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

TRS termination of:
[1] del(.(x,.(y,z))) -> f(=(x,y),x,y,z)
[2] f(true,x,y,z) -> del(.(y,z))
[3] f(false,x,y,z) -> .(x,del(.(y,z)))
[4] =(nil,nil) -> true
[5] =(.(x,y),nil) -> false
[6] =(nil,.(y,z)) -> false
[7] =(.(x,y),.(u,v)) -> and(=(x,u),=(y,v))


Sub problem: 
guided: 

DP termination of:
<Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
<Marked_del(.(x,.(y,z))) , Marked_=(x,y)>
<Marked_f(true,x,y,z) , Marked_del(.(y,z))>
<Marked_f(false,x,y,z) , Marked_del(.(y,z))>
<Marked_=(.(x,y),.(u,v)) , Marked_=(x,u)>
<Marked_=(.(x,y),.(u,v)) , Marked_=(y,v)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(false,x,y,z) , Marked_del(.(y,z))> 
      --> <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
  <Marked_f(true,x,y,z) , Marked_del(.(y,z))> 
     --> <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
  <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)> 
     --> <Marked_f(false,x,y,z) , Marked_del(.(y,z))>
  <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)> 
     --> <Marked_f(true,x,y,z) , Marked_del(.(y,z))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(true,x,y,z) >= del(.(y,z)) ;
  f(false,x,y,z) >= .(x,del(.(y,z))) ;
  =(.(x,y),.(u,v)) >= and(=(x,u),=(y,v)) ;
  =(.(x,y),nil) >= false ;
  =(nil,.(y,z)) >= false ;
  =(nil,nil) >= true ;
  del(.(x,.(y,z))) >= f(=(x,y),x,y,z) ;
  Marked_f(true,x,y,z) >= Marked_del(.(y,z)) ;
  Marked_f(false,x,y,z) >= Marked_del(.(y,z)) ;
  Marked_del(.(x,.(y,z))) >= Marked_f(=(x,y),x,y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_f(true,x,y,z) > Marked_del(.(y,z)) ;
 }
{
  Marked_f(false,x,y,z) > Marked_del(.(y,z)) ;
 }
{
  Marked_del(.(x,.(y,z))) > Marked_f(=(x,y),x,y,z) ;
 }
 } 
=== 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: f(true,x,y,z) >= del(.(y,z))
constraint: f(false,x,y,z) >= .(x,del(.(y,z)))
constraint: =(.(x,y),.(u,v)) >= and(=(x,u),=(y,v))
constraint: =(.(x,y),nil) >= false
constraint: =(nil,.(y,z)) >= false
constraint: =(nil,nil) >= true
constraint: del(.(x,.(y,z))) >= f(=(x,y),x,y,z)
constraint: Marked_f(true,x,y,z) >= Marked_del(.(y,z))
constraint: Marked_f(false,x,y,z) >= Marked_del(.(y,z))
constraint: Marked_del(.(x,.(y,z))) >= Marked_f(=(x,y),x,y,z)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(false,x,y,z) , Marked_del(.(y,z))> 
      --> <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
  <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)> 
     --> <Marked_f(false,x,y,z) , Marked_del(.(y,z))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(true,x,y,z) >= del(.(y,z)) ;
  f(false,x,y,z) >= .(x,del(.(y,z))) ;
  =(.(x,y),.(u,v)) >= and(=(x,u),=(y,v)) ;
  =(.(x,y),nil) >= false ;
  =(nil,.(y,z)) >= false ;
  =(nil,nil) >= true ;
  del(.(x,.(y,z))) >= f(=(x,y),x,y,z) ;
  Marked_f(false,x,y,z) >= Marked_del(.(y,z)) ;
  Marked_del(.(x,.(y,z))) >= Marked_f(=(x,y),x,y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_f(false,x,y,z) > Marked_del(.(y,z)) ;
 }
{
  Marked_del(.(x,.(y,z))) > Marked_f(=(x,y),x,y,z) ;
 }
 } 
=== 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: f(true,x,y,z) >= del(.(y,z))
constraint: f(false,x,y,z) >= .(x,del(.(y,z)))
constraint: =(.(x,y),.(u,v)) >= and(=(x,u),=(y,v))
constraint: =(.(x,y),nil) >= false
constraint: =(nil,.(y,z)) >= false
constraint: =(nil,nil) >= true
constraint: del(.(x,.(y,z))) >= f(=(x,y),x,y,z)
constraint: Marked_f(false,x,y,z) >= Marked_del(.(y,z))
constraint: Marked_del(.(x,.(y,z))) >= Marked_f(=(x,y),x,y,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] del(.(x,.(y,z))) -> f(=(x,y),x,y,z)
[2] f(true,x,y,z) -> del(.(y,z))
[3] f(false,x,y,z) -> .(x,del(.(y,z)))
[4] =(nil,nil) -> true
[5] =(.(x,y),nil) -> false
[6] =(nil,.(y,z)) -> false
[7] =(.(x,y),.(u,v)) -> and(=(x,u),=(y,v))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
<Marked_del(.(x,.(y,z))) , Marked_=(x,y)>
<Marked_f(true,x,y,z) , Marked_del(.(y,z))>
<Marked_f(false,x,y,z) , Marked_del(.(y,z))>
<Marked_=(.(x,y),.(u,v)) , Marked_=(x,u)>
<Marked_=(.(x,y),.(u,v)) , Marked_=(y,v)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
<Marked_f(true,x,y,z) , Marked_del(.(y,z))>
<Marked_f(false,x,y,z) , Marked_del(.(y,z))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ f ] (X0,X1,X2,X3) = 2*X3 + 2*X2 + 1*X1; 
 [ u ] () = 0; 
 [ true ] () = 2; 
 [ Marked_del ] (X0) = 2*X0; 
 [ del ] (X0) = 2*X0; 
 [ nil ] () = 2; 
 [ = ] (X0,X1) = 1*X0; 
 [ v ] () = 0; 
 [ false ] () = 0; 
 [ . ] (X0,X1) = 1*X1 + 1*X0; 
 [ Marked_f ] (X0,X1,X2,X3) = 2*X3 + 2*X2 + 2*X0; 
 [ and ] (X0,X1) = 1*X1; 
 removing <Marked_f(true,x,y,z),Marked_del(.(y,z))>
 [ {
      
     DP termination of:
     <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
<Marked_f(false,x,y,z) , Marked_del(.(y,z))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
<Marked_f(false,x,y,z) , Marked_del(.(y,z))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ f ] (X0,X1,X2,X3) = 1*X3 + 2; 
 [ u ] () = 0; 
 [ true ] () = 0; 
 [ Marked_del ] (X0) = 1*X0; 
 [ del ] (X0) = 1*X0; 
 [ nil ] () = 0; 
 [ = ] (X0,X1) = 0; 
 [ v ] () = 0; 
 [ false ] () = 0; 
 [ . ] (X0,X1) = 1*X1 + 1; 
 [ Marked_f ] (X0,X1,X2,X3) = 1*X3 + 2; 
 [ and ] (X0,X1) = 0; 
 removing <Marked_f(false,x,y,z),Marked_del(.(y,z))>
 [ {
      
     DP termination of:
     <Marked_del(.(x,.(y,z))) , Marked_f(=(x,y),x,y,z)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.136956 seconds (real time)
Cime Exit Status: 0