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

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


Sub problem: 
guided: 

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

{  <Marked_f(x,y,s(z)) , Marked_f(0,1,z)> 
      --> <Marked_f(x,y,s(z)) , Marked_f(0,1,z)>
  <Marked_f(x,y,s(z)) , Marked_f(0,1,z)> 
     --> <Marked_f(0,1,x) , Marked_f(s(x),x,x)>
  <Marked_f(0,1,x) , Marked_f(s(x),x,x)> 
     --> <Marked_f(x,y,s(z)) , Marked_f(0,1,z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(x,y) >= x ;
  g(x,y) >= y ;
  f(0,1,x) >= f(s(x),x,x) ;
  f(x,y,s(z)) >= s(f(0,1,z)) ;
  Marked_f(0,1,x) >= Marked_f(s(x),x,x) ;
  Marked_f(x,y,s(z)) >= Marked_f(0,1,z) ;
 }
 + Disjunctions:{ 
{
  Marked_f(0,1,x) > Marked_f(s(x),x,x) ;
 }
{
  Marked_f(x,y,s(z)) > Marked_f(0,1,z) ;
 }
 } 
=== 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(x,y) >= x
constraint: g(x,y) >= y
constraint: f(0,1,x) >= f(s(x),x,x)
constraint: f(x,y,s(z)) >= s(f(0,1,z))
constraint: Marked_f(0,1,x) >= Marked_f(s(x),x,x)
constraint: Marked_f(x,y,s(z)) >= Marked_f(0,1,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] g(x,y) -> x
[2] g(x,y) -> y
[3] f(0,1,x) -> f(s(x),x,x)
[4] f(x,y,s(z)) -> s(f(0,1,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(0,1,x) , Marked_f(s(x),x,x)>
<Marked_f(x,y,s(z)) , Marked_f(0,1,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(0,1,x) , Marked_f(s(x),x,x)>
<Marked_f(x,y,s(z)) , Marked_f(0,1,z)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ g ] (X0,X1) = 2*X1 + 3*X0 + 2; 
 [ 1 ] () = 2; 
 [ s ] (X0) = 2*X0 + 2; 
 [ f ] (X0,X1,X2) = 3*X2 + 2; 
 [ Marked_f ] (X0,X1,X2) = 3*X2; 
 [ 0 ] () = 0; 
 removing <Marked_f(x,y,s(z)),Marked_f(0,1,z)>
 [ {
      
     DP termination of:
     <Marked_f(0,1,x) , Marked_f(s(x),x,x)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.022151 seconds (real time)
Cime Exit Status: 0