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

TRS termination of:
[1] f(1) -> f(g(1))
[2] f(f(x)) -> f(x)
[3] g(0) -> g(f(0))
[4] g(g(x)) -> g(x)


Sub problem: 
guided: 

DP termination of:
<Marked_f(1) , Marked_f(g(1))>
<Marked_f(1) , Marked_g(1)>
<Marked_g(0) , Marked_g(f(0))>
<Marked_g(0) , Marked_f(0)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(1) , Marked_f(g(1))> --> <Marked_f(1) , Marked_f(g(1))>
}

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

Cime worked for 0.040066 seconds (real time)
Cime Exit Status: 0