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

TRS termination of:
[1] f(0) -> cons(0)
[2] f(s(0)) -> f(p(s(0)))
[3] p(s(X)) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_f(s(0)) , Marked_f(p(s(0)))>
<Marked_f(s(0)) , Marked_p(s(0))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(s(0)) , Marked_f(p(s(0)))> 
      --> <Marked_f(s(0)) , Marked_f(p(s(0)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(0) >= cons(0) ;
  f(s(0)) >= f(p(s(0))) ;
  p(s(X)) >= X ;
  Marked_f(s(0)) >= Marked_f(p(s(0))) ;
 }
 + Disjunctions:{ 
{
  Marked_f(s(0)) > Marked_f(p(s(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 : 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: f(0) >= cons(0)
constraint: f(s(0)) >= f(p(s(0)))
constraint: p(s(X)) >= X
constraint: Marked_f(s(0)) >= Marked_f(p(s(0)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(0) -> cons(0)
[2] f(s(0)) -> f(p(s(0)))
[3] p(s(X)) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(0)) , Marked_f(p(s(0)))>
<Marked_f(s(0)) , Marked_p(s(0))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(0)) , Marked_f(p(s(0)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ cons ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
     [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ s ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 1 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]; 
 [ f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 1 , 0 ] [ 1 , 0 , 1 ] [ 1 , 1 , 1 ] ]; 
 [ Marked_f ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ 0 ] () = [ [ 0 , 0 , 1 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ p ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.472719 seconds (real time)
Cime Exit Status: 0