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

TRS termination of:
[1] div(0,y) -> 0
[2] div(x,y) -> quot(x,y,y)
[3] quot(0,s(y),z) -> 0
[4] quot(s(x),s(y),z) -> quot(x,y,z)
[5] quot(x,0,s(z)) -> s(div(x,s(z)))


Sub problem: 
guided: 

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

{  <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))> 
      --> <Marked_div(x,y) , Marked_quot(x,y,y)>
  <Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)> 
     --> <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
  <Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)> 
     --> <Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)>
  <Marked_div(x,y) , Marked_quot(x,y,y)> 
     --> <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
  <Marked_div(x,y) , Marked_quot(x,y,y)> 
     --> <Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_quot -> 1
Marked_div -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_div(x,y) , Marked_quot(x,y,y)> 
      --> <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
  <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))> 
     --> <Marked_div(x,y) , Marked_quot(x,y,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  div(0,y) >= 0 ;
  div(x,y) >= quot(x,y,y) ;
  quot(0,s(y),z) >= 0 ;
  quot(s(x),s(y),z) >= quot(x,y,z) ;
  quot(x,0,s(z)) >= s(div(x,s(z))) ;
  Marked_quot(x,0,s(z)) >= Marked_div(x,s(z)) ;
  Marked_div(x,y) >= Marked_quot(x,y,y) ;
 }
 + Disjunctions:{ 
{
  Marked_quot(x,0,s(z)) > Marked_div(x,s(z)) ;
 }
{
  Marked_div(x,y) > Marked_quot(x,y,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: div(0,y) >= 0
constraint: div(x,y) >= quot(x,y,y)
constraint: quot(0,s(y),z) >= 0
constraint: quot(s(x),s(y),z) >= quot(x,y,z)
constraint: quot(x,0,s(z)) >= s(div(x,s(z)))
constraint: Marked_quot(x,0,s(z)) >= Marked_div(x,s(z))
constraint: Marked_div(x,y) >= Marked_quot(x,y,y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] div(0,y) -> 0
[2] div(x,y) -> quot(x,y,y)
[3] quot(0,s(y),z) -> 0
[4] quot(s(x),s(y),z) -> quot(x,y,z)
[5] quot(x,0,s(z)) -> s(div(x,s(z)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_div(x,y) , Marked_quot(x,y,y)>
<Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)>
<Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_div(x,y) , Marked_quot(x,y,y)>
<Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)>
<Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
<Marked_div(x,y) , Marked_quot(x,y,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
<Marked_div(x,y) , Marked_quot(x,y,y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ 0 ] () = 3; 
 [ Marked_quot ] (X0,X1,X2) = 3*X1 + 3*X0 + 3; 
 [ quot ] (X0,X1,X2) = 3; 
 [ div ] (X0,X1) = 3; 
 [ Marked_div ] (X0,X1) = 3*X1 + 3*X0 + 3; 
 [ s ] (X0) = 0; 
 removing <Marked_quot(x,0,s(z)),Marked_div(x,s(z))>
 [ {
      
     DP termination of:
     <Marked_div(x,y) , Marked_quot(x,y,y)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.035783 seconds (real time)
Cime Exit Status: 0