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

TRS termination of:
[1] +( *(x,y), *(x,z)) ->  *(x,+(y,z))
[2] +(+(x,y),z) -> +(x,+(y,z))
[3] +( *(x,y),+( *(x,z),u)) -> +( *(x,+(y,z)),u)


Sub problem: 
guided: 

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

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

Cime worked for 0.045161 seconds (real time)
Cime Exit Status: 0