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

TRS termination of:
[1] filter(cons(X,Y),0,M) -> cons(0,n__filter(activate(Y),M,M))
[2] filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M))
[3] sieve(cons(0,Y)) -> cons(0,n__sieve(activate(Y)))
[4] sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N)))
[5] nats(N) -> cons(N,n__nats(s(N)))
[6] zprimes -> sieve(nats(s(s(0))))
[7] filter(X1,X2,X3) -> n__filter(X1,X2,X3)
[8] sieve(X) -> n__sieve(X)
[9] nats(X) -> n__nats(X)
[10] activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3)
[11] activate(n__sieve(X)) -> sieve(X)
[12] activate(n__nats(X)) -> nats(X)
[13] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)>
<Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)>
<Marked_sieve(cons(0,Y)) , Marked_activate(Y)>
<Marked_sieve(cons(s(N),Y)) , Marked_filter(activate(Y),N,N)>
<Marked_sieve(cons(s(N),Y)) , Marked_activate(Y)>
<Marked_zprimes , Marked_sieve(nats(s(s(0))))>
<Marked_zprimes , Marked_nats(s(s(0)))>
<Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
<Marked_activate(n__sieve(X)) , Marked_sieve(X)>
<Marked_activate(n__nats(X)) , Marked_nats(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__sieve(X)) , Marked_sieve(X)> 
      --> <Marked_sieve(cons(s(N),Y)) , Marked_activate(Y)>
  <Marked_activate(n__sieve(X)) , Marked_sieve(X)> 
     --> <Marked_sieve(cons(s(N),Y)) , Marked_filter(activate(Y),N,N)>
  <Marked_activate(n__sieve(X)) , Marked_sieve(X)> 
     --> <Marked_sieve(cons(0,Y)) , Marked_activate(Y)>
  <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)> 
     --> <Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)>
  <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)> 
     --> <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)>
  <Marked_sieve(cons(s(N),Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__sieve(X)) , Marked_sieve(X)>
  <Marked_sieve(cons(s(N),Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
  <Marked_sieve(cons(s(N),Y)) , Marked_filter(activate(Y),N,N)> 
     --> <Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)>
  <Marked_sieve(cons(s(N),Y)) , Marked_filter(activate(Y),N,N)> 
     --> <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)>
  <Marked_sieve(cons(0,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__sieve(X)) , Marked_sieve(X)>
  <Marked_sieve(cons(0,Y)) , Marked_activate(Y)> 
     --> <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
  <Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)> 
     --> <Marked_activate(n__sieve(X)) , Marked_sieve(X)>
  <Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)> 
     --> <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
  <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)> 
     --> <Marked_activate(n__sieve(X)) , Marked_sieve(X)>
  <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)> 
     --> <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  activate(n__filter(X1,X2,X3)) >= filter(X1,X2,X3) ;
  activate(n__sieve(X)) >= sieve(X) ;
  activate(n__nats(X)) >= nats(X) ;
  activate(X) >= X ;
  filter(cons(X,Y),0,M) >= cons(0,n__filter(activate(Y),M,M)) ;
  filter(cons(X,Y),s(N),M) >= cons(X,n__filter(activate(Y),N,M)) ;
  filter(X1,X2,X3) >= n__filter(X1,X2,X3) ;
  sieve(cons(0,Y)) >= cons(0,n__sieve(activate(Y))) ;
  sieve(cons(s(N),Y)) >= cons(s(N),n__sieve(filter(activate(Y),N,N))) ;
  sieve(X) >= n__sieve(X) ;
  nats(X) >= n__nats(X) ;
  nats(N) >= cons(N,n__nats(s(N))) ;
  zprimes >= sieve(nats(s(s(0)))) ;
  Marked_activate(n__filter(X1,X2,X3)) >= Marked_filter(X1,X2,X3) ;
  Marked_activate(n__sieve(X)) >= Marked_sieve(X) ;
  Marked_sieve(cons(0,Y)) >= Marked_activate(Y) ;
  Marked_sieve(cons(s(N),Y)) >= Marked_activate(Y) ;
  Marked_sieve(cons(s(N),Y)) >= Marked_filter(activate(Y),N,N) ;
  Marked_filter(cons(X,Y),0,M) >= Marked_activate(Y) ;
  Marked_filter(cons(X,Y),s(N),M) >= Marked_activate(Y) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__filter(X1,X2,X3)) > Marked_filter(X1,X2,X3) ;
 }
{
  Marked_activate(n__sieve(X)) > Marked_sieve(X) ;
 }
{
  Marked_sieve(cons(0,Y)) > Marked_activate(Y) ;
 }
{
  Marked_sieve(cons(s(N),Y)) > Marked_activate(Y) ;
 }
{
  Marked_sieve(cons(s(N),Y)) > Marked_filter(activate(Y),N,N) ;
 }
{
  Marked_filter(cons(X,Y),0,M) > Marked_activate(Y) ;
 }
{
