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

TRS termination of:
[1] plus(0,Y) -> Y
[2] plus(s(X),Y) -> s(plus(X,Y))
[3] min(X,0) -> X
[4] min(s(X),s(Y)) -> min(X,Y)
[5] min(min(X,Y),Z) -> min(X,plus(Y,Z))
[6] quot(0,s(Y)) -> 0
[7] quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))


Sub problem: 
guided: 

DP termination of:
<Marked_plus(s(X),Y) , Marked_plus(X,Y)>
<Marked_min(s(X),s(Y)) , Marked_min(X,Y)>
<Marked_min(min(X,Y),Z) , Marked_min(X,plus(Y,Z))>
<Marked_min(min(X,Y),Z) , Marked_plus(Y,Z)>
<Marked_quot(s(X),s(Y)) , Marked_quot(min(X,Y),s(Y))>
<Marked_quot(s(X),s(Y)) , Marked_min(X,Y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_quot(s(X),s(Y)) , Marked_quot(min(X,Y),s(Y))> 
      --> <Marked_quot(s(X),s(Y)) , Marked_quot(min(X,Y),s(Y))>
}

{  <Marked_min(min(X,Y),Z) , Marked_min(X,plus(Y,Z))> 
      --> <Marked_min(min(X,Y),Z) , Marked_min(X,plus(Y,Z))>
  <Marked_min(min(X,Y),Z) , Marked_min(X,plus(Y,Z))> 
     --> <Marked_min(s(X),s(Y)) , Marked_min(X,Y)>
  <Marked_min(s(X),s(Y)) , Marked_min(X,Y)> 
     --> <Marked_min(min(X,Y),Z) , Marked_min(X,plus(Y,Z))>
  <Marked_min(s(X),s(Y)) , Marked_min(X,Y)> 
     --> <Marked_min(s(X),s(Y)) , Marked_min(X,Y)>
}

{  <Marked_plus(s(X),Y) , Marked_plus(X,Y)> 
      --> <Marked_plus(s(X),Y) , Marked_plus(X,Y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  plus(0,Y) >= Y ;
  plus(s(X),Y) >= s(plus(X,Y)) ;
  min(s(X),s(Y)) >= min(X,Y) ;
  min(min(X,Y),Z) >= min(X,plus(Y,Z)) ;
  min(X,0) >= X ;
  quot(0,s(Y)) >= 0 ;
  quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) ;
  Marked_quot(s(X),s(Y)) >= Marked_quot(min(X,Y),s(Y)) ;
 }
 + Disjunctions:{ 
{
  Marked_quot(s(X),s(Y)) > Marked_quot(min(X,Y),s(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: plus(0,Y) >= Y
constraint: plus(s(X),Y) >= s(plus(X,Y))
constraint: min(s(X),s(Y)) >= min(X,Y)
constraint: min(min(X,Y),Z) >= min(X,plus(Y,Z))
constraint: min(X,0) >= X
constraint: quot(0,s(Y)) >= 0
constraint: quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y)))
constraint: Marked_quot(s(X),s(Y)) >= Marked_quot(min(X,Y),s(Y))
APPLY CRITERIA (Subterm criterion)

ST: Marked_min -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 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] plus(0,Y) -> Y
[2] plus(s(X),Y) -> s(plus(X,Y))
[3] min(X,0) -> X
[4] min(s(X),s(Y)) -> min(X,Y)
[5] min(min(X,Y),Z) -> min(X,plus(Y,Z))
[6] quot(0,s(Y)) -> 0
[7] quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_plus(s(X),Y) , Marked_plus(X,Y)>
<Marked_min(s(X),s(Y)) , Marked_min(X,Y)>
<Marked_min(min(X,Y),Z) , Marked_min(X,plus(Y,Z))>
<Marked_min(min(X,Y),Z) , Marked_plus(Y,Z)>
<Marked_quot(s(X),s(Y)) , Marked_quot(min(X,Y),s(Y))>
<Marked_quot(s(X),s(Y)) , Marked_min(X,Y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_quot(s(X),s(Y)) , Marked_quot(min(X,Y),s(Y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ plus ] (X0,X1) = 2*X0 + 2*X1 + 0; 
 [ Z ] () = 0; 
 [ s ] (X0) = 2 + 1*X0 + 0; 
 [ Marked_quot ] (X0,X1) = 2*X0 + 0; 
 [ 0 ] () = 0; 
 [ quot ] (X0,X1) = 1*X0 + 0; 
 [ min ] (X0,X1) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_min(s(X),s(Y)) , Marked_min(X,Y)>
<Marked_min(min(X,Y),Z) , Marked_min(X,plus(Y,Z))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_plus(s(X),Y) , Marked_plus(X,Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.044902 seconds (real time)
Cime Exit Status: 0