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

TRS termination of:
[1] fst(0,Z) -> nil
[2] fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
[3] from(X) -> cons(X,n__from(s(X)))
[4] add(0,X) -> X
[5] add(s(X),Y) -> s(n__add(activate(X),Y))
[6] len(nil) -> 0
[7] len(cons(X,Z)) -> s(n__len(activate(Z)))
[8] fst(X1,X2) -> n__fst(X1,X2)
[9] from(X) -> n__from(X)
[10] add(X1,X2) -> n__add(X1,X2)
[11] len(X) -> n__len(X)
[12] activate(n__fst(X1,X2)) -> fst(X1,X2)
[13] activate(n__from(X)) -> from(X)
[14] activate(n__add(X1,X2)) -> add(X1,X2)
[15] activate(n__len(X)) -> len(X)
[16] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_fst(s(X),cons(Y,Z)) , Marked_activate(X)>
<Marked_fst(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_add(s(X),Y) , Marked_activate(X)>
<Marked_len(cons(X,Z)) , Marked_activate(Z)>
<Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)>
<Marked_activate(n__from(X)) , Marked_from(X)>
<Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
<Marked_activate(n__len(X)) , Marked_len(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__len(X)) , Marked_len(X)> 
      --> <Marked_len(cons(X,Z)) , Marked_activate(Z)>
  <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)> 
     --> <Marked_add(s(X),Y) , Marked_activate(X)>
  <Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)> 
     --> <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(Z)>
  <Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)> 
     --> <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(X)>
  <Marked_len(cons(X,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__len(X)) , Marked_len(X)>
  <Marked_len(cons(X,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_len(cons(X,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)>
  <Marked_add(s(X),Y) , Marked_activate(X)> 
     --> <Marked_activate(n__len(X)) , Marked_len(X)>
  <Marked_add(s(X),Y) , Marked_activate(X)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_add(s(X),Y) , Marked_activate(X)> 
     --> <Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)>
  <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__len(X)) , Marked_len(X)>
  <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)>
  <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(X)> 
     --> <Marked_activate(n__len(X)) , Marked_len(X)>
  <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(X)> 
     --> <Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
  <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(X)> 
     --> <Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  fst(0,Z) >= nil ;
  fst(s(X),cons(Y,Z)) >= cons(Y,n__fst(activate(X),activate(Z))) ;
  fst(X1,X2) >= n__fst(X1,X2) ;
  activate(n__fst(X1,X2)) >= fst(X1,X2) ;
  activate(n__from(X)) >= from(X) ;
  activate(n__add(X1,X2)) >= add(X1,X2) ;
  activate(n__len(X)) >= len(X) ;
  activate(X) >= X ;
  from(X) >= cons(X,n__from(s(X))) ;
  from(X) >= n__from(X) ;
  add(0,X) >= X ;
  add(s(X),Y) >= s(n__add(activate(X),Y)) ;
  add(X1,X2) >= n__add(X1,X2) ;
  len(nil) >= 0 ;
  len(cons(X,Z)) >= s(n__len(activate(Z))) ;
  len(X) >= n__len(X) ;
  Marked_activate(n__fst(X1,X2)) >= Marked_fst(X1,X2) ;
  Marked_activate(n__add(X1,X2)) >= Marked_add(X1,X2) ;
  Marked_activate(n__len(X)) >= Marked_len(X) ;
  Marked_len(cons(X,Z)) >= Marked_activate(Z) ;
  Marked_add(s(X),Y) >= Marked_activate(X) ;
  Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(X) ;
  Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(Z) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__fst(X1,X2)) > Marked_fst(X1,X2) ;
