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

TRS termination of:
[1] from(X) -> cons(X,n__from(s(X)))
[2] 2ndspos(0,Z) -> rnil
[3] 2ndspos(s(N),cons(X,n__cons(Y,Z))) ->
 rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
[4] 2ndsneg(0,Z) -> rnil
[5] 2ndsneg(s(N),cons(X,n__cons(Y,Z))) ->
 rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
[6] pi(X) -> 2ndspos(X,from(0))
[7] plus(0,Y) -> Y
[8] plus(s(X),Y) -> s(plus(X,Y))
[9] times(0,Y) -> 0
[10] times(s(X),Y) -> plus(Y,times(X,Y))
[11] square(X) -> times(X,X)
[12] from(X) -> n__from(X)
[13] cons(X1,X2) -> n__cons(X1,X2)
[14] activate(n__from(X)) -> from(X)
[15] activate(n__cons(X1,X2)) -> cons(X1,X2)
[16] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_from(X) , Marked_cons(X,n__from(s(X)))>
<Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_activate(Y)>
<Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndsneg(N,activate(Z))>
<Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_activate(Z)>
<Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_activate(Y)>
<Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndspos(N,activate(Z))>
<Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_activate(Z)>
<Marked_pi(X) , Marked_2ndspos(X,from(0))>
<Marked_pi(X) , Marked_from(0)>
<Marked_plus(s(X),Y) , Marked_plus(X,Y)>
<Marked_times(s(X),Y) , Marked_plus(Y,times(X,Y))>
<Marked_times(s(X),Y) , Marked_times(X,Y)>
<Marked_square(X) , Marked_times(X,X)>
<Marked_activate(n__from(X)) , Marked_from(X)>
<Marked_activate(n__cons(X1,X2)) , Marked_cons(X1,X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndspos(N,activate(Z))> 
      --> <Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndsneg(
                                                        N,activate(Z))>
  <Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndsneg(N,activate(Z))> 
     --> <Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndspos(
                                                       N,activate(Z))>
}

{  <Marked_times(s(X),Y) , Marked_times(X,Y)> 
      --> <Marked_times(s(X),Y) , Marked_times(X,Y)>
}

{  <Marked_plus(s(X),Y) , Marked_plus(X,Y)> 
      --> <Marked_plus(s(X),Y) , Marked_plus(X,Y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(X1,X2) >= n__cons(X1,X2) ;
  from(X) >= cons(X,n__from(s(X))) ;
  from(X) >= n__from(X) ;
  2ndspos(s(N),cons(X,n__cons(Y,Z))) >= rcons(posrecip(activate(Y)),
                                         2ndsneg(N,activate(Z))) ;
  2ndspos(0,Z) >= rnil ;
  activate(n__from(X)) >= from(X) ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(X) >= X ;
  2ndsneg(s(N),cons(X,n__cons(Y,Z))) >= rcons(negrecip(activate(Y)),
                                         2ndspos(N,activate(Z))) ;
  2ndsneg(0,Z) >= rnil ;
  pi(X) >= 2ndspos(X,from(0)) ;
  plus(s(X),Y) >= s(plus(X,Y)) ;
  plus(0,Y) >= Y ;
  times(s(X),Y) >= plus(Y,times(X,Y)) ;
  times(0,Y) >= 0 ;
  square(X) >= times(X,X) ;
  Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) >= Marked_2ndsneg(N,activate(Z)) ;
  Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) >= Marked_2ndspos(N,activate(Z)) ;
 }
 + Disjunctions:{ 
{
  Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) > Marked_2ndsneg(N,activate(Z)) ;
 }
{
  Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) > Marked_2ndspos(N,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: cons(X1,X2) >= n__cons(X1,X2)
constraint: from(X) >= cons(X,n__from(s(X)))
constraint: from(X) >= n__from(X)
constraint: 2ndspos(s(N),cons(X,n__cons(Y,Z))) >= rcons(posrecip(activate(Y)),
                                                   2ndsneg(N,activate(Z)))
