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

TRS termination of:
[1] nats -> adx(zeros)
[2] zeros -> cons(n__0,n__zeros)
[3] incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
[4] adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
[5] hd(cons(X,Y)) -> activate(X)
[6] tl(cons(X,Y)) -> activate(Y)
[7] 0 -> n__0
[8] zeros -> n__zeros
[9] s(X) -> n__s(X)
[10] incr(X) -> n__incr(X)
[11] adx(X) -> n__adx(X)
[12] activate(n__0) -> 0
[13] activate(n__zeros) -> zeros
[14] activate(n__s(X)) -> s(X)
[15] activate(n__incr(X)) -> incr(activate(X))
[16] activate(n__adx(X)) -> adx(activate(X))
[17] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_nats , Marked_adx(zeros)>
<Marked_nats , Marked_zeros>
<Marked_incr(cons(X,Y)) , Marked_activate(X)>
<Marked_incr(cons(X,Y)) , Marked_activate(Y)>
<Marked_adx(cons(X,Y)) , Marked_incr(cons(activate(X),n__adx(activate(Y))))>
<Marked_adx(cons(X,Y)) , Marked_activate(X)>
<Marked_adx(cons(X,Y)) , Marked_activate(Y)>
<Marked_hd(cons(X,Y)) , Marked_activate(X)>
<Marked_tl(cons(X,Y)) , Marked_activate(Y)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__zeros) , Marked_zeros>
<Marked_activate(n__s(X)) , Marked_s(X)>
<Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
<Marked_activate(n__incr(X)) , Marked_activate(X)>
<Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
<Marked_activate(n__adx(X)) , Marked_activate(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__adx(X)) , Marked_activate(X)> 
      --> <Marked_activate(n__adx(X)) , Marked_activate(X)>
  <Marked_activate(n__adx(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_activate(n__adx(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_activate(n__adx(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
  <Marked_activate(n__adx(X)) , Marked_adx(activate(X))> 
     --> <Marked_adx(cons(X,Y)) , Marked_activate(Y)>
  <Marked_activate(n__adx(X)) , Marked_adx(activate(X))> 
     --> <Marked_adx(cons(X,Y)) , Marked_activate(X)>
  <Marked_activate(n__adx(X)) , Marked_adx(activate(X))> 
     --> <Marked_adx(cons(X,Y)) , Marked_incr(cons(activate(X),
                                               n__adx(activate(Y))))>
  <Marked_activate(n__incr(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_activate(X)>
  <Marked_activate(n__incr(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_activate(n__incr(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_activate(n__incr(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
  <Marked_activate(n__incr(X)) , Marked_incr(activate(X))> 
     --> <Marked_incr(cons(X,Y)) , Marked_activate(Y)>
  <Marked_activate(n__incr(X)) , Marked_incr(activate(X))> 
     --> <Marked_incr(cons(X,Y)) , Marked_activate(X)>
  <Marked_adx(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__adx(X)) , Marked_activate(X)>
  <Marked_adx(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_adx(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_adx(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
  <Marked_adx(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_activate(X)>
  <Marked_adx(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_adx(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_adx(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
  <Marked_adx(cons(X,Y)) , Marked_incr(cons(activate(X),n__adx(activate(Y))))> 
     --> <Marked_incr(cons(X,Y)) , Marked_activate(Y)>
  <Marked_adx(cons(X,Y)) , Marked_incr(cons(activate(X),n__adx(activate(Y))))> 
     --> <Marked_incr(cons(X,Y)) , Marked_activate(X)>
  <Marked_incr(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__adx(X)) , Marked_activate(X)>
  <Marked_incr(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_incr(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_incr(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
  <Marked_incr(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_activate(X)>
  <Marked_incr(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_incr(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_incr(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  adx(cons(X,Y)) >= incr(cons(activate(X),n__adx(activate(Y)))) ;
  adx(X) >= n__adx(X) ;
  zeros >= cons(n__0,n__zeros) ;
  zeros >= n__zeros ;
  nats >= adx(zeros) ;
  activate(n__0) >= 0 ;
  activate(n__zeros) >= zeros ;
  activate(n__s(X)) >= s(X) ;
  activate(n__incr(X)) >= incr(activate(X)) ;
  activate(n__adx(X)) >= adx(activate(X)) ;
  activate(X) >= X ;
  incr(cons(X,Y)) >= cons(n__s(activate(X)),n__incr(activate(Y))) ;
  incr(X) >= n__incr(X) ;
  hd(cons(X,Y)) >= activate(X) ;
  tl(cons(X,Y)) >= activate(Y) ;
  0 >= n__0 ;
  s(X) >= n__s(X) ;
  Marked_activate(n__incr(X)) >= Marked_activate(X) ;
  Marked_activate(n__incr(X)) >= Marked_incr(activate(X)) ;
  Marked_activate(n__adx(X)) >= Marked_activate(X) ;
  Marked_activate(n__adx(X)) >= Marked_adx(activate(X)) ;
  Marked_adx(cons(X,Y)) >= Marked_activate(X) ;
  Marked_adx(cons(X,Y)) >= Marked_activate(Y) ;
  Marked_adx(cons(X,Y)) >= Marked_incr(cons(activate(X),n__adx(activate(Y)))) ;
  Marked_incr(cons(X,Y)) >= Marked_activate(X) ;
