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

TRS termination of:
[1] minus(n__0,Y) -> 0
[2] minus(n__s(X),n__s(Y)) -> minus(activate(X),activate(Y))
[3] geq(X,n__0) -> true
[4] geq(n__0,n__s(Y)) -> false
[5] geq(n__s(X),n__s(Y)) -> geq(activate(X),activate(Y))
[6] div(0,n__s(Y)) -> 0
[7] div(s(X),n__s(Y)) ->
 if(geq(X,activate(Y)),n__s(div(minus(X,activate(Y)),n__s(activate(Y)))),n__0)
[8] if(true,X,Y) -> activate(X)
[9] if(false,X,Y) -> activate(Y)
[10] 0 -> n__0
[11] s(X) -> n__s(X)
[12] activate(n__0) -> 0
[13] activate(n__s(X)) -> s(X)
[14] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_minus(n__0,Y) , Marked_0>
<Marked_minus(n__s(X),n__s(Y)) , Marked_minus(activate(X),activate(Y))>
<Marked_minus(n__s(X),n__s(Y)) , Marked_activate(X)>
<Marked_minus(n__s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_geq(n__s(X),n__s(Y)) , Marked_geq(activate(X),activate(Y))>
<Marked_geq(n__s(X),n__s(Y)) , Marked_activate(X)>
<Marked_geq(n__s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_div(s(X),n__s(Y)) , Marked_if(geq(X,activate(Y)),
                             n__s(div(minus(X,activate(Y)),n__s(activate(Y)))),
                             n__0)>
<Marked_div(s(X),n__s(Y)) , Marked_geq(X,activate(Y))>
<Marked_div(s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_div(s(X),n__s(Y)) , Marked_div(minus(X,activate(Y)),n__s(activate(Y)))>
<Marked_div(s(X),n__s(Y)) , Marked_minus(X,activate(Y))>
<Marked_div(s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_div(s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_if(true,X,Y) , Marked_activate(X)>
<Marked_if(false,X,Y) , Marked_activate(Y)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__s(X)) , Marked_s(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_div(s(X),n__s(Y)) , Marked_div(minus(X,activate(Y)),
                                n__s(activate(Y)))> 
      --> <Marked_div(s(X),n__s(Y)) , Marked_div(minus(X,activate(Y)),
                                       n__s(activate(Y)))>
}

{  <Marked_geq(n__s(X),n__s(Y)) , Marked_geq(activate(X),activate(Y))> 
      --> <Marked_geq(n__s(X),n__s(Y)) , Marked_geq(activate(X),activate(Y))>
}

{  <Marked_minus(n__s(X),n__s(Y)) , Marked_minus(activate(X),activate(Y))> 
      --> <Marked_minus(n__s(X),n__s(Y)) , Marked_minus(activate(X),
                                            activate(Y))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0 >= n__0 ;
  minus(n__0,Y) >= 0 ;
  minus(n__s(X),n__s(Y)) >= minus(activate(X),activate(Y)) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(X) >= X ;
  geq(n__0,n__s(Y)) >= false ;
  geq(n__s(X),n__s(Y)) >= geq(activate(X),activate(Y)) ;
  geq(X,n__0) >= true ;
  div(0,n__s(Y)) >= 0 ;
  div(s(X),n__s(Y)) >= if(geq(X,activate(Y)),
                        n__s(div(minus(X,activate(Y)),n__s(activate(Y)))),
                        n__0) ;
  if(true,X,Y) >= activate(X) ;
  if(false,X,Y) >= activate(Y) ;
  s(X) >= n__s(X) ;
  Marked_div(s(X),n__s(Y)) >= Marked_div(minus(X,activate(Y)),
                               n__s(activate(Y))) ;
 }
 + Disjunctions:{ 
{
  Marked_div(s(X),n__s(Y)) > Marked_div(minus(X,activate(Y)),n__s(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: 0 >= n__0
constraint: minus(n__0,Y) >= 0
constraint: minus(n__s(X),n__s(Y)) >= minus(activate(X),activate(Y))
constraint: activate(n__0) >= 0
constraint: activate(n__s(X)) >= s(X)
constraint: activate(X) >= X
constraint: geq(n__0,n__s(Y)) >= false
