- : 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)) -> p(minus(X,Y))
[3] p(s(X)) -> X
[4] div(0,s(Y)) -> 0
[5] div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))


Sub problem: 
guided: 

DP termination of:
<Marked_minus(s(X),s(Y)) , Marked_p(minus(X,Y))>
<Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)>
<Marked_div(s(X),s(Y)) , Marked_div(minus(X,Y),s(Y))>
<Marked_div(s(X),s(Y)) , Marked_minus(X,Y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_div(s(X),s(Y)) , Marked_div(minus(X,Y),s(Y))> 
      --> <Marked_div(s(X),s(Y)) , Marked_div(minus(X,Y),s(Y))>
}

{  <Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)> 
      --> <Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(s(X),s(Y)) >= p(minus(X,Y)) ;
  minus(X,0) >= X ;
  p(s(X)) >= X ;
  div(0,s(Y)) >= 0 ;
  div(s(X),s(Y)) >= s(div(minus(X,Y),s(Y))) ;
  Marked_div(s(X),s(Y)) >= Marked_div(minus(X,Y),s(Y)) ;
 }
 + Disjunctions:{ 
{
  Marked_div(s(X),s(Y)) > Marked_div(minus(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: minus(s(X),s(Y)) >= p(minus(X,Y))
constraint: minus(X,0) >= X
constraint: p(s(X)) >= X
constraint: div(0,s(Y)) >= 0
constraint: div(s(X),s(Y)) >= s(div(minus(X,Y),s(Y)))
constraint: Marked_div(s(X),s(Y)) >= Marked_div(minus(X,Y),s(Y))
APPLY CRITERIA (Subterm criterion)

ST: Marked_minus -> 1

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)) -> p(minus(X,Y))
[3] p(s(X)) -> X
[4] div(0,s(Y)) -> 0
[5] div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(s(X),s(Y)) , Marked_p(minus(X,Y))>
<Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)>
<Marked_div(s(X),s(Y)) , Marked_div(minus(X,Y),s(Y))>
<Marked_div(s(X),s(Y)) , Marked_minus(X,Y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_div(s(X),s(Y)) , Marked_div(minus(X,Y),s(Y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0,X1) = 1*X0 + 0; 
 [ div ] (X0,X1) = 2*X0 + 0; 
 [ p ] (X0) = 2 + 1*X0 + 0; 
 [ 0 ] () = 0; 
 [ Marked_div ] (X0,X1) = 2*X0 + 0; 
 [ s ] (X0) = 2 + 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.037602 seconds (real time)
Cime Exit Status: 0