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

TRS termination of:
[1] times(x,0) -> 0
[2] times(x,s(y)) -> plus(times(x,y),x)
[3] plus(x,0) -> x
[4] plus(0,x) -> x
[5] plus(x,s(y)) -> s(plus(x,y))
[6] plus(s(x),y) -> s(plus(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_times(x,s(y)) , Marked_plus(times(x,y),x)>
<Marked_times(x,s(y)) , Marked_times(x,y)>
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_times(x,s(y)) , Marked_times(x,y)> 
      --> <Marked_times(x,s(y)) , Marked_times(x,y)>
}

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

 ]} 
{
 
DP termination of:
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { times  >  plus ; times  >  s ;
                                   plus  <  times ; plus  >  s ; s  <  times ;
                                   s  <  plus ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.040129 seconds (real time)
Cime Exit Status: 0