constraint: geq(n__s(X),n__s(Y)) >= geq(activate(X),activate(Y))
constraint: geq(X,n__0) >= true
constraint: div(0,n__s(Y)) >= 0
constraint: div(s(X),n__s(Y)) >= if(geq(X,activate(Y)),
                                  n__s(div(minus(X,activate(Y)),
                                        n__s(activate(Y)))),n__0)
constraint: if(true,X,Y) >= activate(X)
constraint: if(false,X,Y) >= activate(Y)
constraint: s(X) >= n__s(X)
constraint: Marked_div(s(X),n__s(Y)) >= Marked_div(minus(X,activate(Y)),
                                         n__s(activate(Y)))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0 >= n__0 ;
  minus(n__0,Y) >= 0 ;
  minus(n__s(X),n__s(Y)) >= minus(activate(X),activate(Y)) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(X) >= X ;
  geq(n__0,n__s(Y)) >= false ;
  geq(n__s(X),n__s(Y)) >= geq(activate(X),activate(Y)) ;
  geq(X,n__0) >= true ;
  div(0,n__s(Y)) >= 0 ;
  div(s(X),n__s(Y)) >= if(geq(X,activate(Y)),
                        n__s(div(minus(X,activate(Y)),n__s(activate(Y)))),
                        n__0) ;
  if(true,X,Y) >= activate(X) ;
  if(false,X,Y) >= activate(Y) ;
  s(X) >= n__s(X) ;
  Marked_geq(n__s(X),n__s(Y)) >= Marked_geq(activate(X),activate(Y)) ;
 }
 + Disjunctions:{ 
{
  Marked_geq(n__s(X),n__s(Y)) > Marked_geq(activate(X),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: 0 >= n__0
constraint: minus(n__0,Y) >= 0
constraint: minus(n__s(X),n__s(Y)) >= minus(activate(X),activate(Y))
constraint: activate(n__0) >= 0
constraint: activate(n__s(X)) >= s(X)
constraint: activate(X) >= X
constraint: geq(n__0,n__s(Y)) >= false
constraint: geq(n__s(X),n__s(Y)) >= geq(activate(X),activate(Y))
constraint: geq(X,n__0) >= true
constraint: div(0,n__s(Y)) >= 0
constraint: div(s(X),n__s(Y)) >= if(geq(X,activate(Y)),
                                  n__s(div(minus(X,activate(Y)),
                                        n__s(activate(Y)))),n__0)
constraint: if(true,X,Y) >= activate(X)
constraint: if(false,X,Y) >= activate(Y)
constraint: s(X) >= n__s(X)
constraint: Marked_geq(n__s(X),n__s(Y)) >= Marked_geq(activate(X),activate(Y))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0 >= n__0 ;
  minus(n__0,Y) >= 0 ;
  minus(n__s(X),n__s(Y)) >= minus(activate(X),activate(Y)) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(X) ;
  activate(X) >= X ;
  geq(n__0,n__s(Y)) >= false ;
  geq(n__s(X),n__s(Y)) >= geq(activate(X),activate(Y)) ;
  geq(X,n__0) >= true ;
  div(0,n__s(Y)) >= 0 ;
  div(s(X),n__s(Y)) >= if(geq(X,activate(Y)),
                        n__s(div(minus(X,activate(Y)),n__s(activate(Y)))),
                        n__0) ;
  if(true,X,Y) >= activate(X) ;
  if(false,X,Y) >= activate(Y) ;
  s(X) >= n__s(X) ;
  Marked_minus(n__s(X),n__s(Y)) >= Marked_minus(activate(X),activate(Y)) ;
 }
 + Disjunctions:{ 
{
  Marked_minus(n__s(X),n__s(Y)) > Marked_minus(activate(X),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: 0 >= n__0
constraint: minus(n__0,Y) >= 0
constraint: minus(n__s(X),n__s(Y)) >= minus(activate(X),activate(Y))
constraint: activate(n__0) >= 0
constraint: activate(n__s(X)) >= s(X)
constraint: activate(X) >= X
constraint: geq(n__0,n__s(Y)) >= false
constraint: geq(n__s(X),n__s(Y)) >= geq(activate(X),activate(Y))
constraint: geq(X,n__0) >= true
constraint: div(0,n__s(Y)) >= 0
constraint: div(s(X),n__s(Y)) >= if(geq(X,activate(Y)),
                                  n__s(div(minus(X,activate(Y)),
                                        n__s(activate(Y)))),n__0)
