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

TRS termination of:
[1] a__eq(0,0) -> true
[2] a__eq(s(X),s(Y)) -> a__eq(X,Y)
[3] a__eq(X,Y) -> false
[4] a__inf(X) -> cons(X,inf(s(X)))
[5] a__take(0,X) -> nil
[6] a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
[7] a__length(nil) -> 0
[8] a__length(cons(X,L)) -> s(length(L))
[9] mark(eq(X1,X2)) -> a__eq(X1,X2)
[10] mark(inf(X)) -> a__inf(mark(X))
[11] mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
[12] mark(length(X)) -> a__length(mark(X))
[13] mark(0) -> 0
[14] mark(true) -> true
[15] mark(s(X)) -> s(X)
[16] mark(false) -> false
[17] mark(cons(X1,X2)) -> cons(X1,X2)
[18] mark(nil) -> nil
[19] a__eq(X1,X2) -> eq(X1,X2)
[20] a__inf(X) -> inf(X)
[21] a__take(X1,X2) -> take(X1,X2)
[22] a__length(X) -> length(X)


Sub problem: 
guided: 

DP termination of:
<Marked_a__eq(s(X),s(Y)) , Marked_a__eq(X,Y)>
<Marked_mark(eq(X1,X2)) , Marked_a__eq(X1,X2)>
<Marked_mark(inf(X)) , Marked_a__inf(mark(X))>
<Marked_mark(inf(X)) , Marked_mark(X)>
<Marked_mark(take(X1,X2)) , Marked_a__take(mark(X1),mark(X2))>
<Marked_mark(take(X1,X2)) , Marked_mark(X1)>
<Marked_mark(take(X1,X2)) , Marked_mark(X2)>
<Marked_mark(length(X)) , Marked_a__length(mark(X))>
<Marked_mark(length(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_mark(length(X)) , Marked_mark(X)> 
      --> <Marked_mark(length(X)) , Marked_mark(X)>
  <Marked_mark(length(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(length(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(length(X)) , Marked_mark(X)> 
     --> <Marked_mark(inf(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(length(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(inf(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(length(X)) , Marked_mark(X)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(take(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(inf(X)) , Marked_mark(X)>
  <Marked_mark(inf(X)) , Marked_mark(X)> 
     --> <Marked_mark(length(X)) , Marked_mark(X)>
  <Marked_mark(inf(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(inf(X)) , Marked_mark(X)> 
     --> <Marked_mark(take(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(inf(X)) , Marked_mark(X)> 
     --> <Marked_mark(inf(X)) , Marked_mark(X)>
}

{  <Marked_a__eq(s(X),s(Y)) , Marked_a__eq(X,Y)> 
      --> <Marked_a__eq(s(X),s(Y)) , Marked_a__eq(X,Y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__eq(0,0) >= true ;
  a__eq(s(X),s(Y)) >= a__eq(X,Y) ;
  a__eq(X,Y) >= false ;
  a__eq(X1,X2) >= eq(X1,X2) ;
  a__inf(X) >= cons(X,inf(s(X))) ;
  a__inf(X) >= inf(X) ;
  a__take(0,X) >= nil ;
  a__take(s(X),cons(Y,L)) >= cons(Y,take(X,L)) ;
  a__take(X1,X2) >= take(X1,X2) ;
  a__length(cons(X,L)) >= s(length(L)) ;
  a__length(nil) >= 0 ;
  a__length(X) >= length(X) ;
  mark(true) >= true ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(X) ;
  mark(false) >= false ;
  mark(cons(X1,X2)) >= cons(X1,X2) ;
  mark(inf(X)) >= a__inf(mark(X)) ;
  mark(nil) >= nil ;
  mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ;
  mark(length(X)) >= a__length(mark(X)) ;
  mark(eq(X1,X2)) >= a__eq(X1,X2) ;
  Marked_mark(inf(X)) >= Marked_mark(X) ;
  Marked_mark(take(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(take(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(length(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(inf(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(take(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(take(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(length(X)) > Marked_mark(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: a__eq(0,0) >= true
constraint: a__eq(s(X),s(Y)) >= a__eq(X,Y)
constraint: a__eq(X,Y) >= false
constraint: a__eq(X1,X2) >= eq(X1,X2)
constraint: a__inf(X) >= cons(X,inf(s(X)))
constraint: a__inf(X) >= inf(X)
constraint: a__take(0,X) >= nil
