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

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


Sub problem: 
guided: 

DP termination of:
<Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_quot(x,0,s(z)) , Marked_quot(x,plus(z,s(0)),s(z))>
<Marked_quot(x,0,s(z)) , Marked_plus(z,s(0))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_quot(x,0,s(z)) , Marked_quot(x,plus(z,s(0)),s(z))> 
      --> <Marked_quot(x,0,s(z)) , Marked_quot(x,plus(z,s(0)),s(z))>
  <Marked_quot(x,0,s(z)) , Marked_quot(x,plus(z,s(0)),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_quot(x,0,s(z)) , Marked_quot(x,plus(z,s(0)),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_plus(s(x),y) , Marked_plus(x,y)> 
      --> <Marked_plus(s(x),y) , Marked_plus(x,y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_quot -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

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

Cime worked for 0.063435 seconds (real time)
Cime Exit Status: 0