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

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


Sub problem: 
guided: 

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

{  <Marked_g(0,x) , Marked_g(f(x,x),x)> 
      --> <Marked_g(0,x) , Marked_g(f(x,x),x)>
}

{  <Marked_f(s(x),s(y)) , Marked_f(x,y)> 
      --> <Marked_f(s(x),s(y)) , Marked_f(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(x),s(y)) >= s(f(x,y)) ;
  f(x,0) >= s(0) ;
  g(0,x) >= g(f(x,x),x) ;
  Marked_g(0,x) >= Marked_g(f(x,x),x) ;
 }
 + Disjunctions:{ 
{
  Marked_g(0,x) > Marked_g(f(x,x),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(s(x),s(y)) >= s(f(x,y))
constraint: f(x,0) >= s(0)
constraint: g(0,x) >= g(f(x,x),x)
constraint: Marked_g(0,x) >= Marked_g(f(x,x),x)
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(x,0) -> s(0)
[2] f(s(x),s(y)) -> s(f(x,y))
[3] g(0,x) -> g(f(x,x),x)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(x),s(y)) , Marked_f(x,y)>
<Marked_g(0,x) , Marked_g(f(x,x),x)>
<Marked_g(0,x) , Marked_f(x,x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_g(0,x) , Marked_g(f(x,x),x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ s ] (X0) = 0; 
 [ Marked_g ] (X0,X1) = 2*X0 + 0; 
 [ f ] (X0,X1) = 0; 
 [ 0 ] () = 3 + 0; 
 [ g ] (X0,X1) = 0; 
 ]} 
{
 
DP termination of:
<Marked_f(s(x),s(y)) , Marked_f(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.019714 seconds (real time)
Cime Exit Status: 0