 }
{
  Marked_activate(n__add(X1,X2)) > Marked_add(X1,X2) ;
 }
{
  Marked_activate(n__len(X)) > Marked_len(X) ;
 }
{
  Marked_len(cons(X,Z)) > Marked_activate(Z) ;
 }
{
  Marked_add(s(X),Y) > Marked_activate(X) ;
 }
{
  Marked_fst(s(X),cons(Y,Z)) > Marked_activate(X) ;
 }
{
  Marked_fst(s(X),cons(Y,Z)) > Marked_activate(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: fst(0,Z) >= nil
constraint: fst(s(X),cons(Y,Z)) >= cons(Y,n__fst(activate(X),activate(Z)))
constraint: fst(X1,X2) >= n__fst(X1,X2)
constraint: activate(n__fst(X1,X2)) >= fst(X1,X2)
constraint: activate(n__from(X)) >= from(X)
constraint: activate(n__add(X1,X2)) >= add(X1,X2)
constraint: activate(n__len(X)) >= len(X)
constraint: activate(X) >= X
constraint: from(X) >= cons(X,n__from(s(X)))
constraint: from(X) >= n__from(X)
constraint: add(0,X) >= X
constraint: add(s(X),Y) >= s(n__add(activate(X),Y))
constraint: add(X1,X2) >= n__add(X1,X2)
constraint: len(nil) >= 0
constraint: len(cons(X,Z)) >= s(n__len(activate(Z)))
constraint: len(X) >= n__len(X)
constraint: Marked_activate(n__fst(X1,X2)) >= Marked_fst(X1,X2)
constraint: Marked_activate(n__add(X1,X2)) >= Marked_add(X1,X2)
constraint: Marked_activate(n__len(X)) >= Marked_len(X)
constraint: Marked_len(cons(X,Z)) >= Marked_activate(Z)
constraint: Marked_add(s(X),Y) >= Marked_activate(X)
constraint: Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(X)
constraint: Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(Z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] fst(0,Z) -> nil
[2] fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
[3] from(X) -> cons(X,n__from(s(X)))
[4] add(0,X) -> X
[5] add(s(X),Y) -> s(n__add(activate(X),Y))
[6] len(nil) -> 0
[7] len(cons(X,Z)) -> s(n__len(activate(Z)))
[8] fst(X1,X2) -> n__fst(X1,X2)
[9] from(X) -> n__from(X)
[10] add(X1,X2) -> n__add(X1,X2)
[11] len(X) -> n__len(X)
[12] activate(n__fst(X1,X2)) -> fst(X1,X2)
[13] activate(n__from(X)) -> from(X)
[14] activate(n__add(X1,X2)) -> add(X1,X2)
[15] activate(n__len(X)) -> len(X)
[16] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(X)>
<Marked_fst(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_add(s(X),Y) , Marked_activate(X)>
<Marked_len(cons(X,Z)) , Marked_activate(Z)>
<Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)>
<Marked_activate(n__from(X)) , Marked_from(X)>
<Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
<Marked_activate(n__len(X)) , Marked_len(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_fst(s(X),cons(Y,Z)) , Marked_activate(X)>
<Marked_fst(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_add(s(X),Y) , Marked_activate(X)>
<Marked_len(cons(X,Z)) , Marked_activate(Z)>
<Marked_activate(n__fst(X1,X2)) , Marked_fst(X1,X2)>
<Marked_activate(n__add(X1,X2)) , Marked_add(X1,X2)>
<Marked_activate(n__len(X)) , Marked_len(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ from ] (X0) = 0; 
 [ n__fst ] (X0,X1) = 1 + 2*X0 + 1*X1 + 0; 
 [ n__len ] (X0) = 1 + 1*X0 + 0; 
 [ 0 ] () = 0; 
 [ n__add ] (X0,X1) = 1 + 2*X0 + 3*X1 + 0; 
 [ s ] (X0) = 1*X0 + 0; 
 [ Marked_len ] (X0) = 2 + 3*X0 + 0; 
 [ fst ] (X0,X1) = 1 + 2*X0 + 1*X1 + 0; 
 [ Marked_fst ] (X0,X1) = 2 + 3*X0 + 3*X1 + 0; 
 [ add ] (X0,X1) = 1 + 2*X0 + 3*X1 + 0; 
 [ activate ] (X0) = 1*X0 + 0; 
 [ Marked_activate ] (X0) = 1 + 3*X0 + 0; 
 [ cons ] (X0,X1) = 1*X1 + 0; 
 [ len ] (X0) = 1 + 1*X0 + 0; 
 [ n__from ] (X0) = 0; 
 [ Marked_add ] (X0,X1) = 2 + 3*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.086408 seconds (real time)
Cime Exit Status: 0