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

TRS termination of:
[1] minus(0,Y) -> 0
[2] minus(s(X),s(Y)) -> minus(X,Y)
[3] geq(X,0) -> true
[4] geq(0,s(Y)) -> false
[5] geq(s(X),s(Y)) -> geq(X,Y)
[6] div(0,s(Y)) -> 0
[7] div(s(X),s(Y)) -> if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)
[8] if(true,X,Y) -> X
[9] if(false,X,Y) -> Y


Sub problem: 
guided: 

DP termination of:
<Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)>
<Marked_geq(s(X),s(Y)) , Marked_geq(X,Y)>
<Marked_div(s(X),s(Y)) , Marked_if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)>
<Marked_div(s(X),s(Y)) , Marked_geq(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 3 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_geq(s(X),s(Y)) , Marked_geq(X,Y)> 
      --> <Marked_geq(s(X),s(Y)) , Marked_geq(X,Y)>
}

{  <Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)> 
      --> <Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(0,Y) >= 0 ;
  minus(s(X),s(Y)) >= minus(X,Y) ;
  geq(0,s(Y)) >= false ;
  geq(s(X),s(Y)) >= geq(X,Y) ;
  geq(X,0) >= true ;
  div(0,s(Y)) >= 0 ;
  div(s(X),s(Y)) >= if(geq(X,Y),s(div(minus(X,Y),s(Y))),0) ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= 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(0,Y) >= 0
constraint: minus(s(X),s(Y)) >= minus(X,Y)
constraint: geq(0,s(Y)) >= false
constraint: geq(s(X),s(Y)) >= geq(X,Y)
constraint: geq(X,0) >= true
constraint: div(0,s(Y)) >= 0
constraint: div(s(X),s(Y)) >= if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)
constraint: if(true,X,Y) >= X
constraint: if(false,X,Y) >= Y
constraint: Marked_div(s(X),s(Y)) >= Marked_div(minus(X,Y),s(Y))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(0,Y) >= 0 ;
  minus(s(X),s(Y)) >= minus(X,Y) ;
  geq(0,s(Y)) >= false ;
  geq(s(X),s(Y)) >= geq(X,Y) ;
  geq(X,0) >= true ;
  div(0,s(Y)) >= 0 ;
  div(s(X),s(Y)) >= if(geq(X,Y),s(div(minus(X,Y),s(Y))),0) ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  Marked_geq(s(X),s(Y)) >= Marked_geq(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_geq(s(X),s(Y)) > Marked_geq(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: minus(0,Y) >= 0
constraint: minus(s(X),s(Y)) >= minus(X,Y)
constraint: geq(0,s(Y)) >= false
constraint: geq(s(X),s(Y)) >= geq(X,Y)
constraint: geq(X,0) >= true
constraint: div(0,s(Y)) >= 0
constraint: div(s(X),s(Y)) >= if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)
constraint: if(true,X,Y) >= X
constraint: if(false,X,Y) >= Y
constraint: Marked_geq(s(X),s(Y)) >= Marked_geq(X,Y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(0,Y) >= 0 ;
  minus(s(X),s(Y)) >= minus(X,Y) ;
  geq(0,s(Y)) >= false ;
  geq(s(X),s(Y)) >= geq(X,Y) ;
  geq(X,0) >= true ;
  div(0,s(Y)) >= 0 ;
  div(s(X),s(Y)) >= if(geq(X,Y),s(div(minus(X,Y),s(Y))),0) ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  Marked_minus(s(X),s(Y)) >= Marked_minus(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_minus(s(X),s(Y)) > Marked_minus(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: minus(0,Y) >= 0
constraint: minus(s(X),s(Y)) >= minus(X,Y)
constraint: geq(0,s(Y)) >= false
constraint: geq(s(X),s(Y)) >= geq(X,Y)
constraint: geq(X,0) >= true
constraint: div(0,s(Y)) >= 0
constraint: div(s(X),s(Y)) >= if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)
constraint: if(true,X,Y) >= X
constraint: if(false,X,Y) >= Y
constraint: Marked_minus(s(X),s(Y)) >= Marked_minus(X,Y)
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(0,Y) -> 0
[2] minus(s(X),s(Y)) -> minus(X,Y)
[3] geq(X,0) -> true
[4] geq(0,s(Y)) -> false
[5] geq(s(X),s(Y)) -> geq(X,Y)
[6] div(0,s(Y)) -> 0
[7] div(s(X),s(Y)) -> if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)
[8] if(true,X,Y) -> X
[9] if(false,X,Y) -> Y
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)>
<Marked_geq(s(X),s(Y)) , Marked_geq(X,Y)>
<Marked_div(s(X),s(Y)) , Marked_if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)>
<Marked_div(s(X),s(Y)) , Marked_geq(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 = 
      [ 0 ] () = 0; 
 [ geq ] (X0,X1) = 0; 
 [ s ] (X0) = 2 + 0; 
 [ div ] (X0,X1) = 2*X0 + 0; 
 [ minus ] (X0,X1) = 0; 
 [ Marked_div ] (X0,X1) = 3*X0 + 0; 
 [ false ] () = 0; 
 [ true ] () = 0; 
 [ if ] (X0,X1,X2) = 2 + 1*X1 + 1*X2 + 0; 
 ]} 
{
 
DP termination of:
<Marked_geq(s(X),s(Y)) , Marked_geq(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ geq ] (X0,X1) = 0; 
 [ s ] (X0) = 1 + 1*X0 + 0; 
 [ Marked_geq ] (X0,X1) = 1*X1 + 0; 
 [ div ] (X0,X1) = 1*X0 + 0; 
 [ minus ] (X0,X1) = 1*X0 + 0; 
 [ false ] () = 0; 
 [ true ] () = 0; 
 [ if ] (X0,X1,X2) = 1*X1 + 1*X2 + 0; 
 ]} 
{
 
DP termination of:
<Marked_minus(s(X),s(Y)) , Marked_minus(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ geq ] (X0,X1) = 0; 
 [ s ] (X0) = 1 + 3*X0 + 0; 
 [ div ] (X0,X1) = 2*X0 + 0; 
 [ minus ] (X0,X1) = 0; 
 [ false ] () = 0; 
 [ true ] () = 0; 
 [ Marked_minus ] (X0,X1) = 1*X0 + 0; 
 [ if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.141486 seconds (real time)
Cime Exit Status: 0