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

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


Sub problem: 
guided: 

DP termination of:
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_double(s(x)) , Marked_double(x)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,s(y))>
<Marked_plus(s(x),y) , Marked_plus(minus(x,y),double(y))>
<Marked_plus(s(x),y) , Marked_minus(x,y)>
<Marked_plus(s(x),y) , Marked_double(y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_plus(s(x),y) , Marked_plus(minus(x,y),double(y))> 
      --> <Marked_plus(s(x),y) , Marked_plus(minus(x,y),double(y))>
  <Marked_plus(s(x),y) , Marked_plus(minus(x,y),double(y))> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,s(y))>
  <Marked_plus(s(x),y) , Marked_plus(minus(x,y),double(y))> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,y)>
  <Marked_plus(s(x),y) , Marked_plus(x,s(y))> 
     --> <Marked_plus(s(x),y) , Marked_plus(minus(x,y),double(y))>
  <Marked_plus(s(x),y) , Marked_plus(x,s(y))> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,s(y))>
  <Marked_plus(s(x),y) , Marked_plus(x,s(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(minus(x,y),double(y))>
  <Marked_plus(s(x),y) , Marked_plus(x,y)> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,s(y))>
  <Marked_plus(s(x),y) , Marked_plus(x,y)> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,y)>
}

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

{  <Marked_double(s(x)) , Marked_double(x)> 
      --> <Marked_double(s(x)) , Marked_double(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  double(0) >= 0 ;
  double(s(x)) >= s(s(double(x))) ;
  plus(0,y) >= y ;
  plus(s(x),y) >= s(plus(minus(x,y),double(y))) ;
  plus(s(x),y) >= s(plus(x,y)) ;
  plus(s(x),y) >= plus(x,s(y)) ;
  Marked_plus(s(x),y) >= Marked_plus(minus(x,y),double(y)) ;
  Marked_plus(s(x),y) >= Marked_plus(x,s(y)) ;
  Marked_plus(s(x),y) >= Marked_plus(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_plus(s(x),y) > Marked_plus(minus(x,y),double(y)) ;
 }
{
  Marked_plus(s(x),y) > Marked_plus(x,s(y)) ;
 }
{
  Marked_plus(s(x),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: minus(s(x),s(y)) >= minus(x,y)
constraint: minus(x,0) >= x
constraint: double(0) >= 0
constraint: double(s(x)) >= s(s(double(x)))
constraint: plus(0,y) >= y
constraint: plus(s(x),y) >= s(plus(minus(x,y),double(y)))
constraint: plus(s(x),y) >= s(plus(x,y))
constraint: plus(s(x),y) >= plus(x,s(y))
constraint: Marked_plus(s(x),y) >= Marked_plus(minus(x,y),double(y))
constraint: Marked_plus(s(x),y) >= Marked_plus(x,s(y))
constraint: Marked_plus(s(x),y) >= Marked_plus(x,y)
APPLY CRITERIA (Subterm criterion)

ST: Marked_minus -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_double -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] minus(x,0) -> x
[2] minus(s(x),s(y)) -> minus(x,y)
[3] double(0) -> 0
[4] double(s(x)) -> s(s(double(x)))
[5] plus(0,y) -> y
[6] plus(s(x),y) -> s(plus(x,y))
[7] plus(s(x),y) -> plus(x,s(y))
[8] plus(s(x),y) -> s(plus(minus(x,y),double(y)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_double(s(x)) , Marked_double(x)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,s(y))>
<Marked_plus(s(x),y) , Marked_plus(minus(x,y),double(y))>
<Marked_plus(s(x),y) , Marked_minus(x,y)>
<Marked_plus(s(x),y) , Marked_double(y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,s(y))>
<Marked_plus(s(x),y) , Marked_plus(minus(x,y),double(y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: minus -> 0
     and precedence:
     prec (All symbols are Lex.): { s  <  double ; s  <  plus ;
                                   s  <  Marked_plus ; double  >  s ;
                                   double  <  plus ; double  <  Marked_plus ;
                                   plus  >  s ; plus  >  double ;
                                   Marked_plus  >  s ; Marked_plus  >  double ;
                                   }

 ]} 
{
 
DP termination of:
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_double(s(x)) , Marked_double(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.057522 seconds (real time)
Cime Exit Status: 0