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

TRS termination of:
[1] f(+(x,0)) -> f(x)
[2] +(x,+(y,z)) -> +(+(x,y),z)


Sub problem: 
guided: 

DP termination of:
<Marked_f(+(x,0)) , Marked_f(x)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(+(x,0)) , Marked_f(x)> --> <Marked_f(+(x,0)) , Marked_f(x)>
}

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

Cime worked for 0.027868 seconds (real time)
Cime Exit Status: 0