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

TRS termination of:
[1] purge(nil) -> nil
[2] purge(.(x,y)) -> .(x,purge(remove(x,y)))
[3] remove(x,nil) -> nil
[4] remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))


Sub problem: 
guided: 

DP termination of:
<Marked_purge(.(x,y)) , Marked_purge(remove(x,y))>
<Marked_purge(.(x,y)) , Marked_remove(x,y)>
<Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
<Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_purge(.(x,y)) , Marked_purge(remove(x,y))> 
      --> <Marked_purge(.(x,y)) , Marked_purge(remove(x,y))>
}

{  <Marked_remove(x,.(y,z)) , Marked_remove(x,z)> 
      --> <Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
  <Marked_remove(x,.(y,z)) , Marked_remove(x,z)> 
     --> <Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
  <Marked_remove(x,.(y,z)) , Marked_remove(x,z)> 
     --> <Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
  <Marked_remove(x,.(y,z)) , Marked_remove(x,z)> 
     --> <Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  purge(nil) >= nil ;
  purge(.(x,y)) >= .(x,purge(remove(x,y))) ;
  remove(x,nil) >= nil ;
  remove(x,.(y,z)) >= if(=(x,y),remove(x,z),.(y,remove(x,z))) ;
  Marked_purge(.(x,y)) >= Marked_purge(remove(x,y)) ;
 }
 + Disjunctions:{ 
{
  Marked_purge(.(x,y)) > Marked_purge(remove(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: purge(nil) >= nil
constraint: purge(.(x,y)) >= .(x,purge(remove(x,y)))
constraint: remove(x,nil) >= nil
constraint: remove(x,.(y,z)) >= if(=(x,y),remove(x,z),.(y,remove(x,z)))
constraint: Marked_purge(.(x,y)) >= Marked_purge(remove(x,y))
APPLY CRITERIA (Subterm criterion)

ST: Marked_remove -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] purge(nil) -> nil
[2] purge(.(x,y)) -> .(x,purge(remove(x,y)))
[3] remove(x,nil) -> nil
[4] remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_purge(.(x,y)) , Marked_purge(remove(x,y))>
<Marked_purge(.(x,y)) , Marked_remove(x,y)>
<Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
<Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_purge(.(x,y)) , Marked_purge(remove(x,y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ if ] (X0,X1,X2) = 0; 
 [ . ] (X0,X1) = 3 + 2*X0 + 3*X1 + 0; 
 [ purge ] (X0) = 2*X0 + 0; 
 [ = ] (X0,X1) = 0; 
 [ remove ] (X0,X1) = 0; 
 [ Marked_purge ] (X0) = 2*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
<Marked_remove(x,.(y,z)) , Marked_remove(x,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.049618 seconds (real time)
Cime Exit Status: 0