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

TRS termination of:
[1] ack(0,y) -> s(y)
[2] ack(s(x),0) -> ack(x,s(0))
[3] ack(s(x),s(y)) -> ack(x,ack(s(x),y))


Sub problem: 
guided: 

DP termination of:
<Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
      --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
     --> <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
  <Marked_ack(s(x),0) , Marked_ack(x,s(0))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),0) , Marked_ack(x,s(0))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(0,y) >= s(y) ;
  Marked_ack(s(x),s(y)) >= Marked_ack(s(x),y) ;
  Marked_ack(s(x),s(y)) >= Marked_ack(x,ack(s(x),y)) ;
  Marked_ack(s(x),0) >= Marked_ack(x,s(0)) ;
 }
 + Disjunctions:{ 
{
  Marked_ack(s(x),s(y)) > Marked_ack(s(x),y) ;
 }
{
  Marked_ack(s(x),s(y)) > Marked_ack(x,ack(s(x),y)) ;
 }
{
  Marked_ack(s(x),0) > Marked_ack(x,s(0)) ;
 }
 } 
=== 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 ===
=== STOPING TIMER virtual ===
constraint: ack(s(x),s(y)) >= ack(x,ack(s(x),y))
constraint: ack(s(x),0) >= ack(x,s(0))
constraint: ack(0,y) >= s(y)
constraint: Marked_ack(s(x),s(y)) >= Marked_ack(s(x),y)
constraint: Marked_ack(s(x),s(y)) >= Marked_ack(x,ack(s(x),y))
constraint: Marked_ack(s(x),0) >= Marked_ack(x,s(0))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] ack(0,y) -> s(y)
[2] ack(s(x),0) -> ack(x,s(0))
[3] ack(s(x),s(y)) -> ack(x,ack(s(x),y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { s  <  ack ; s  <  Marked_ack ; ack  >  s ;
                                   ack  <  Marked_ack ; Marked_ack  >  s ;
                                   Marked_ack  >  ack ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.034034 seconds (real time)
Cime Exit Status: 0