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

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


Sub problem: 
guided: 

DP termination of:
<Marked_++(.(x,y),z) , Marked_++(y,z)>
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_++(++(x,y),z) , Marked_++(y,z)> 
      --> <Marked_++(++(x,y),z) , Marked_++(y,z)>
  <Marked_++(++(x,y),z) , Marked_++(y,z)> 
     --> <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
  <Marked_++(++(x,y),z) , Marked_++(y,z)> 
     --> <Marked_++(.(x,y),z) , Marked_++(y,z)>
  <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))> 
     --> <Marked_++(++(x,y),z) , Marked_++(y,z)>
  <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))> 
     --> <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
  <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))> 
     --> <Marked_++(.(x,y),z) , Marked_++(y,z)>
  <Marked_++(.(x,y),z) , Marked_++(y,z)> 
     --> <Marked_++(++(x,y),z) , Marked_++(y,z)>
  <Marked_++(.(x,y),z) , Marked_++(y,z)> 
     --> <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
  <Marked_++(.(x,y),z) , Marked_++(y,z)> 
     --> <Marked_++(.(x,y),z) , Marked_++(y,z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ++(++(x,y),z) >= ++(x,++(y,z)) ;
  ++(nil,y) >= y ;
  ++(.(x,y),z) >= .(x,++(y,z)) ;
  ++(x,nil) >= x ;
  Marked_++(++(x,y),z) >= Marked_++(x,++(y,z)) ;
  Marked_++(++(x,y),z) >= Marked_++(y,z) ;
  Marked_++(.(x,y),z) >= Marked_++(y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_++(++(x,y),z) > Marked_++(x,++(y,z)) ;
 }
{
  Marked_++(++(x,y),z) > Marked_++(y,z) ;
 }
{
  Marked_++(.(x,y),z) > Marked_++(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: ++(++(x,y),z) >= ++(x,++(y,z))
constraint: ++(nil,y) >= y
constraint: ++(.(x,y),z) >= .(x,++(y,z))
constraint: ++(x,nil) >= x
constraint: Marked_++(++(x,y),z) >= Marked_++(x,++(y,z))
constraint: Marked_++(++(x,y),z) >= Marked_++(y,z)
constraint: Marked_++(.(x,y),z) >= Marked_++(y,z)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_++(.(x,y),z) , Marked_++(y,z)> 
      --> <Marked_++(.(x,y),z) , Marked_++(y,z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ++(++(x,y),z) >= ++(x,++(y,z)) ;
  ++(nil,y) >= y ;
  ++(.(x,y),z) >= .(x,++(y,z)) ;
  ++(x,nil) >= x ;
  Marked_++(.(x,y),z) >= Marked_++(y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_++(.(x,y),z) > Marked_++(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: ++(++(x,y),z) >= ++(x,++(y,z))
constraint: ++(nil,y) >= y
constraint: ++(.(x,y),z) >= .(x,++(y,z))
constraint: ++(x,nil) >= x
constraint: Marked_++(.(x,y),z) >= Marked_++(y,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] ++(nil,y) -> y
[2] ++(x,nil) -> x
[3] ++(.(x,y),z) -> .(x,++(y,z))
[4] ++(++(x,y),z) -> ++(x,++(y,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_++(.(x,y),z) , Marked_++(y,z)>
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_++(.(x,y),z) , Marked_++(y,z)>
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ ++ ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 [ . ] (X0,X1) = 1*X1 + 3*X0; 
 [ nil ] () = 2; 
 [ Marked_++ ] (X0,X1) = 1*X1 + 2*X0; 
 removing <Marked_++(++(x,y),z),Marked_++(x,++(y,z))><Marked_++(++(x,y),z),
Marked_++(y,z)>
 [ {
      
     DP termination of:
     <Marked_++(.(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_++(.(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ ++ ] (X0,X1) = 2*X0 + 1*X1 + 0; 
 [ . ] (X0,X1) = 2 + 3*X0 + 1*X1 + 0; 
 [ nil ] () = 3 + 0; 
 [ Marked_++ ] (X0,X1) = 3*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.029280 seconds (real time)
Cime Exit Status: 0