- : unit = ()
- : 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 (Subterm criterion)

ST: Marked_2ndsneg -> 1
Marked_2ndspos -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_times -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 1

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: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_times(s(X),Y) , Marked_times(X,Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_plus(s(X),Y) , Marked_plus(X,Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.013118 seconds (real time)
Cime Exit Status: 0