambda(X,T),lambda(Xp,Tp)) >= Marked_eq(T,Tp) ;
  Marked_eq(lambda(X,T),lambda(Xp,Tp)) >= Marked_eq(X,Xp) ;
 }
 + Disjunctions:{ 
{
  Marked_eq(cons(T,L),cons(Tp,Lp)) > Marked_eq(T,Tp) ;
 }
{
  Marked_eq(cons(T,L),cons(Tp,Lp)) > Marked_eq(L,Lp) ;
 }
{
  Marked_eq(var(L),var(Lp)) > Marked_eq(L,Lp) ;
 }
{
  Marked_eq(apply(T,S),apply(Tp,Sp)) > Marked_eq(T,Tp) ;
 }
{
  Marked_eq(apply(T,S),apply(Tp,Sp)) > Marked_eq(S,Sp) ;
 }
{
  Marked_eq(lambda(X,T),lambda(Xp,Tp)) > Marked_eq(T,Tp) ;
 }
{
  Marked_eq(lambda(X,T),lambda(Xp,Tp)) > Marked_eq(X,Xp) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 73.823334 seconds (real time)
Cime Exit Status: 0