constraint: a__take(s(X),cons(Y,L)) >= cons(Y,take(X,L))
constraint: a__take(X1,X2) >= take(X1,X2)
constraint: a__length(cons(X,L)) >= s(length(L))
constraint: a__length(nil) >= 0
constraint: a__length(X) >= length(X)
constraint: mark(true) >= true
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(X)
constraint: mark(false) >= false
constraint: mark(cons(X1,X2)) >= cons(X1,X2)
constraint: mark(inf(X)) >= a__inf(mark(X))
constraint: mark(nil) >= nil
constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2))
constraint: mark(length(X)) >= a__length(mark(X))
constraint: mark(eq(X1,X2)) >= a__eq(X1,X2)
constraint: Marked_mark(inf(X)) >= Marked_mark(X)
constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(take(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(length(X)) >= Marked_mark(X)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__eq(0,0) >= true ;
  a__eq(s(X),s(Y)) >= a__eq(X,Y) ;
  a__eq(X,Y) >= false ;
  a__eq(X1,X2) >= eq(X1,X2) ;
  a__inf(X) >= cons(X,inf(s(X))) ;
  a__inf(X) >= inf(X) ;
  a__take(0,X) >= nil ;
  a__take(s(X),cons(Y,L)) >= cons(Y,take(X,L)) ;
  a__take(X1,X2) >= take(X1,X2) ;
  a__length(cons(X,L)) >= s(length(L)) ;
  a__length(nil) >= 0 ;
  a__length(X) >= length(X) ;
  mark(true) >= true ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(X) ;
  mark(false) >= false ;
  mark(cons(X1,X2)) >= cons(X1,X2) ;
  mark(inf(X)) >= a__inf(mark(X)) ;
  mark(nil) >= nil ;
  mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ;
  mark(length(X)) >= a__length(mark(X)) ;
  mark(eq(X1,X2)) >= a__eq(X1,X2) ;
  Marked_a__eq(s(X),s(Y)) >= Marked_a__eq(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_a__eq(s(X),s(Y)) > Marked_a__eq(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__eq(0,0) >= true
constraint: a__eq(s(X),s(Y)) >= a__eq(X,Y)
constraint: a__eq(X,Y) >= false
constraint: a__eq(X1,X2) >= eq(X1,X2)
constraint: a__inf(X) >= cons(X,inf(s(X)))
constraint: a__inf(X) >= inf(X)
constraint: a__take(0,X) >= nil
constraint: a__take(s(X),cons(Y,L)) >= cons(Y,take(X,L))
constraint: a__take(X1,X2) >= take(X1,X2)
constraint: a__length(cons(X,L)) >= s(length(L))
constraint: a__length(nil) >= 0
constraint: a__length(X) >= length(X)
constraint: mark(true) >= true
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(X)
constraint: mark(false) >= false
constraint: mark(cons(X1,X2)) >= cons(X1,X2)
constraint: mark(inf(X)) >= a__inf(mark(X))
constraint: mark(nil) >= nil
constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2))
constraint: mark(length(X)) >= a__length(mark(X))
constraint: mark(eq(X1,X2)) >= a__eq(X1,X2)
constraint: Marked_a__eq(s(X),s(Y)) >= Marked_a__eq(X,Y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(inf(X)) , Marked_mark(X)> 
      --> <Marked_mark(inf(X)) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__eq(0,0) >= true ;
  a__eq(s(X),s(Y)) >= a__eq(X,Y) ;
  a__eq(X,Y) >= false ;
  a__eq(X1,X2) >= eq(X1,X2) ;
  a__inf(X) >= cons(X,inf(s(X))) ;
  a__inf(X) >= inf(X) ;
  a__take(0,X) >= nil ;
  a__take(s(X),cons(Y,L)) >= cons(Y,take(X,L)) ;
  a__take(X1,X2) >= take(X1,X2) ;
  a__length(cons(X,L)) >= s(length(L)) ;
  a__length(nil) >= 0 ;
  a__length(X) >= length(X) ;
  mark(true) >= true ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(X) ;
  mark(false) >= false ;
  mark(cons(X1,X2)) >= cons(X1,X2) ;
  mark(inf(X)) >= a__inf(mark(X)) ;
  mark(nil) >= nil ;
  mark(take(X1,X2)) >= a__take(mark(X1),mark(X2)) ;
  mark(length(X)) >= a__length(mark(X)) ;
  mark(eq(X1,X2)) >= a__eq(X1,X2) ;
  Marked_mark(inf(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(inf(X)) > Marked_mark(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: a__eq(0,0) >= true
constraint: a__eq(s(X),s(Y)) >= a__eq(X,Y)
constraint: a__eq(X,Y) >= false
constraint: a__eq(X1,X2) >= eq(X1,X2)
constraint: a__inf(X) >= cons(X,inf(s(X)))
constraint: a__inf(X) >= inf(X)
