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

TRS termination of:
[1] -(x,0) -> x
[2] -(0,s(y)) -> 0
[3] -(s(x),s(y)) -> -(x,y)
[4] lt(x,0) -> false
[5] lt(0,s(y)) -> true
[6] lt(s(x),s(y)) -> lt(x,y)
[7] if(true,x,y) -> x
[8] if(false,x,y) -> y
[9] div(x,0) -> 0
[10] div(0,y) -> 0
[11] div(s(x),s(y)) -> if(lt(x,y),0,s(div(-(x,y),s(y))))


Sub problem: 
guided: 

DP termination of:
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
<Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
<Marked_div(s(x),s(y)) , Marked_if(lt(x,y),0,s(div(-(x,y),s(y))))>
<Marked_div(s(x),s(y)) , Marked_lt(x,y)>
<Marked_div(s(x),s(y)) , Marked_div(-(x,y),s(y))>
<Marked_div(s(x),s(y)) , Marked_-(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_div(s(x),s(y)) , Marked_div(-(x,y),s(y))> 
      --> <Marked_div(s(x),s(y)) , Marked_div(-(x,y),s(y))>
}

{  <Marked_lt(s(x),s(y)) , Marked_lt(x,y)> 
      --> <Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
}

{  <Marked_-(s(x),s(y)) , Marked_-(x,y)> 
      --> <Marked_-(s(x),s(y)) , Marked_-(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  -(0,s(y)) >= 0 ;
  -(s(x),s(y)) >= -(x,y) ;
  -(x,0) >= x ;
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  if(false,x,y) >= y ;
  if(true,x,y) >= x ;
  div(0,y) >= 0 ;
  div(s(x),s(y)) >= if(lt(x,y),0,s(div(-(x,y),s(y)))) ;
  div(x,0) >= 0 ;
  Marked_div(s(x),s(y)) >= Marked_div(-(x,y),s(y)) ;
 }
 + Disjunctions:{ 
{
  Marked_div(s(x),s(y)) > Marked_div(-(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: -(0,s(y)) >= 0
constraint: -(s(x),s(y)) >= -(x,y)
constraint: -(x,0) >= x
constraint: lt(0,s(y)) >= true
constraint: lt(s(x),s(y)) >= lt(x,y)
constraint: lt(x,0) >= false
constraint: if(false,x,y) >= y
constraint: if(true,x,y) >= x
constraint: div(0,y) >= 0
constraint: div(s(x),s(y)) >= if(lt(x,y),0,s(div(-(x,y),s(y))))
constraint: div(x,0) >= 0
constraint: Marked_div(s(x),s(y)) >= Marked_div(-(x,y),s(y))
APPLY CRITERIA (Subterm criterion)

ST: Marked_lt -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_- -> 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] -(x,0) -> x
[2] -(0,s(y)) -> 0
[3] -(s(x),s(y)) -> -(x,y)
[4] lt(x,0) -> false
[5] lt(0,s(y)) -> true
[6] lt(s(x),s(y)) -> lt(x,y)
[7] if(true,x,y) -> x
[8] if(false,x,y) -> y
[9] div(x,0) -> 0
[10] div(0,y) -> 0
[11] div(s(x),s(y)) -> if(lt(x,y),0,s(div(-(x,y),s(y))))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_-(s(x),s(y)) , Marked_-(x,y)>
<Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
<Marked_div(s(x),s(y)) , Marked_if(lt(x,y),0,s(div(-(x,y),s(y))))>
<Marked_div(s(x),s(y)) , Marked_lt(x,y)>
<Marked_div(s(x),s(y)) , Marked_div(-(x,y),s(y))>
<Marked_div(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_div(s(x),s(y)) , Marked_div(-(x,y),s(y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ - ] (X0,X1) = 1*X0 + 0; 
 [ Marked_div ] (X0,X1) = 3*X0 + 0; 
 [ lt ] (X0,X1) = 0; 
 [ s ] (X0) = 2 + 1*X0 + 0; 
 [ if ] (X0,X1,X2) = 2*X1 + 1*X2 + 0; 
 [ 0 ] () = 0; 
 [ true ] () = 0; 
 [ false ] () = 0; 
 [ div ] (X0,X1) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.068013 seconds (real time)
Cime Exit Status: 0