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

TRS termination of:
[1] c(c(c(y))) -> c(c(a(y,0)))
[2] c(a(a(0,x),y)) -> a(c(c(c(0))),y)
[3] c(y) -> y


Sub problem: 
guided: 

DP termination of:
<Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
<Marked_c(c(c(y))) , Marked_c(a(y,0))>
<Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
<Marked_c(a(a(0,x),y)) , Marked_c(c(0))>
<Marked_c(a(a(0,x),y)) , Marked_c(0)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_c(a(a(0,x),y)) , Marked_c(c(0))> 
      --> <Marked_c(a(a(0,x),y)) , Marked_c(c(0))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(0))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(0))> 
     --> <Marked_c(c(c(y))) , Marked_c(a(y,0))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(0))> 
     --> <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(0))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))> 
     --> <Marked_c(c(c(y))) , Marked_c(a(y,0))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))> 
     --> <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
  <Marked_c(c(c(y))) , Marked_c(a(y,0))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(0))>
  <Marked_c(c(c(y))) , Marked_c(a(y,0))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
  <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(0))>
  <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
  <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))> 
     --> <Marked_c(c(c(y))) , Marked_c(a(y,0))>
  <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))> 
     --> <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  c(c(c(y))) >= c(c(a(y,0))) ;
  c(a(a(0,x),y)) >= a(c(c(c(0))),y) ;
  c(y) >= y ;
  Marked_c(c(c(y))) >= Marked_c(c(a(y,0))) ;
  Marked_c(c(c(y))) >= Marked_c(a(y,0)) ;
  Marked_c(a(a(0,x),y)) >= Marked_c(c(c(0))) ;
  Marked_c(a(a(0,x),y)) >= Marked_c(c(0)) ;
 }
 + Disjunctions:{ 
{
  Marked_c(c(c(y))) > Marked_c(c(a(y,0))) ;
 }
{
  Marked_c(c(c(y))) > Marked_c(a(y,0)) ;
 }
{
  Marked_c(a(a(0,x),y)) > Marked_c(c(c(0))) ;
 }
{
  Marked_c(a(a(0,x),y)) > Marked_c(c(0)) ;
 }
 } 
=== 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 : 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: c(c(c(y))) >= c(c(a(y,0)))
constraint: c(a(a(0,x),y)) >= a(c(c(c(0))),y)
constraint: c(y) >= y
constraint: Marked_c(c(c(y))) >= Marked_c(c(a(y,0)))
constraint: Marked_c(c(c(y))) >= Marked_c(a(y,0))
constraint: Marked_c(a(a(0,x),y)) >= Marked_c(c(c(0)))
constraint: Marked_c(a(a(0,x),y)) >= Marked_c(c(0))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))> 
      --> <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))> 
     --> <Marked_c(c(c(y))) , Marked_c(a(y,0))>
  <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))> 
     --> <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
  <Marked_c(c(c(y))) , Marked_c(a(y,0))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
  <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))> 
     --> <Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
  <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))> 
     --> <Marked_c(c(c(y))) , Marked_c(a(y,0))>
  <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))> 
     --> <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  c(c(c(y))) >= c(c(a(y,0))) ;
  c(a(a(0,x),y)) >= a(c(c(c(0))),y) ;
  c(y) >= y ;
  Marked_c(c(c(y))) >= Marked_c(c(a(y,0))) ;
  Marked_c(c(c(y))) >= Marked_c(a(y,0)) ;
  Marked_c(a(a(0,x),y)) >= Marked_c(c(c(0))) ;
 }
 + Disjunctions:{ 
{
  Marked_c(c(c(y))) > Marked_c(c(a(y,0))) ;
 }
{
  Marked_c(c(c(y))) > Marked_c(a(y,0)) ;
 }
{
  Marked_c(a(a(0,x),y)) > Marked_c(c(c(0))) ;
 }
 } 
=== 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 : 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: c(c(c(y))) >= c(c(a(y,0)))
constraint: c(a(a(0,x),y)) >= a(c(c(c(0))),y)
constraint: c(y) >= y
constraint: Marked_c(c(c(y))) >= Marked_c(c(a(y,0)))
constraint: Marked_c(c(c(y))) >= Marked_c(a(y,0))
constraint: Marked_c(a(a(0,x),y)) >= Marked_c(c(c(0)))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))> 
      --> <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  c(c(c(y))) >= c(c(a(y,0))) ;
  c(a(a(0,x),y)) >= a(c(c(c(0))),y) ;
  c(y) >= y ;
  Marked_c(c(c(y))) >= Marked_c(c(a(y,0))) ;
 }
 + Disjunctions:{ 
{
  Marked_c(c(c(y))) > Marked_c(c(a(y,0))) ;
 }
 } 
=== 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: c(c(c(y))) >= c(c(a(y,0)))
constraint: c(a(a(0,x),y)) >= a(c(c(c(0))),y)
constraint: c(y) >= y
constraint: Marked_c(c(c(y))) >= Marked_c(c(a(y,0)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] c(c(c(y))) -> c(c(a(y,0)))
[2] c(a(a(0,x),y)) -> a(c(c(c(0))),y)
[3] c(y) -> y
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
<Marked_c(c(c(y))) , Marked_c(a(y,0))>
<Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
<Marked_c(a(a(0,x),y)) , Marked_c(c(0))>
<Marked_c(a(a(0,x),y)) , Marked_c(0)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
<Marked_c(c(c(y))) , Marked_c(a(y,0))>
<Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
<Marked_c(a(a(0,x),y)) , Marked_c(c(0))>
 ,
 CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ c ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ a ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ Marked_c ] (X0) = [ [ 0 , 0 , 1 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 removing <Marked_c(a(a(0,x),y)),Marked_c(c(0))>
 [ {
      
     DP termination of:
     <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
<Marked_c(c(c(y))) , Marked_c(a(y,0))>
<Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
<Marked_c(c(c(y))) , Marked_c(a(y,0))>
<Marked_c(a(a(0,x),y)) , Marked_c(c(c(0)))>
 ,
 CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ c ] (X0) = [ [ 1 , 1 , 0 ] [ 0 , 1 , 0 ] [ 1 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ a ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ Marked_c ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 removing <Marked_c(a(a(0,x),y)),Marked_c(c(c(0)))>
 [ {
      
     DP termination of:
     <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
<Marked_c(c(c(y))) , Marked_c(a(y,0))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_c(c(c(y))) , Marked_c(c(a(y,0)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ c ] (X0) = 3 + 1*X0 + 0; 
 [ 0 ] () = 0; 
 [ a ] (X0,X1) = 0; 
 [ Marked_c ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 4.756777 seconds (real time)
Cime Exit Status: 0