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

TRS termination of:
[1] f(h(x)) -> f(i(x))
[2] g(i(x)) -> g(h(x))
[3] h(a) -> b
[4] i(a) -> b


Sub problem: 
guided: 

DP termination of:
<Marked_f(h(x)) , Marked_f(i(x))>
<Marked_f(h(x)) , Marked_i(x)>
<Marked_g(i(x)) , Marked_g(h(x))>
<Marked_g(i(x)) , Marked_h(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(h(x)) , Marked_f(i(x))> --> <Marked_f(h(x)) , Marked_f(i(x))>
}

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

Cime worked for 0.033205 seconds (real time)
Cime Exit Status: 0