  Marked_incr(cons(X,Y)) >= Marked_activate(Y) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__incr(X)) > Marked_activate(X) ;
 }
{
  Marked_activate(n__incr(X)) > Marked_incr(activate(X)) ;
 }
{
  Marked_activate(n__adx(X)) > Marked_activate(X) ;
 }
{
  Marked_activate(n__adx(X)) > Marked_adx(activate(X)) ;
 }
{
  Marked_adx(cons(X,Y)) > Marked_activate(X) ;
 }
{
  Marked_adx(cons(X,Y)) > Marked_activate(Y) ;
 }
{
  Marked_adx(cons(X,Y)) > Marked_incr(cons(activate(X),n__adx(activate(Y)))) ;
 }
{
  Marked_incr(cons(X,Y)) > Marked_activate(X) ;
 }
{
  Marked_incr(cons(X,Y)) > Marked_activate(Y) ;
 }
 } 
=== 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: adx(cons(X,Y)) >= incr(cons(activate(X),n__adx(activate(Y))))
constraint: adx(X) >= n__adx(X)
constraint: zeros >= cons(n__0,n__zeros)
constraint: zeros >= n__zeros
constraint: nats >= adx(zeros)
constraint: activate(n__0) >= 0
constraint: activate(n__zeros) >= zeros
constraint: activate(n__s(X)) >= s(X)
constraint: activate(n__incr(X)) >= incr(activate(X))
constraint: activate(n__adx(X)) >= adx(activate(X))
constraint: activate(X) >= X
constraint: incr(cons(X,Y)) >= cons(n__s(activate(X)),n__incr(activate(Y)))
constraint: incr(X) >= n__incr(X)
constraint: hd(cons(X,Y)) >= activate(X)
constraint: tl(cons(X,Y)) >= activate(Y)
constraint: 0 >= n__0
constraint: s(X) >= n__s(X)
constraint: Marked_activate(n__incr(X)) >= Marked_activate(X)
constraint: Marked_activate(n__incr(X)) >= Marked_incr(activate(X))
constraint: Marked_activate(n__adx(X)) >= Marked_activate(X)
constraint: Marked_activate(n__adx(X)) >= Marked_adx(activate(X))
constraint: Marked_adx(cons(X,Y)) >= Marked_activate(X)
constraint: Marked_adx(cons(X,Y)) >= Marked_activate(Y)
constraint: Marked_adx(cons(X,Y)) >= Marked_incr(cons(activate(X),
                                                  n__adx(activate(Y))))
constraint: Marked_incr(cons(X,Y)) >= Marked_activate(X)
constraint: Marked_incr(cons(X,Y)) >= Marked_activate(Y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__adx(X)) , Marked_adx(activate(X))> 
      --> <Marked_adx(cons(X,Y)) , Marked_incr(cons(activate(X),
                                                n__adx(activate(Y))))>
  <Marked_activate(n__incr(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_activate(n__incr(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_activate(n__incr(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
  <Marked_activate(n__incr(X)) , Marked_incr(activate(X))> 
     --> <Marked_incr(cons(X,Y)) , Marked_activate(Y)>
  <Marked_activate(n__incr(X)) , Marked_incr(activate(X))> 
     --> <Marked_incr(cons(X,Y)) , Marked_activate(X)>
  <Marked_adx(cons(X,Y)) , Marked_incr(cons(activate(X),n__adx(activate(Y))))> 
     --> <Marked_incr(cons(X,Y)) , Marked_activate(Y)>
  <Marked_adx(cons(X,Y)) , Marked_incr(cons(activate(X),n__adx(activate(Y))))> 
     --> <Marked_incr(cons(X,Y)) , Marked_activate(X)>
  <Marked_incr(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_incr(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_incr(cons(X,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
  <Marked_incr(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__adx(X)) , Marked_adx(activate(X))>
  <Marked_incr(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_activate(X)>
  <Marked_incr(cons(X,Y)) , Marked_activate(X)> 
     --> <Marked_activate(n__incr(X)) , Marked_incr(activate(X))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  adx(cons(X,Y)) >= incr(cons(activate(X),n__adx(activate(Y)))) ;
  adx(X) >= n__adx(X) ;
  zeros >= cons(n__0,n__zeros) ;
  zeros >= n__zeros ;
  nats >= adx(zeros) ;
  activate(n__0) >= 0 ;
  activate(n__zeros) >= zeros ;
  activate(n__s(X)) >= s(X) ;
  activate(n__incr(X)) >= incr(activate(X)) ;
  activate(n__adx(X)) >= adx(activate(X)) ;
  activate(X) >= X ;
  incr(cons(X,Y)) >= cons(n__s(activate(X)),n__incr(activate(Y))) ;
  incr(X) >= n__incr(X) ;
  hd(cons(X,Y)) >= activate(X) ;
  tl(cons(X,Y)) >= activate(Y) ;
  0 >= n__0 ;
  s(X) >= n__s(X) ;
  Marked_activate(n__incr(X)) >= Marked_activate(X) ;
  Marked_activate(n__incr(X)) >= Marked_incr(activate(X)) ;
  Marked_activate(n__adx(X)) >= Marked_adx(activate(X)) ;
  Marked_adx(cons(X,Y)) >= Marked_incr(cons(activate(X),n__adx(activate(Y)))) ;
  Marked_incr(cons(X,Y)) >= Marked_activate(X) ;
  Marked_incr(cons(X,Y)) >= Marked_activate(Y) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__incr(X)) > Marked_activate(X) ;
 }
{
  Marked_activate(n__incr(X)) > Marked_incr(activate(X)) ;
 }
{
  Marked_activate(n__adx(X)) > Marked_adx(activate(X)) ;
 }
{
  Marked_adx(cons(X,Y)) > Marked_incr(cons(activate(X),n__adx(activate(Y)))) ;
 }
{
  Marked_incr(cons(X,Y)) > Marked_activate(X) ;
 }
{
  Marked_incr(cons(X,Y)) > Marked_activate(Y) ;
 }
 } 
=== 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 : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found 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
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== 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 41.184875 seconds (real time)
Cime Exit Status: 0