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

TRS termination of:
[1] active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
[2] active(from(X)) -> mark(cons(X,from(s(X))))
[3] active(2nd(X)) -> 2nd(active(X))
[4] active(cons(X1,X2)) -> cons(active(X1),X2)
[5] active(from(X)) -> from(active(X))
[6] active(s(X)) -> s(active(X))
[7] 2nd(mark(X)) -> mark(2nd(X))
[8] cons(mark(X1),X2) -> mark(cons(X1,X2))
[9] from(mark(X)) -> mark(from(X))
[10] s(mark(X)) -> mark(s(X))
[11] proper(2nd(X)) -> 2nd(proper(X))
[12] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[13] proper(from(X)) -> from(proper(X))
[14] proper(s(X)) -> s(proper(X))
[15] 2nd(ok(X)) -> ok(2nd(X))
[16] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[17] from(ok(X)) -> ok(from(X))
[18] s(ok(X)) -> ok(s(X))
[19] top(mark(X)) -> top(proper(X))
[20] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(from(X)) , Marked_cons(X,from(s(X)))>
<Marked_active(from(X)) , Marked_from(s(X))>
<Marked_active(from(X)) , Marked_s(X)>
<Marked_active(2nd(X)) , Marked_2nd(active(X))>
<Marked_active(2nd(X)) , Marked_active(X)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(from(X)) , Marked_from(active(X))>
<Marked_active(from(X)) , Marked_active(X)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_2nd(mark(X)) , Marked_2nd(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_from(mark(X)) , Marked_from(X)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_proper(2nd(X)) , Marked_2nd(proper(X))>
<Marked_proper(2nd(X)) , Marked_proper(X)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(from(X)) , Marked_from(proper(X))>
<Marked_proper(from(X)) , Marked_proper(X)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_2nd(ok(X)) , Marked_2nd(X)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_from(ok(X)) , Marked_from(X)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 7 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(ok(X)) , Marked_top(active(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
}

{  <Marked_proper(s(X)) , Marked_proper(X)> 
      --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(from(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(2nd(X)) , Marked_proper(X)>
  <Marked_proper(from(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(from(X)) , Marked_proper(X)> 
     --> <Marked_proper(from(X)) , Marked_proper(X)>
  <Marked_proper(from(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(from(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(from(X)) , Marked_proper(X)> 
     --> <Marked_proper(2nd(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(from(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(2nd(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(from(X)) , Marked_proper(X)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(cons(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(2nd(X)) , Marked_proper(X)>
  <Marked_proper(2nd(X)) , Marked_proper(X)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(2nd(X)) , Marked_proper(X)> 
     --> <Marked_proper(from(X)) , Marked_proper(X)>
  <Marked_proper(2nd(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(2nd(X)) , Marked_proper(X)> 
     --> <Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(2nd(X)) , Marked_proper(X)> 
     --> <Marked_proper(2nd(X)) , Marked_proper(X)>
}

{  <Marked_active(s(X)) , Marked_active(X)> 
      --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(from(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(2nd(X)) , Marked_active(X)>
  <Marked_active(from(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(from(X)) , Marked_active(X)> 
     --> <Marked_active(from(X)) , Marked_active(X)>
  <Marked_active(from(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(from(X)) , Marked_active(X)> 
     --> <Marked_active(2nd(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(from(X)) , Marked_active(X)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(cons(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(2nd(X)) , Marked_active(X)>
  <Marked_active(2nd(X)) , Marked_active(X)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(2nd(X)) , Marked_active(X)> 
     --> <Marked_active(from(X)) , Marked_active(X)>
  <Marked_active(2nd(X)) , Marked_active(X)> 
     --> <Marked_active(cons(X1,X2)) , Marked_active(X1)>
  <Marked_active(2nd(X)) , Marked_active(X)> 
     --> <Marked_active(2nd(X)) , Marked_active(X)>
}

{  <Marked_2nd(ok(X)) , Marked_2nd(X)> --> <Marked_2nd(ok(X)) , Marked_2nd(X)>
  <Marked_2nd(ok(X)) , Marked_2nd(X)> --> <Marked_2nd(mark(X)) , Marked_2nd(X)>
  <Marked_2nd(mark(X)) , Marked_2nd(X)> --> <Marked_2nd(ok(X)) , Marked_2nd(X)>
  <Marked_2nd(mark(X)) , Marked_2nd(X)> 
     --> <Marked_2nd(mark(X)) , Marked_2nd(X)>
}

{  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
      --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}

{  <Marked_from(ok(X)) , Marked_from(X)> 
      --> <Marked_from(ok(X)) , Marked_from(X)>
  <Marked_from(ok(X)) , Marked_from(X)> 
     --> <Marked_from(mark(X)) , Marked_from(X)>
  <Marked_from(mark(X)) , Marked_from(X)> 
     --> <Marked_from(ok(X)) , Marked_from(X)>
  <Marked_from(mark(X)) , Marked_from(X)> 
     --> <Marked_from(mark(X)) , Marked_from(X)>
}

