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

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


Sub problem: 
guided: 

DP termination of:
<Marked_f(c(s(x),y)) , Marked_f(c(x,s(y)))>
<Marked_g(c(x,s(y))) , Marked_g(c(s(x),y))>
<Marked_g(s(f(x))) , Marked_g(f(x))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_f(c(s(x),y)) , Marked_f(c(x,s(y)))> 
      --> <Marked_f(c(s(x),y)) , Marked_f(c(x,s(y)))>
}

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

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

ST: Marked_g -> 1

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

Cime worked for 0.080567 seconds (real time)
Cime Exit Status: 0