constraint: 2ndspos(0,Z) >= rnil
constraint: activate(n__from(X)) >= from(X)
constraint: activate(n__cons(X1,X2)) >= cons(X1,X2)
constraint: activate(X) >= X
constraint: 2ndsneg(s(N),cons(X,n__cons(Y,Z))) >= rcons(negrecip(activate(Y)),
                                                   2ndspos(N,activate(Z)))
constraint: 2ndsneg(0,Z) >= rnil
constraint: pi(X) >= 2ndspos(X,from(0))
constraint: plus(s(X),Y) >= s(plus(X,Y))
constraint: plus(0,Y) >= Y
constraint: times(s(X),Y) >= plus(Y,times(X,Y))
constraint: times(0,Y) >= 0
constraint: square(X) >= times(X,X)
constraint: Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) >= Marked_2ndsneg(
                                                          N,activate(Z))
constraint: Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) >= Marked_2ndspos(
                                                          N,activate(Z))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(X1,X2) >= n__cons(X1,X2) ;
  from(X) >= cons(X,n__from(s(X))) ;
  from(X) >= n__from(X) ;
  2ndspos(s(N),cons(X,n__cons(Y,Z))) >= rcons(posrecip(activate(Y)),
                                         2ndsneg(N,activate(Z))) ;
  2ndspos(0,Z) >= rnil ;
  activate(n__from(X)) >= from(X) ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(X) >= X ;
  2ndsneg(s(N),cons(X,n__cons(Y,Z))) >= rcons(negrecip(activate(Y)),
                                         2ndspos(N,activate(Z))) ;
  2ndsneg(0,Z) >= rnil ;
  pi(X) >= 2ndspos(X,from(0)) ;
  plus(s(X),Y) >= s(plus(X,Y)) ;
  plus(0,Y) >= Y ;
  times(s(X),Y) >= plus(Y,times(X,Y)) ;
  times(0,Y) >= 0 ;
  square(X) >= times(X,X) ;
  Marked_times(s(X),Y) >= Marked_times(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_times(s(X),Y) > Marked_times(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 ===
=== STOPING TIMER virtual ===
constraint: cons(X1,X2) >= n__cons(X1,X2)
constraint: from(X) >= cons(X,n__from(s(X)))
constraint: from(X) >= n__from(X)
constraint: 2ndspos(s(N),cons(X,n__cons(Y,Z))) >= rcons(posrecip(activate(Y)),
                                                   2ndsneg(N,activate(Z)))
constraint: 2ndspos(0,Z) >= rnil
constraint: activate(n__from(X)) >= from(X)
constraint: activate(n__cons(X1,X2)) >= cons(X1,X2)
constraint: activate(X) >= X
constraint: 2ndsneg(s(N),cons(X,n__cons(Y,Z))) >= rcons(negrecip(activate(Y)),
                                                   2ndspos(N,activate(Z)))
constraint: 2ndsneg(0,Z) >= rnil
constraint: pi(X) >= 2ndspos(X,from(0))
constraint: plus(s(X),Y) >= s(plus(X,Y))
constraint: plus(0,Y) >= Y
constraint: times(s(X),Y) >= plus(Y,times(X,Y))
constraint: times(0,Y) >= 0
constraint: square(X) >= times(X,X)
constraint: Marked_times(s(X),Y) >= Marked_times(X,Y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(X1,X2) >= n__cons(X1,X2) ;
  from(X) >= cons(X,n__from(s(X))) ;
  from(X) >= n__from(X) ;
  2ndspos(s(N),cons(X,n__cons(Y,Z))) >= rcons(posrecip(activate(Y)),
                                         2ndsneg(N,activate(Z))) ;
  2ndspos(0,Z) >= rnil ;
  activate(n__from(X)) >= from(X) ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(X) >= X ;
  2ndsneg(s(N),cons(X,n__cons(Y,Z))) >= rcons(negrecip(activate(Y)),
                                         2ndspos(N,activate(Z))) ;
  2ndsneg(0,Z) >= rnil ;
  pi(X) >= 2ndspos(X,from(0)) ;
  plus(s(X),Y) >= s(plus(X,Y)) ;
  plus(0,Y) >= Y ;
  times(s(X),Y) >= plus(Y,times(X,Y)) ;
  times(0,Y) >= 0 ;
  square(X) >= times(X,X) ;
  Marked_plus(s(X),Y) >= Marked_plus(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_plus(s(X),Y) > Marked_plus(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 ===
