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

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


Sub problem: 
guided: 

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

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

Cime worked for 0.093495 seconds (real time)
Cime Exit Status: 0