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

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


Sub problem: 
guided: 

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

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

{  <Marked_f(c(s(x),y)) , Marked_f(c(x,s(y)))> 
      --> <Marked_f(c(s(x),y)) , Marked_f(c(x,s(y)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(c(x,s(y))) >= g(c(s(x),y)) ;
  f(c(s(x),y)) >= f(c(x,s(y))) ;
  f(f(x)) >= f(d(f(x))) ;
  f(x) >= 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: g(c(x,s(y))) >= g(c(s(x),y))
constraint: f(c(s(x),y)) >= f(c(x,s(y)))
constraint: f(f(x)) >= f(d(f(x)))
constraint: f(x) >= x
constraint: 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:
{
  g(c(x,s(y))) >= g(c(s(x),y)) ;
  f(c(s(x),y)) >= f(c(x,s(y))) ;
  f(f(x)) >= f(d(f(x))) ;
  f(x) >= 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: g(c(x,s(y))) >= g(c(s(x),y))
constraint: f(c(s(x),y)) >= f(c(x,s(y)))
constraint: f(f(x)) >= f(d(f(x)))
constraint: f(x) >= x
constraint: Marked_f(c(s(x),y)) >= Marked_f(c(x,s(y)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] g(c(x,s(y))) -> g(c(s(x),y))
[2] f(c(s(x),y)) -> f(c(x,s(y)))
[3] f(f(x)) -> f(d(f(x)))
[4] f(x) -> x
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_g(c(x,s(y))) , Marked_g(c(s(x),y))>
<Marked_f(c(s(x),y)) , Marked_f(c(x,s(y)))>
<Marked_f(f(x)) , Marked_f(d(f(x)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_g(c(x,s(y))) , Marked_g(c(s(x),y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ g ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
     [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ d ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ s ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ Marked_g ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ c ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ f ] (X0) = [ [ 1 , 0 , 0 ] [ 1 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
{
 
DP termination of:
<Marked_f(c(s(x),y)) , Marked_f(c(x,s(y)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ g ] (X0) = 0; 
 [ d ] (X0) = 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ c ] (X0,X1) = 3*X0 + 0; 
 [ Marked_f ] (X0) = 2*X0 + 0; 
 [ f ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.479593 seconds (real time)
Cime Exit Status: 0