=== STOPING TIMER virtual ===
constraint: cons(X1,X2) >= n__cons(X1,X2)
constraint: from(X) >= cons(X,n__from(s(X)))
constraint: from(X) >= n__from(X)
constraint: 2ndspos(s(N),cons(X,n__cons(Y,Z))) >= rcons(posrecip(activate(Y)),
                                                   2ndsneg(N,activate(Z)))
constraint: 2ndspos(0,Z) >= rnil
constraint: activate(n__from(X)) >= from(X)
constraint: activate(n__cons(X1,X2)) >= cons(X1,X2)
constraint: activate(X) >= X
constraint: 2ndsneg(s(N),cons(X,n__cons(Y,Z))) >= rcons(negrecip(activate(Y)),
                                                   2ndspos(N,activate(Z)))
constraint: 2ndsneg(0,Z) >= rnil
constraint: pi(X) >= 2ndspos(X,from(0))
constraint: plus(s(X),Y) >= s(plus(X,Y))
constraint: plus(0,Y) >= Y
constraint: times(s(X),Y) >= plus(Y,times(X,Y))
constraint: times(0,Y) >= 0
constraint: square(X) >= times(X,X)
constraint: Marked_plus(s(X),Y) >= Marked_plus(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] from(X) -> cons(X,n__from(s(X)))
[2] 2ndspos(0,Z) -> rnil
[3] 2ndspos(s(N),cons(X,n__cons(Y,Z))) ->
 rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
[4] 2ndsneg(0,Z) -> rnil
[5] 2ndsneg(s(N),cons(X,n__cons(Y,Z))) ->
 rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
[6] pi(X) -> 2ndspos(X,from(0))
[7] plus(0,Y) -> Y
[8] plus(s(X),Y) -> s(plus(X,Y))
[9] times(0,Y) -> 0
[10] times(s(X),Y) -> plus(Y,times(X,Y))
[11] square(X) -> times(X,X)
[12] from(X) -> n__from(X)
[13] cons(X1,X2) -> n__cons(X1,X2)
[14] activate(n__from(X)) -> from(X)
[15] activate(n__cons(X1,X2)) -> cons(X1,X2)
[16] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_from(X) , Marked_cons(X,n__from(s(X)))>
<Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_activate(Y)>
<Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndsneg(N,activate(Z))>
<Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_activate(Z)>
<Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_activate(Y)>
<Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndspos(N,activate(Z))>
<Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_activate(Z)>
<Marked_pi(X) , Marked_2ndspos(X,from(0))>
<Marked_pi(X) , Marked_from(0)>
<Marked_plus(s(X),Y) , Marked_plus(X,Y)>
<Marked_times(s(X),Y) , Marked_plus(Y,times(X,Y))>
<Marked_times(s(X),Y) , Marked_times(X,Y)>
<Marked_square(X) , Marked_times(X,X)>
<Marked_activate(n__from(X)) , Marked_from(X)>
<Marked_activate(n__cons(X1,X2)) , Marked_cons(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_2ndspos(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndsneg(N,activate(Z))>
<Marked_2ndsneg(s(N),cons(X,n__cons(Y,Z))) , Marked_2ndspos(N,activate(Z))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ cons ] (X0,X1) = 1 + 2*X1 + 0; 
 [ square ] (X0) = 1*X0 + 0; 
 [ posrecip ] (X0) = 0; 
 [ Marked_2ndspos ] (X0,X1) = 2*X1 + 0; 
 [ rnil ] () = 0; 
 [ negrecip ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ 2ndsneg ] (X0,X1) = 0; 
 [ 0 ] () = 0; 
 [ plus ] (X0,X1) = 1*X1 + 0; 
 [ n__from ] (X0) = 1 + 0; 
 [ activate ] (X0) = 3*X0 + 0; 
 [ Marked_2ndsneg ] (X0,X1) = 2*X1 + 0; 
 [ 2ndspos ] (X0,X1) = 2 + 0; 
 [ pi ] (X0) = 3 + 1*X0 + 0; 
 [ from ] (X0) = 3 + 0; 
 [ n__cons ] (X0,X1) = 1 + 2*X1 + 0; 
 [ rcons ] (X0,X1) = 0; 
 [ times ] (X0,X1) = 0; 
 ]} 
{
 
DP termination of:
<Marked_times(s(X),Y) , Marked_times(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { cons  <  from ; cons  <  2ndspos ;
                                   cons  <  activate ; cons  <  2ndsneg ;
                                   cons  >  n__cons ; cons  <  pi ;