{  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  active(2nd(cons(X,cons(Y,Z)))) >= mark(Y) ;
  active(2nd(X)) >= 2nd(active(X)) ;
  active(cons(X1,X2)) >= cons(active(X1),X2) ;
  active(from(X)) >= mark(cons(X,from(s(X)))) ;
  active(from(X)) >= from(active(X)) ;
  active(s(X)) >= s(active(X)) ;
  2nd(mark(X)) >= mark(2nd(X)) ;
  2nd(ok(X)) >= ok(2nd(X)) ;
  cons(mark(X1),X2) >= mark(cons(X1,X2)) ;
  cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ;
  from(mark(X)) >= mark(from(X)) ;
  from(ok(X)) >= ok(from(X)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  proper(2nd(X)) >= 2nd(proper(X)) ;
  proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ;
  proper(from(X)) >= from(proper(X)) ;
  proper(s(X)) >= s(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 } 
=== 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: active(2nd(cons(X,cons(Y,Z)))) >= mark(Y)
constraint: active(2nd(X)) >= 2nd(active(X))
constraint: active(cons(X1,X2)) >= cons(active(X1),X2)
constraint: active(from(X)) >= mark(cons(X,from(s(X))))
constraint: active(from(X)) >= from(active(X))
constraint: active(s(X)) >= s(active(X))
constraint: 2nd(mark(X)) >= mark(2nd(X))
constraint: 2nd(ok(X)) >= ok(2nd(X))
constraint: cons(mark(X1),X2) >= mark(cons(X1,X2))
constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2))
constraint: from(mark(X)) >= mark(from(X))
constraint: from(ok(X)) >= ok(from(X))
constraint: s(mark(X)) >= mark(s(X))
constraint: s(ok(X)) >= ok(s(X))
constraint: proper(2nd(X)) >= 2nd(proper(X))
constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2))
constraint: proper(from(X)) >= from(proper(X))
constraint: proper(s(X)) >= s(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_top(mark(X)) >= Marked_top(proper(X))
constraint: Marked_top(ok(X)) >= Marked_top(active(X))
APPLY CRITERIA (Subterm criterion)

ST: Marked_proper -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_active -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_2nd -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_cons -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_from -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_s -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
      --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_cons -> 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] active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
[2] active(from(X)) -> mark(cons(X,from(s(X))))
[3] active(2nd(X)) -> 2nd(active(X))
[4] active(cons(X1,X2)) -> cons(active(X1),X2)
[5] active(from(X)) -> from(active(X))
[6] active(s(X)) -> s(active(X))
[7] 2nd(mark(X)) -> mark(2nd(X))
[8] cons(mark(X1),X2) -> mark(cons(X1,X2))
[9] from(mark(X)) -> mark(from(X))
[10] s(mark(X)) -> mark(s(X))
[11] proper(2nd(X)) -> 2nd(proper(X))
[12] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
[13] proper(from(X)) -> from(proper(X))
[14] proper(s(X)) -> s(proper(X))
[15] 2nd(ok(X)) -> ok(2nd(X))
[16] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
[17] from(ok(X)) -> ok(from(X))
[18] s(ok(X)) -> ok(s(X))
[19] top(mark(X)) -> top(proper(X))
[20] top(ok(X)) -> top(active(X))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(from(X)) , Marked_cons(X,from(s(X)))>
<Marked_active(from(X)) , Marked_from(s(X))>
<Marked_active(from(X)) , Marked_s(X)>
<Marked_active(2nd(X)) , Marked_2nd(active(X))>
<Marked_active(2nd(X)) , Marked_active(X)>
<Marked_active(cons(X1,X2)) , Marked_cons(active(X1),X2)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(from(X)) , Marked_from(active(X))>
<Marked_active(from(X)) , Marked_active(X)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_2nd(mark(X)) , Marked_2nd(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_from(mark(X)) , Marked_from(X)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_proper(2nd(X)) , Marked_2nd(proper(X))>
<Marked_proper(2nd(X)) , Marked_proper(X)>
<Marked_proper(cons(X1,X2)) , Marked_cons(proper(X1),proper(X2))>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(from(X)) , Marked_from(proper(X))>
<Marked_proper(from(X)) , Marked_proper(X)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_2nd(ok(X)) , Marked_2nd(X)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
<Marked_from(ok(X)) , Marked_from(X)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 2 + 1*X0 + 0; 
 [ top ] (X0) = 3*X0 + 0; 
 [ from ] (X0) = 2 + 2*X0 + 0; 
 [ 2nd ] (X0) = 1 + 2*X0 + 0; 
 [ proper ] (X0) = 1*X0 + 0; 
 [ active ] (X0) = 2*X0 + 0; 
 [ Marked_top ] (X0) = 3*X0 + 0; 
 [ s ] (X0) = 1*X0 + 0; 
 [ cons ] (X0,X1) = 2*X0 + 1*X1 + 0; 
 [ ok ] (X0) = 2 + 2*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_proper(2nd(X)) , Marked_proper(X)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X1)>
<Marked_proper(cons(X1,X2)) , Marked_proper(X2)>
<Marked_proper(from(X)) , Marked_proper(X)>
<Marked_proper(s(X)) , Marked_proper(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_active(2nd(X)) , Marked_active(X)>
<Marked_active(cons(X1,X2)) , Marked_active(X1)>
<Marked_active(from(X)) , Marked_active(X)>
<Marked_active(s(X)) , Marked_active(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_2nd(mark(X)) , Marked_2nd(X)>
<Marked_2nd(ok(X)) , Marked_2nd(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(ok(X1),ok(X2)) , Marked_cons(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_from(mark(X)) , Marked_from(X)>
<Marked_from(ok(X)) , Marked_from(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(ok(X)) , Marked_s(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.097155 seconds (real time)
Cime Exit Status: 0