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

TRS termination of:
[1]  *(x,+(y,z)) -> +( *(x,y), *(x,z))
[2]  *(+(y,z),x) -> +( *(x,y), *(x,z))
[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_+( *(x,y), *(x,z))>
<Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
<Marked_*(+(y,z),x) , Marked_+( *(x,y), *(x,z))>
<Marked_*(+(y,z),x) , Marked_*(x,y)>
<Marked_*(+(y,z),x) , Marked_*(x,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_+(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 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_*(+(y,z),x) , Marked_*(x,z)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(+(y,z),x) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <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_*(+(y,z),x) , Marked_*(x,z)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(+(y,z),x) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(+(y,z),x) , Marked_*(x,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(y,z),x) , Marked_*(x,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(+(y,z),x) , Marked_*(x,z)> --> <Marked_*(+(y,z),x) , Marked_*(x,z)>
  <Marked_*(+(y,z),x) , Marked_*(x,z)> --> <Marked_*(+(y,z),x) , Marked_*(x,y)>
  <Marked_*(+(y,z),x) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(+(y,z),x) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(+(y,z),x) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(y,z),x) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(+(y,z),x) , Marked_*(x,y)> --> <Marked_*(+(y,z),x) , Marked_*(x,z)>
  <Marked_*(+(y,z),x) , Marked_*(x,y)> --> <Marked_*(+(y,z),x) , Marked_*(x,y)>
  <Marked_*(+(y,z),x) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(+(y,z),x) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(+(y,z),x) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(+(y,z),x) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(+(y,z),x) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(+(y,z),x) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
}

{  <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_+(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))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  +(+(x,y),z) >= +(x,+(y,z)) ;
   *(+(y,z),x) >= +( *(x,y), *(x,z)) ;
   *( *(x,y),z) >=  *(x, *(y,z)) ;
   *(x,+(y,z)) >= +( *(x,y), *(x,z)) ;
  Marked_*(+(y,z),x) >= Marked_*(x,y) ;
  Marked_*(+(y,z),x) >= Marked_*(x,z) ;
  Marked_*( *(x,y),z) >= Marked_*(x, *(y,z)) ;
  Marked_*( *(x,y),z) >= Marked_*(y,z) ;
  Marked_*(x,+(y,z)) >= Marked_*(x,y) ;
  Marked_*(x,+(y,z)) >= Marked_*(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_*(+(y,z),x) > Marked_*(x,y) ;
 }
{
  Marked_*(+(y,z),x) > Marked_*(x,z) ;
 }
{
  Marked_*( *(x,y),z) > Marked_*(x, *(y,z)) ;
 }
{
  Marked_*( *(x,y),z) > Marked_*(y,z) ;
 }
{
  Marked_*(x,+(y,z)) > Marked_*(x,y) ;
 }
{
  Marked_*(x,+(y,z)) > Marked_*(x,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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: +(+(x,y),z) >= +(x,+(y,z))
constraint:  *(+(y,z),x) >= +( *(x,y), *(x,z))
constraint:  *( *(x,y),z) >=  *(x, *(y,z))
constraint:  *(x,+(y,z)) >= +( *(x,y), *(x,z))
constraint: Marked_*(+(y,z),x) >= Marked_*(x,y)
constraint: Marked_*(+(y,z),x) >= Marked_*(x,z)
constraint: Marked_*( *(x,y),z) >= Marked_*(x, *(y,z))
constraint: Marked_*( *(x,y),z) >= Marked_*(y,z)
constraint: Marked_*(x,+(y,z)) >= Marked_*(x,y)
constraint: Marked_*(x,+(y,z)) >= Marked_*(x,z)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  +(+(x,y),z) >= +(x,+(y,z)) ;
   *(+(y,z),x) >= +( *(x,y), *(x,z)) ;
   *( *(x,y),z) >=  *(x, *(y,z)) ;
   *(x,+(y,z)) >= +( *(x,y), *(x,z)) ;
  Marked_+(+(x,y),z) >= Marked_+(x,+(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) ;
 }
 } 
=== 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: +(+(x,y),z) >= +(x,+(y,z))
constraint:  *(+(y,z),x) >= +( *(x,y), *(x,z))
constraint:  *( *(x,y),z) >=  *(x, *(y,z))
constraint:  *(x,+(y,z)) >= +( *(x,y), *(x,z))
constraint: Marked_+(+(x,y),z) >= Marked_+(x,+(y,z))
constraint: Marked_+(+(x,y),z) >= Marked_+(y,z)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_*(x,+(y,z)) , Marked_*(x,z)> 
      --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  +(+(x,y),z) >= +(x,+(y,z)) ;
   *(+(y,z),x) >= +( *(x,y), *(x,z)) ;
   *( *(x,y),z) >=  *(x, *(y,z)) ;
   *(x,+(y,z)) >= +( *(x,y), *(x,z)) ;
  Marked_*(x,+(y,z)) >= Marked_*(x,y) ;
  Marked_*(x,+(y,z)) >= Marked_*(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_*(x,+(y,z)) > Marked_*(x,y) ;
 }
{
  Marked_*(x,+(y,z)) > Marked_*(x,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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: +(+(x,y),z) >= +(x,+(y,z))
constraint:  *(+(y,z),x) >= +( *(x,y), *(x,z))
constraint:  *( *(x,y),z) >=  *(x, *(y,z))
constraint:  *(x,+(y,z)) >= +( *(x,y), *(x,z))
constraint: Marked_*(x,+(y,z)) >= Marked_*(x,y)
constraint: Marked_*(x,+(y,z)) >= Marked_*(x,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1]  *(x,+(y,z)) -> +( *(x,y), *(x,z))
[2]  *(+(y,z),x) -> +( *(x,y), *(x,z))
[3]  *( *(x,y),z) ->  *(x, *(y,z))
[4] +(+(x,y),z) -> +(x,+(y,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_*(x,+(y,z)) , Marked_+( *(x,y), *(x,z))>
<Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
<Marked_*(+(y,z),x) , Marked_+( *(x,y), *(x,z))>
<Marked_*(+(y,z),x) , Marked_*(x,y)>
<Marked_*(+(y,z),x) , Marked_*(x,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_+(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
<Marked_*(+(y,z),x) , Marked_*(x,y)>
<Marked_*(+(y,z),x) , Marked_*(x,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 + 2*X0 + 2; 
 [ * ] (X0,X1) = 2*X1*X0 + 2*X1 + 2*X0 + 1; 
 [ Marked_* ] (X0,X1) = 2*X1*X0 + 2*X0; 
 removing <Marked_*(+(y,z),x),Marked_*(x,y)><Marked_*(+(y,z),x),Marked_*(x,z)><
Marked_*( *(x,y),z),Marked_*(x, *(y,z))><Marked_*( *(x,y),z),Marked_*(y,z)>
 [ {
      
     DP termination of:
     <Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ + ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; 
 [ * ] (X0,X1) = 1*X0 + 1*X1 + 2*X1*X0 + 0; 
 [ Marked_* ] (X0,X1) = 1*X1 + 2*X1*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ + ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 [ Marked_+ ] (X0,X1) = 2*X0 + 1*X1 + 0; 
 [ * ] (X0,X1) = 2*X0 + 1*X1 + 2*X1*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.270246 seconds (real time)
Cime Exit Status: 0