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

TRS termination of:
[1] and(true,X) -> X
[2] and(false,Y) -> false
[3] if(true,X,Y) -> X
[4] if(false,X,Y) -> Y
[5] add(0,X) -> X
[6] add(s(X),Y) -> s(add(X,Y))
[7] first(0,X) -> nil
[8] first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
[9] from(X) -> cons(X,from(s(X)))


Sub problem: 
guided: 

DP termination of:
<Marked_add(s(X),Y) , Marked_add(X,Y)>
<Marked_first(s(X),cons(Y,Z)) , Marked_first(X,Z)>
<Marked_from(X) , Marked_from(s(X))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_add(s(X),Y) , Marked_add(X,Y)> 
      --> <Marked_add(s(X),Y) , Marked_add(X,Y)>
}

{  <Marked_first(s(X),cons(Y,Z)) , Marked_first(X,Z)> 
      --> <Marked_first(s(X),cons(Y,Z)) , Marked_first(X,Z)>
}

{  <Marked_from(X) , Marked_from(s(X))> 
      --> <Marked_from(X) , Marked_from(s(X))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(true,X) >= X ;
  and(false,Y) >= false ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  add(0,X) >= X ;
  add(s(X),Y) >= s(add(X,Y)) ;
  first(0,X) >= nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  from(X) >= cons(X,from(s(X))) ;
  Marked_add(s(X),Y) >= Marked_add(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_add(s(X),Y) > Marked_add(X,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: and(true,X) >= X
constraint: and(false,Y) >= false
constraint: if(true,X,Y) >= X
constraint: if(false,X,Y) >= Y
constraint: add(0,X) >= X
constraint: add(s(X),Y) >= s(add(X,Y))
constraint: first(0,X) >= nil
constraint: first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z))
constraint: from(X) >= cons(X,from(s(X)))
constraint: Marked_add(s(X),Y) >= Marked_add(X,Y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(true,X) >= X ;
  and(false,Y) >= false ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  add(0,X) >= X ;
  add(s(X),Y) >= s(add(X,Y)) ;
  first(0,X) >= nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  from(X) >= cons(X,from(s(X))) ;
  Marked_first(s(X),cons(Y,Z)) >= Marked_first(X,Z) ;
 }
 + Disjunctions:{ 
{
  Marked_first(s(X),cons(Y,Z)) > Marked_first(X,Z) ;
 }
 } 
=== 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(true,X) >= X
constraint: and(false,Y) >= false
constraint: if(true,X,Y) >= X
constraint: if(false,X,Y) >= Y
constraint: add(0,X) >= X
constraint: add(s(X),Y) >= s(add(X,Y))
constraint: first(0,X) >= nil
constraint: first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z))
constraint: from(X) >= cons(X,from(s(X)))
constraint: Marked_first(s(X),cons(Y,Z)) >= Marked_first(X,Z)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(true,X) >= X ;
  and(false,Y) >= false ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  add(0,X) >= X ;
  add(s(X),Y) >= s(add(X,Y)) ;
  first(0,X) >= nil ;
  first(s(X),cons(Y,Z)) >= cons(Y,first(X,Z)) ;
  from(X) >= cons(X,from(s(X))) ;
  Marked_from(X) >= Marked_from(s(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_from(X) > Marked_from(s(X)) ;
 }
 } 
=== 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 : 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 0.235409 seconds (real time)
Cime Exit Status: 0