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

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


Sub problem: 
guided: 

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

{  <Marked_*(x,oplus(y,z)) , Marked_*(x,z)> 
      --> <Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,z)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,z)> 
     --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,z)> 
     --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,z)> 
     --> <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,y)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,y)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,y)> 
     --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,y)> 
     --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,y)> 
     --> <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(x,oplus(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,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> 
     --> <Marked_*(x,oplus(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,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> 
     --> <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
  <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
  <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
  <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)> 
     --> <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
   *(1,y) >= y ;
   *(+(x,y),z) >= oplus( *(x,z), *(y,z)) ;
   *(x, *(y,z)) >=  *(otimes(x,y),z) ;
   *(x,oplus(y,z)) >= oplus( *(x,y), *(x,z)) ;
  Marked_*(+(x,y),z) >= Marked_*(x,z) ;
  Marked_*(+(x,y),z) >= Marked_*(y,z) ;
  Marked_*(x, *(y,z)) >= Marked_*(otimes(x,y),z) ;
  Marked_*(x,oplus(y,z)) >= Marked_*(x,y) ;
  Marked_*(x,oplus(y,z)) >= Marked_*(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_*(+(x,y),z) > Marked_*(x,z) ;
 }
{
  Marked_*(+(x,y),z) > Marked_*(y,z) ;
 }
{
  Marked_*(x, *(y,z)) > Marked_*(otimes(x,y),z) ;
 }
{
  Marked_*(x,oplus(y,z)) > Marked_*(x,y) ;
 }
{
  Marked_*(x,oplus(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint:  *(1,y) >= y
constraint:  *(+(x,y),z) >= oplus( *(x,z), *(y,z))
constraint:  *(x, *(y,z)) >=  *(otimes(x,y),z)
constraint:  *(x,oplus(y,z)) >= oplus( *(x,y), *(x,z))
constraint: Marked_*(+(x,y),z) >= Marked_*(x,z)
constraint: Marked_*(+(x,y),z) >= Marked_*(y,z)
constraint: Marked_*(x, *(y,z)) >= Marked_*(otimes(x,y),z)
constraint: Marked_*(x,oplus(y,z)) >= Marked_*(x,y)
constraint: Marked_*(x,oplus(y,z)) >= Marked_*(x,z)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_*(x,oplus(y,z)) , Marked_*(x,z)> 
      --> <Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,z)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,z)> 
     --> <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,y)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,y)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
  <Marked_*(x,oplus(y,z)) , Marked_*(x,y)> 
     --> <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
  <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
  <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)> 
     --> <Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
  <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)> 
     --> <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
   *(1,y) >= y ;
   *(+(x,y),z) >= oplus( *(x,z), *(y,z)) ;
   *(x, *(y,z)) >=  *(otimes(x,y),z) ;
   *(x,oplus(y,z)) >= oplus( *(x,y), *(x,z)) ;
  Marked_*(x, *(y,z)) >= Marked_*(otimes(x,y),z) ;
  Marked_*(x,oplus(y,z)) >= Marked_*(x,y) ;
  Marked_*(x,oplus(y,z)) >= Marked_*(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_*(x, *(y,z)) > Marked_*(otimes(x,y),z) ;
 }
{
  Marked_*(x,oplus(y,z)) > Marked_*(x,y) ;
 }
{
  Marked_*(x,oplus(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 ===
=== STOPING TIMER virtual ===
constraint:  *(1,y) >= y
constraint:  *(+(x,y),z) >= oplus( *(x,z), *(y,z))
constraint:  *(x, *(y,z)) >=  *(otimes(x,y),z)
constraint:  *(x,oplus(y,z)) >= oplus( *(x,y), *(x,z))
constraint: Marked_*(x, *(y,z)) >= Marked_*(otimes(x,y),z)
constraint: Marked_*(x,oplus(y,z)) >= Marked_*(x,y)
constraint: Marked_*(x,oplus(y,z)) >= Marked_*(x,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1]  *(x, *(y,z)) ->  *(otimes(x,y),z)
[2]  *(1,y) -> y
[3]  *(+(x,y),z) -> oplus( *(x,z), *(y,z))
[4]  *(x,oplus(y,z)) -> oplus( *(x,y), *(x,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
<Marked_*(+(x,y),z) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_*(y,z)>
<Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
<Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
<Marked_*(+(x,y),z) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_*(y,z)>
<Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
<Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ * ] (X0,X1) = 1*X1 + 3*X0; 
 [ + ] (X0,X1) = 3*X1 + 1*X0 + 2; 
 [ 1 ] () = 2; 
 [ otimes ] (X0,X1) = 0; 
 [ Marked_* ] (X0,X1) = 1*X0; 
 [ oplus ] (X0,X1) = 0; 
 removing <Marked_*(+(x,y),z),Marked_*(x,z)><Marked_*(+(x,y),z),Marked_*(y,z)>
 [ {
      
     DP termination of:
     <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
<Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
<Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(x, *(y,z)) , Marked_*(otimes(x,y),z)>
<Marked_*(x,oplus(y,z)) , Marked_*(x,y)>
<Marked_*(x,oplus(y,z)) , Marked_*(x,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: otimes -> 1Marked_* -> 1
     and precedence:
     prec (All symbols are Lex.): {  *  >  oplus ; oplus  <   * ; }

 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.053093 seconds (real time)
Cime Exit Status: 0