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

TRS termination of:
[1] f(s(X)) -> f(X)
[2] g(cons(0,Y)) -> g(Y)
[3] g(cons(s(X),Y)) -> s(X)
[4] h(cons(X,Y)) -> h(g(cons(X,Y)))


Sub problem: 
guided: 

DP termination of:
<Marked_f(s(X)) , Marked_f(X)>
<Marked_g(cons(0,Y)) , Marked_g(Y)>
<Marked_h(cons(X,Y)) , Marked_h(g(cons(X,Y)))>
<Marked_h(cons(X,Y)) , Marked_g(cons(X,Y))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_f(s(X)) , Marked_f(X)> --> <Marked_f(s(X)) , Marked_f(X)>
}

{  <Marked_h(cons(X,Y)) , Marked_h(g(cons(X,Y)))> 
      --> <Marked_h(cons(X,Y)) , Marked_h(g(cons(X,Y)))>
}

{  <Marked_g(cons(0,Y)) , Marked_g(Y)> --> <Marked_g(cons(0,Y)) , Marked_g(Y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(X)) >= f(X) ;
  g(cons(s(X),Y)) >= s(X) ;
  g(cons(0,Y)) >= g(Y) ;
  h(cons(X,Y)) >= h(g(cons(X,Y))) ;
  Marked_f(s(X)) >= Marked_f(X) ;
 }
 + Disjunctions:{ 
{
  Marked_f(s(X)) > Marked_f(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(s(X)) >= f(X)
constraint: g(cons(s(X),Y)) >= s(X)
constraint: g(cons(0,Y)) >= g(Y)
constraint: h(cons(X,Y)) >= h(g(cons(X,Y)))
constraint: Marked_f(s(X)) >= Marked_f(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(X)) >= f(X) ;
  g(cons(s(X),Y)) >= s(X) ;
  g(cons(0,Y)) >= g(Y) ;
  h(cons(X,Y)) >= h(g(cons(X,Y))) ;
  Marked_h(cons(X,Y)) >= Marked_h(g(cons(X,Y))) ;
 }
 + Disjunctions:{ 
{
  Marked_h(cons(X,Y)) > Marked_h(g(cons(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(s(X)) >= f(X)
constraint: g(cons(s(X),Y)) >= s(X)
constraint: g(cons(0,Y)) >= g(Y)
constraint: h(cons(X,Y)) >= h(g(cons(X,Y)))
constraint: Marked_h(cons(X,Y)) >= Marked_h(g(cons(X,Y)))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(X)) >= f(X) ;
  g(cons(s(X),Y)) >= s(X) ;
  g(cons(0,Y)) >= g(Y) ;
  h(cons(X,Y)) >= h(g(cons(X,Y))) ;
  Marked_g(cons(0,Y)) >= Marked_g(Y) ;
 }
 + Disjunctions:{ 
{
  Marked_g(cons(0,Y)) > Marked_g(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(s(X)) >= f(X)
constraint: g(cons(s(X),Y)) >= s(X)
constraint: g(cons(0,Y)) >= g(Y)
constraint: h(cons(X,Y)) >= h(g(cons(X,Y)))
constraint: Marked_g(cons(0,Y)) >= Marked_g(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(s(X)) -> f(X)
[2] g(cons(0,Y)) -> g(Y)
[3] g(cons(s(X),Y)) -> s(X)
[4] h(cons(X,Y)) -> h(g(cons(X,Y)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(X)) , Marked_f(X)>
<Marked_g(cons(0,Y)) , Marked_g(Y)>
<Marked_h(cons(X,Y)) , Marked_h(g(cons(X,Y)))>
<Marked_h(cons(X,Y)) , Marked_g(cons(X,Y))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(X)) , Marked_f(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ f ] (X0) = 3*X0 + 0; 
 [ Marked_f ] (X0) = 3*X0 + 0; 
 [ 0 ] () = 2 + 0; 
 [ g ] (X0) = 1*X0 + 0; 
 [ s ] (X0) = 1 + 1*X0 + 0; 
 [ h ] (X0) = 0; 
 [ cons ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_h(cons(X,Y)) , Marked_h(g(cons(X,Y)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ f ] (X0) = 0; 
 [ 0 ] () = 2 + 0; 
 [ g ] (X0) = 1 + 0; 
 [ Marked_h ] (X0) = 1*X0 + 0; 
 [ s ] (X0) = 0; 
 [ h ] (X0) = 2*X0 + 0; 
 [ cons ] (X0,X1) = 2 + 3*X0 + 3*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_g(cons(0,Y)) , Marked_g(Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ f ] (X0) = 0; 
 [ 0 ] () = 0; 
 [ g ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ h ] (X0) = 2*X0 + 0; 
 [ cons ] (X0,X1) = 1 + 3*X0 + 3*X1 + 0; 
 [ Marked_g ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.074603 seconds (real time)
Cime Exit Status: 0