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

TRS termination of:
[1] f(0) -> s(0)
[2] f(s(0)) -> s(s(0))
[3] f(s(0)) ->  *(s(s(0)),f(0))
[4] f(+(x,s(0))) -> +(s(s(0)),f(x))
[5] f(+(x,y)) ->  *(f(x),f(y))


Sub problem: 
guided: 

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

{  <Marked_f(+(x,y)) , Marked_f(y)> --> <Marked_f(+(x,y)) , Marked_f(y)>
  <Marked_f(+(x,y)) , Marked_f(y)> --> <Marked_f(+(x,y)) , Marked_f(x)>
  <Marked_f(+(x,y)) , Marked_f(y)> --> <Marked_f(+(x,s(0))) , Marked_f(x)>
  <Marked_f(+(x,y)) , Marked_f(x)> --> <Marked_f(+(x,y)) , Marked_f(y)>
  <Marked_f(+(x,y)) , Marked_f(x)> --> <Marked_f(+(x,y)) , Marked_f(x)>
  <Marked_f(+(x,y)) , Marked_f(x)> --> <Marked_f(+(x,s(0))) , Marked_f(x)>
  <Marked_f(+(x,s(0))) , Marked_f(x)> --> <Marked_f(+(x,y)) , Marked_f(y)>
  <Marked_f(+(x,s(0))) , Marked_f(x)> --> <Marked_f(+(x,y)) , Marked_f(x)>
  <Marked_f(+(x,s(0))) , Marked_f(x)> --> <Marked_f(+(x,s(0))) , Marked_f(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(0)) >= s(s(0)) ;
  f(s(0)) >=  *(s(s(0)),f(0)) ;
  f(0) >= s(0) ;
  f(+(x,s(0))) >= +(s(s(0)),f(x)) ;
  f(+(x,y)) >=  *(f(x),f(y)) ;
  Marked_f(+(x,s(0))) >= Marked_f(x) ;
  Marked_f(+(x,y)) >= Marked_f(x) ;
  Marked_f(+(x,y)) >= Marked_f(y) ;
 }
 + Disjunctions:{ 
{
  Marked_f(+(x,s(0))) > Marked_f(x) ;
 }
{
  Marked_f(+(x,y)) > Marked_f(x) ;
 }
{
  Marked_f(+(x,y)) > Marked_f(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: f(s(0)) >= s(s(0))
constraint: f(s(0)) >=  *(s(s(0)),f(0))
constraint: f(0) >= s(0)
constraint: f(+(x,s(0))) >= +(s(s(0)),f(x))
constraint: f(+(x,y)) >=  *(f(x),f(y))
constraint: Marked_f(+(x,s(0))) >= Marked_f(x)
constraint: Marked_f(+(x,y)) >= Marked_f(x)
constraint: Marked_f(+(x,y)) >= Marked_f(y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(0) -> s(0)
[2] f(s(0)) -> s(s(0))
[3] f(s(0)) ->  *(s(s(0)),f(0))
[4] f(+(x,s(0))) -> +(s(s(0)),f(x))
[5] f(+(x,y)) ->  *(f(x),f(y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(0)) , Marked_f(0)>
<Marked_f(+(x,s(0))) , Marked_f(x)>
<Marked_f(+(x,y)) , Marked_f(x)>
<Marked_f(+(x,y)) , Marked_f(y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(+(x,s(0))) , Marked_f(x)>
<Marked_f(+(x,y)) , Marked_f(x)>
<Marked_f(+(x,y)) , Marked_f(y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ s ] (X0) = 1 + 0; 
 [ + ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; 
 [ f ] (X0) = 2 + 2*X0 + 0; 
 [ 0 ] () = 2 + 0; 
 [ Marked_f ] (X0) = 1*X0 + 0; 
 [ * ] (X0,X1) = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.054185 seconds (real time)
Cime Exit Status: 0