constraint: if(true,X,Y) >= activate(X)
constraint: if(false,X,Y) >= activate(Y)
constraint: s(X) >= n__s(X)
constraint: Marked_minus(n__s(X),n__s(Y)) >= Marked_minus(activate(X),
                                              activate(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] minus(n__0,Y) -> 0
[2] minus(n__s(X),n__s(Y)) -> minus(activate(X),activate(Y))
[3] geq(X,n__0) -> true
[4] geq(n__0,n__s(Y)) -> false
[5] geq(n__s(X),n__s(Y)) -> geq(activate(X),activate(Y))
[6] div(0,n__s(Y)) -> 0
[7] div(s(X),n__s(Y)) ->
 if(geq(X,activate(Y)),n__s(div(minus(X,activate(Y)),n__s(activate(Y)))),n__0)
[8] if(true,X,Y) -> activate(X)
[9] if(false,X,Y) -> activate(Y)
[10] 0 -> n__0
[11] s(X) -> n__s(X)
[12] activate(n__0) -> 0
[13] activate(n__s(X)) -> s(X)
[14] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(n__0,Y) , Marked_0>
<Marked_minus(n__s(X),n__s(Y)) , Marked_minus(activate(X),activate(Y))>
<Marked_minus(n__s(X),n__s(Y)) , Marked_activate(X)>
<Marked_minus(n__s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_geq(n__s(X),n__s(Y)) , Marked_geq(activate(X),activate(Y))>
<Marked_geq(n__s(X),n__s(Y)) , Marked_activate(X)>
<Marked_geq(n__s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_div(s(X),n__s(Y)) , Marked_if(geq(X,activate(Y)),
                             n__s(div(minus(X,activate(Y)),n__s(activate(Y)))),
                             n__0)>
<Marked_div(s(X),n__s(Y)) , Marked_geq(X,activate(Y))>
<Marked_div(s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_div(s(X),n__s(Y)) , Marked_div(minus(X,activate(Y)),n__s(activate(Y)))>
<Marked_div(s(X),n__s(Y)) , Marked_minus(X,activate(Y))>
<Marked_div(s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_div(s(X),n__s(Y)) , Marked_activate(Y)>
<Marked_if(true,X,Y) , Marked_activate(X)>
<Marked_if(false,X,Y) , Marked_activate(Y)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__s(X)) , Marked_s(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_div(s(X),n__s(Y)) , Marked_div(minus(X,activate(Y)),
                                  n__s(activate(Y)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ div ] (X0,X1) = 3 + 0; 
 [ n__s ] (X0) = 0; 
 [ n__0 ] () = 0; 
 [ s ] (X0) = 2 + 0; 
 [ geq ] (X0,X1) = 0; 
 [ minus ] (X0,X1) = 0; 
 [ if ] (X0,X1,X2) = 2 + 2*X1 + 2*X2 + 0; 
 [ true ] () = 0; 
 [ activate ] (X0) = 2 + 2*X0 + 0; 
 [ false ] () = 0; 
 [ Marked_div ] (X0,X1) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_geq(n__s(X),n__s(Y)) , Marked_geq(activate(X),activate(Y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ Marked_geq ] (X0,X1) = 3*X1 + 0; 
 [ div ] (X0,X1) = 3*X0 + 0; 
 [ n__s ] (X0) = 3 + 1*X0 + 0; 
 [ n__0 ] () = 0; 
 [ s ] (X0) = 3 + 1*X0 + 0; 
 [ geq ] (X0,X1) = 0; 
 [ minus ] (X0,X1) = 0; 
 [ if ] (X0,X1,X2) = 3*X1 + 1*X2 + 0; 
 [ true ] () = 0; 
 [ activate ] (X0) = 1*X0 + 0; 
 [ false ] () = 0; 
 ]} 
{
 
DP termination of:
<Marked_minus(n__s(X),n__s(Y)) , Marked_minus(activate(X),activate(Y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ div ] (X0,X1) = 1*X0 + 0; 
 [ n__s ] (X0) = 3 + 2*X0 + 0; 
 [ n__0 ] () = 0; 
 [ s ] (X0) = 3 + 2*X0 + 0; 
 [ geq ] (X0,X1) = 2*X0 + 0; 
 [ minus ] (X0,X1) = 0; 
 [ Marked_minus ] (X0,X1) = 2*X0 + 0; 
 [ if ] (X0,X1,X2) = 1*X0 + 1*X1 + 2*X2 + 0; 
 [ true ] () = 0; 
 [ activate ] (X0) = 1*X0 + 0; 
 [ false ] () = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.267850 seconds (real time)
Cime Exit Status: 0