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

TRS termination of:
[1] and(x,false) -> false
[2] and(x,not(false)) -> x
[3] not(not(x)) -> x
[4] implies(false,y) -> not(false)
[5] implies(x,false) -> not(x)
[6] implies(not(x),not(y)) -> implies(y,and(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_implies(false,y) , Marked_not(false)>
<Marked_implies(x,false) , Marked_not(x)>
<Marked_implies(not(x),not(y)) , Marked_implies(y,and(x,y))>
<Marked_implies(not(x),not(y)) , Marked_and(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_implies(not(x),not(y)) , Marked_implies(y,and(x,y))> 
      --> <Marked_implies(not(x),not(y)) , Marked_implies(y,and(x,y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  and(x,false) >= false ;
  and(x,not(false)) >= x ;
  not(not(x)) >= x ;
  implies(false,y) >= not(false) ;
  implies(not(x),not(y)) >= implies(y,and(x,y)) ;
  implies(x,false) >= not(x) ;
  Marked_implies(not(x),not(y)) >= Marked_implies(y,and(x,y)) ;
 }
 + Disjunctions:{ 
{
  Marked_implies(not(x),not(y)) > Marked_implies(y,and(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(x,false) >= false
constraint: and(x,not(false)) >= x
constraint: not(not(x)) >= x
constraint: implies(false,y) >= not(false)
constraint: implies(not(x),not(y)) >= implies(y,and(x,y))
constraint: implies(x,false) >= not(x)
constraint: Marked_implies(not(x),not(y)) >= Marked_implies(y,and(x,y))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] and(x,false) -> false
[2] and(x,not(false)) -> x
[3] not(not(x)) -> x
[4] implies(false,y) -> not(false)
[5] implies(x,false) -> not(x)
[6] implies(not(x),not(y)) -> implies(y,and(x,y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_implies(false,y) , Marked_not(false)>
<Marked_implies(x,false) , Marked_not(x)>
<Marked_implies(not(x),not(y)) , Marked_implies(y,and(x,y))>
<Marked_implies(not(x),not(y)) , Marked_and(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_implies(not(x),not(y)) , Marked_implies(y,and(x,y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ false ] () = 2 + 0; 
 [ Marked_implies ] (X0,X1) = 2*X0 + 3*X1 + 0; 
 [ not ] (X0) = 3 + 2*X0 + 0; 
 [ and ] (X0,X1) = 2 + 1*X0 + 0; 
 [ implies ] (X0,X1) = 2 + 3*X0 + 2*X1 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.024050 seconds (real time)
Cime Exit Status: 0