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

TRS termination of:
[1] f(0) -> cons(0,n__f(n__s(n__0)))
[2] f(s(0)) -> f(p(s(0)))
[3] p(s(0)) -> 0
[4] f(X) -> n__f(X)
[5] s(X) -> n__s(X)
[6] 0 -> n__0
[7] activate(n__f(X)) -> f(activate(X))
[8] activate(n__s(X)) -> s(activate(X))
[9] activate(n__0) -> 0
[10] activate(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))>
<Marked_activate(n__f(X)) , Marked_f(activate(X))>
<Marked_activate(n__f(X)) , Marked_activate(X)>
<Marked_activate(n__s(X)) , Marked_s(activate(X))>
<Marked_activate(n__s(X)) , Marked_activate(X)>
<Marked_activate(n__0) , Marked_0>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_activate(n__s(X)) , Marked_activate(X)> 
      --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__f(X)) , Marked_activate(X)>
  <Marked_activate(n__f(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__f(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__f(X)) , Marked_activate(X)>
}

{  <Marked_f(s(0)) , Marked_f(p(s(0)))> 
      --> <Marked_f(s(0)) , Marked_f(p(s(0)))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_activate -> 1

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0 >= n__0 ;
  f(0) >= cons(0,n__f(n__s(n__0))) ;
  f(s(0)) >= f(p(s(0))) ;
  f(X) >= n__f(X) ;
  p(s(0)) >= 0 ;
  s(X) >= n__s(X) ;
  activate(n__f(X)) >= f(activate(X)) ;
  activate(n__s(X)) >= s(activate(X)) ;
  activate(n__0) >= 0 ;
  activate(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: 0 >= n__0
constraint: f(0) >= cons(0,n__f(n__s(n__0)))
constraint: f(s(0)) >= f(p(s(0)))
constraint: f(X) >= n__f(X)
constraint: p(s(0)) >= 0
constraint: s(X) >= n__s(X)
constraint: activate(n__f(X)) >= f(activate(X))
constraint: activate(n__s(X)) >= s(activate(X))
constraint: activate(n__0) >= 0
constraint: activate(X) >= X
constraint: Marked_f(s(0)) >= Marked_f(p(s(0)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(0) -> cons(0,n__f(n__s(n__0)))
[2] f(s(0)) -> f(p(s(0)))
[3] p(s(0)) -> 0
[4] f(X) -> n__f(X)
[5] s(X) -> n__s(X)
[6] 0 -> n__0
[7] activate(n__f(X)) -> f(activate(X))
[8] activate(n__s(X)) -> s(activate(X))
[9] activate(n__0) -> 0
[10] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(0)) , Marked_f(p(s(0)))>
<Marked_f(s(0)) , Marked_p(s(0))>
<Marked_activate(n__f(X)) , Marked_f(activate(X))>
<Marked_activate(n__f(X)) , Marked_activate(X)>
<Marked_activate(n__s(X)) , Marked_s(activate(X))>
<Marked_activate(n__s(X)) , Marked_activate(X)>
<Marked_activate(n__0) , Marked_0>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_activate(n__f(X)) , Marked_activate(X)>
<Marked_activate(n__s(X)) , Marked_activate(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_f(s(0)) , Marked_f(p(s(0)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ cons ] (X0,X1) = 0; 
 [ activate ] (X0) = 1*X0 + 0; 
 [ n__0 ] () = 1 + 0; 
 [ Marked_f ] (X0) = 2*X0 + 0; 
 [ n__f ] (X0) = 0; 
 [ p ] (X0) = 1 + 0; 
 [ 0 ] () = 1 + 0; 
 [ f ] (X0) = 0; 
 [ n__s ] (X0) = 2*X0 + 0; 
 [ s ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.054970 seconds (real time)
Cime Exit Status: 0