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

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


Sub problem: 
guided: 

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

{  <Marked_c(b(y,c(x))) , Marked_a(0,0)> --> <Marked_a(x,y) , Marked_c(y)>
  <Marked_c(b(y,c(x))) , Marked_c(b(a(0,0),y))> 
     --> <Marked_c(b(y,c(x))) , Marked_a(0,0)>
  <Marked_c(b(y,c(x))) , Marked_c(b(a(0,0),y))> 
     --> <Marked_c(b(y,c(x))) , Marked_c(b(a(0,0),y))>
  <Marked_c(b(y,c(x))) , Marked_c(b(a(0,0),y))> 
     --> <Marked_c(b(y,c(x))) , Marked_c(c(b(a(0,0),y)))>
  <Marked_c(b(y,c(x))) , Marked_c(c(b(a(0,0),y)))> 
     --> <Marked_c(b(y,c(x))) , Marked_a(0,0)>
  <Marked_c(b(y,c(x))) , Marked_c(c(b(a(0,0),y)))> 
     --> <Marked_c(b(y,c(x))) , Marked_c(b(a(0,0),y))>
  <Marked_c(b(y,c(x))) , Marked_c(c(b(a(0,0),y)))> 
     --> <Marked_c(b(y,c(x))) , Marked_c(c(b(a(0,0),y)))>
  <Marked_a(x,y) , Marked_c(y)> --> <Marked_c(b(y,c(x))) , Marked_a(0,0)>
  <Marked_a(x,y) , Marked_c(y)> 
     --> <Marked_c(b(y,c(x))) , Marked_c(b(a(0,0),y))>
  <Marked_a(x,y) , Marked_c(y)> 
     --> <Marked_c(b(y,c(x))) , Marked_c(c(b(a(0,0),y)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  b(y,0) >= y ;
  c(b(y,c(x))) >= c(c(b(a(0,0),y))) ;
  a(x,y) >= b(x,b(0,c(y))) ;
  Marked_c(b(y,c(x))) >= Marked_c(b(a(0,0),y)) ;
  Marked_c(b(y,c(x))) >= Marked_c(c(b(a(0,0),y))) ;
  Marked_c(b(y,c(x))) >= Marked_a(0,0) ;
  Marked_a(x,y) >= Marked_c(y) ;
 }
 + Disjunctions:{ 
{
  Marked_c(b(y,c(x))) > Marked_c(b(a(0,0),y)) ;
 }
{
  Marked_c(b(y,c(x))) > Marked_c(c(b(a(0,0),y))) ;
 }
{
  Marked_c(b(y,c(x))) > Marked_a(0,0) ;
 }
{
  Marked_a(x,y) > Marked_c(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: b(y,0) >= y
constraint: c(b(y,c(x))) >= c(c(b(a(0,0),y)))
constraint: a(x,y) >= b(x,b(0,c(y)))
constraint: Marked_c(b(y,c(x))) >= Marked_c(b(a(0,0),y))
constraint: Marked_c(b(y,c(x))) >= Marked_c(c(b(a(0,0),y)))
constraint: Marked_c(b(y,c(x))) >= Marked_a(0,0)
constraint: Marked_a(x,y) >= Marked_c(y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

Cime worked for 4.486078 seconds (real time)
Cime Exit Status: 0