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

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


Sub problem: 
guided: 

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

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

Cime worked for 0.078505 seconds (real time)
Cime Exit Status: 0