                                   n__from  <  from ; n__from  <  2ndspos ;
                                   n__from  <  activate ; n__from  <  2ndsneg ;
                                   n__from  <  pi ; s  <  from ;
                                   s  <  2ndspos ; s  <  activate ;
                                   s  <  2ndsneg ; s  <  pi ; s  <  plus ;
                                   s  <  times ; s  <  square ; from  >  cons ;
                                   from  >  n__from ; from  >  s ;
                                   from  <  2ndspos ; from  <  activate ;
                                   from  <  2ndsneg ; from  >  n__cons ;
                                   from  <  pi ; rnil  <  2ndspos ;
                                   rnil  <  2ndsneg ; rnil  <  pi ;
                                   2ndspos  >  cons ; 2ndspos  >  n__from ;
                                   2ndspos  >  s ; 2ndspos  >  from ;
                                   2ndspos  >  rnil ; 2ndspos  >  rcons ;
                                   2ndspos  >  posrecip ;
                                   2ndspos  >  activate ; 2ndspos  =  2ndsneg ;
                                   2ndspos  >  n__cons ; 2ndspos  >  negrecip ;
                                   2ndspos  <  pi ; 0  <  pi ;
                                   rcons  <  2ndspos ; rcons  <  2ndsneg ;
                                   rcons  <  pi ; posrecip  <  2ndspos ;
                                   posrecip  <  2ndsneg ; posrecip  <  pi ;
                                   activate  >  cons ; activate  >  n__from ;
                                   activate  >  s ; activate  >  from ;
                                   activate  <  2ndspos ;
                                   activate  <  2ndsneg ;
                                   activate  >  n__cons ; activate  <  pi ;
                                   2ndsneg  >  cons ; 2ndsneg  >  n__from ;
                                   2ndsneg  >  s ; 2ndsneg  >  from ;
                                   2ndsneg  >  rnil ; 2ndsneg  =  2ndspos ;
                                   2ndsneg  >  rcons ; 2ndsneg  >  posrecip ;
                                   2ndsneg  >  activate ; 2ndsneg  >  n__cons ;
                                   2ndsneg  >  negrecip ; 2ndsneg  <  pi ;
                                   n__cons  <  cons ; n__cons  <  from ;
                                   n__cons  <  2ndspos ; n__cons  <  activate ;
                                   n__cons  <  2ndsneg ; n__cons  <  pi ;
                                   negrecip  <  2ndspos ;
                                   negrecip  <  2ndsneg ; negrecip  <  pi ;
                                   pi  >  cons ; pi  >  n__from ; pi  >  s ;
                                   pi  >  from ; pi  >  rnil ; pi  >  2ndspos ;
                                   pi  >  0 ; pi  >  rcons ; pi  >  posrecip ;
                                   pi  >  activate ; pi  >  2ndsneg ;
                                   pi  >  n__cons ; pi  >  negrecip ;
                                   plus  >  s ; plus  <  times ;
                                   plus  <  square ; times  >  s ;
                                   times  >  plus ; times  <  square ;
                                   square  >  s ; square  >  plus ;
                                   square  >  times ; }

 ]} 
{
 
DP termination of:
<Marked_plus(s(X),Y) , Marked_plus(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { cons  <  from ; cons  <  2ndspos ;