  Marked_filter(cons(X,Y),s(N),M) > Marked_activate(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: activate(n__filter(X1,X2,X3)) >= filter(X1,X2,X3)
constraint: activate(n__sieve(X)) >= sieve(X)
constraint: activate(n__nats(X)) >= nats(X)
constraint: activate(X) >= X
constraint: filter(cons(X,Y),0,M) >= cons(0,n__filter(activate(Y),M,M))
constraint: filter(cons(X,Y),s(N),M) >= cons(X,n__filter(activate(Y),N,M))
constraint: filter(X1,X2,X3) >= n__filter(X1,X2,X3)
constraint: sieve(cons(0,Y)) >= cons(0,n__sieve(activate(Y)))
constraint: sieve(cons(s(N),Y)) >= cons(s(N),n__sieve(filter(activate(Y),N,N)))
constraint: sieve(X) >= n__sieve(X)
constraint: nats(X) >= n__nats(X)
constraint: nats(N) >= cons(N,n__nats(s(N)))
constraint: zprimes >= sieve(nats(s(s(0))))
constraint: Marked_activate(n__filter(X1,X2,X3)) >= Marked_filter(X1,X2,X3)
constraint: Marked_activate(n__sieve(X)) >= Marked_sieve(X)
constraint: Marked_sieve(cons(0,Y)) >= Marked_activate(Y)
constraint: Marked_sieve(cons(s(N),Y)) >= Marked_activate(Y)
constraint: Marked_sieve(cons(s(N),Y)) >= Marked_filter(activate(Y),N,N)
constraint: Marked_filter(cons(X,Y),0,M) >= Marked_activate(Y)
constraint: Marked_filter(cons(X,Y),s(N),M) >= Marked_activate(Y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)> 
      --> <Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)>
  <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)> 
     --> <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)>
  <Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)> 
     --> <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
  <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)> 
     --> <Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_activate -> 1
Marked_filter -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] filter(cons(X,Y),0,M) -> cons(0,n__filter(activate(Y),M,M))
[2] filter(cons(X,Y),s(N),M) -> cons(X,n__filter(activate(Y),N,M))
[3] sieve(cons(0,Y)) -> cons(0,n__sieve(activate(Y)))
[4] sieve(cons(s(N),Y)) -> cons(s(N),n__sieve(filter(activate(Y),N,N)))
[5] nats(N) -> cons(N,n__nats(s(N)))
[6] zprimes -> sieve(nats(s(s(0))))
[7] filter(X1,X2,X3) -> n__filter(X1,X2,X3)
[8] sieve(X) -> n__sieve(X)
[9] nats(X) -> n__nats(X)
[10] activate(n__filter(X1,X2,X3)) -> filter(X1,X2,X3)
[11] activate(n__sieve(X)) -> sieve(X)
[12] activate(n__nats(X)) -> nats(X)
[13] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)>
<Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)>
<Marked_sieve(cons(0,Y)) , Marked_activate(Y)>
<Marked_sieve(cons(s(N),Y)) , Marked_filter(activate(Y),N,N)>
<Marked_sieve(cons(s(N),Y)) , Marked_activate(Y)>
<Marked_zprimes , Marked_sieve(nats(s(s(0))))>
<Marked_zprimes , Marked_nats(s(s(0)))>
<Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
<Marked_activate(n__sieve(X)) , Marked_sieve(X)>
<Marked_activate(n__nats(X)) , Marked_nats(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)>
<Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)>
<Marked_sieve(cons(0,Y)) , Marked_activate(Y)>
<Marked_sieve(cons(s(N),Y)) , Marked_filter(activate(Y),N,N)>
<Marked_sieve(cons(s(N),Y)) , Marked_activate(Y)>
<Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
<Marked_activate(n__sieve(X)) , Marked_sieve(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ cons ] (X0,X1) = 1*X1; 
 [ n__nats ] (X0) = 0; 
 [ filter ] (X0,X1,X2) = 1*X0; 
 [ n__filter ] (X0,X1,X2) = 1*X0; 
 [ zprimes ] () = 3; 
 [ n__sieve ] (X0) = 2*X0 + 1; 
 [ Marked_filter ] (X0,X1,X2) = 2*X0; 
 [ 0 ] () = 0; 
 [ nats ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ Marked_sieve ] (X0) = 2*X0; 
 [ activate ] (X0) = 1*X0; 
 [ Marked_activate ] (X0) = 2*X0; 
 [ sieve ] (X0) = 2*X0 + 1; 
 removing <Marked_activate(n__sieve(X)),Marked_sieve(X)>
 [ {
      
     DP termination of:
     <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)>
<Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)>
<Marked_sieve(cons(0,Y)) , Marked_activate(Y)>
<Marked_sieve(cons(s(N),Y)) , Marked_filter(activate(Y),N,N)>
<Marked_sieve(cons(s(N),Y)) , Marked_activate(Y)>
<Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_filter(cons(X,Y),0,M) , Marked_activate(Y)>
<Marked_filter(cons(X,Y),s(N),M) , Marked_activate(Y)>
<Marked_activate(n__filter(X1,X2,X3)) , Marked_filter(X1,X2,X3)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.135774 seconds (real time)
Cime Exit Status: 0