                                   cons  <  activate ; cons  <  2ndsneg ;
                                   cons  >  n__cons ; cons  <  pi ;
                                   n__from  <  from ; n__from  <  2ndspos ;
                                   n__from  <  activate ; n__from  <  2ndsneg ;
                                   n__from  <  pi ; s  <  from ;
                                   s  <  2ndspos ; s  <  activate ;
                                   s  <  2ndsneg ; s  <  pi ; s  <  plus ;
                                   s  <  times ; s  <  square ; from  >  cons ;
                                   from  >  n__from ; from  >  s ;
                                   from  <  2ndspos ; from  <  activate ;
                                   from  <  2ndsneg ; from  >  n__cons ;
                                   from  <  pi ; rnil  <  2ndspos ;
                                   rnil  <  2ndsneg ; rnil  <  pi ;
                                   2ndspos  >  cons ; 2ndspos  >  n__from ;
                                   2ndspos  >  s ; 2ndspos  >  from ;
                                   2ndspos  >  rnil ; 2ndspos  >  rcons ;
                                   2ndspos  >  posrecip ;
                                   2ndspos  >  activate ; 2ndspos  =  2ndsneg ;
                                   2ndspos  >  n__cons ; 2ndspos  >  negrecip ;
                                   2ndspos  <  pi ; 0  <  pi ;
                                   rcons  <  2ndspos ; rcons  <  2ndsneg ;
                                   rcons  <  pi ; posrecip  <  2ndspos ;
                                   posrecip  <  2ndsneg ; posrecip  <  pi ;
                                   activate  >  cons ; activate  >  n__from ;
                                   activate  >  s ; activate  >  from ;
                                   activate  <  2ndspos ;
                                   activate  <  2ndsneg ;
                                   activate  >  n__cons ; activate  <  pi ;
                                   2ndsneg  >  cons ; 2ndsneg  >  n__from ;
                                   2ndsneg  >  s ; 2ndsneg  >  from ;
                                   2ndsneg  >  rnil ; 2ndsneg  =  2ndspos ;
                                   2ndsneg  >  rcons ; 2ndsneg  >  posrecip ;
                                   2ndsneg  >  activate ; 2ndsneg  >  n__cons ;
                                   2ndsneg  >  negrecip ; 2ndsneg  <  pi ;
                                   n__cons  <  cons ; n__cons  <  from ;
                                   n__cons  <  2ndspos ; n__cons  <  activate ;
                                   n__cons  <  2ndsneg ; n__cons  <  pi ;
                                   negrecip  <  2ndspos ;
                                   negrecip  <  2ndsneg ; negrecip  <  pi ;
                                   pi  >  cons ; pi  >  n__from ; pi  >  s ;
                                   pi  >  from ; pi  >  rnil ; pi  >  2ndspos ;
                                   pi  >  0 ; pi  >  rcons ; pi  >  posrecip ;
                                   pi  >  activate ; pi  >  2ndsneg ;
                                   pi  >  n__cons ; pi  >  negrecip ;
                                   plus  >  s ; plus  <  times ;
                                   plus  <  square ; times  >  s ;
                                   times  >  plus ; times  <  square ;
                                   square  >  s ; square  >  plus ;
                                   square  >  times ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.294887 seconds (real time)
Cime Exit Status: 0