constraint: a__take(0,X) >= nil
constraint: a__take(s(X),cons(Y,L)) >= cons(Y,take(X,L))
constraint: a__take(X1,X2) >= take(X1,X2)
constraint: a__length(cons(X,L)) >= s(length(L))
constraint: a__length(nil) >= 0
constraint: a__length(X) >= length(X)
constraint: mark(true) >= true
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(X)
constraint: mark(false) >= false
constraint: mark(cons(X1,X2)) >= cons(X1,X2)
constraint: mark(inf(X)) >= a__inf(mark(X))
constraint: mark(nil) >= nil
constraint: mark(take(X1,X2)) >= a__take(mark(X1),mark(X2))
constraint: mark(length(X)) >= a__length(mark(X))
constraint: mark(eq(X1,X2)) >= a__eq(X1,X2)
constraint: Marked_mark(inf(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__eq(0,0) -> true
[2] a__eq(s(X),s(Y)) -> a__eq(X,Y)
[3] a__eq(X,Y) -> false
[4] a__inf(X) -> cons(X,inf(s(X)))
[5] a__take(0,X) -> nil
[6] a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
[7] a__length(nil) -> 0
[8] a__length(cons(X,L)) -> s(length(L))
[9] mark(eq(X1,X2)) -> a__eq(X1,X2)
[10] mark(inf(X)) -> a__inf(mark(X))
[11] mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
[12] mark(length(X)) -> a__length(mark(X))
[13] mark(0) -> 0
[14] mark(true) -> true
[15] mark(s(X)) -> s(X)
[16] mark(false) -> false
[17] mark(cons(X1,X2)) -> cons(X1,X2)
[18] mark(nil) -> nil
[19] a__eq(X1,X2) -> eq(X1,X2)
[20] a__inf(X) -> inf(X)
[21] a__take(X1,X2) -> take(X1,X2)
[22] a__length(X) -> length(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__eq(s(X),s(Y)) , Marked_a__eq(X,Y)>
<Marked_mark(eq(X1,X2)) , Marked_a__eq(X1,X2)>
<Marked_mark(inf(X)) , Marked_a__inf(mark(X))>
<Marked_mark(inf(X)) , Marked_mark(X)>
<Marked_mark(take(X1,X2)) , Marked_a__take(mark(X1),mark(X2))>
<Marked_mark(take(X1,X2)) , Marked_mark(X1)>
<Marked_mark(take(X1,X2)) , Marked_mark(X2)>
<Marked_mark(length(X)) , Marked_a__length(mark(X))>
<Marked_mark(length(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(inf(X)) , Marked_mark(X)>
<Marked_mark(take(X1,X2)) , Marked_mark(X1)>
<Marked_mark(take(X1,X2)) , Marked_mark(X2)>
<Marked_mark(length(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ true ] () = 0; 
 [ nil ] () = 0; 
 [ false ] () = 0; 
 [ length ] (X0) = 2*X0 + 1; 
 [ 0 ] () = 0; 
 [ take ] (X0,X1) = 1*X1 + 1*X0 + 1; 
 [ inf ] (X0) = 1*X0; 
 [ eq ] (X0,X1) = 1*X1; 
 [ a__eq ] (X0,X1) = 1*X1; 
 [ a__take ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 [ cons ] (X0,X1) = 1*X1; 
 [ mark ] (X0) = 2*X0; 
 [ s ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 3*X0; 
 [ a__length ] (X0) = 2*X0 + 1; 
 [ a__inf ] (X0) = 1*X0; 
 removing <Marked_mark(take(X1,X2)),Marked_mark(X1)><Marked_mark(take(X1,X2)),
Marked_mark(X2)><Marked_mark(length(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_mark(inf(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(inf(X)) , Marked_mark(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ nil ] () = 0; 
 [ false ] () = 0; 
 [ length ] (X0) = 0; 
 [ 0 ] () = 0; 
 [ take ] (X0,X1) = 3 + 2*X0 + 1*X1 + 0; 
 [ inf ] (X0) = 2 + 1*X0 + 0; 
 [ eq ] (X0,X1) = 0; 
 [ a__eq ] (X0,X1) = 0; 
 [ a__take ] (X0,X1) = 3 + 2*X0 + 1*X1 + 0; 
 [ cons ] (X0,X1) = 2 + 0; 
 [ mark ] (X0) = 3 + 3*X0 + 0; 
 [ s ] (X0) = 2 + 3*X0 + 0; 
 [ Marked_mark ] (X0) = 3*X0 + 0; 
 [ a__length ] (X0) = 3 + 0; 
 [ a__inf ] (X0) = 2 + 1*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_a__eq(s(X),s(Y)) , Marked_a__eq(X,Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ true ] () = 0; 
 [ nil ] () = 0; 
 [ false ] () = 0; 
 [ length ] (X0) = 0; 
 [ 0 ] () = 0; 
 [ Marked_a__eq ] (X0,X1) = 1*X0 + 0; 
 [ take ] (X0,X1) = 2 + 0; 
 [ inf ] (X0) = 2 + 0; 
 [ eq ] (X0,X1) = 0; 
 [ a__eq ] (X0,X1) = 0; 
 [ a__take ] (X0,X1) = 2 + 0; 
 [ cons ] (X0,X1) = 0; 
 [ mark ] (X0) = 2 + 2*X0 + 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ a__length ] (X0) = 1 + 0; 
 [ a__inf ] (X0) = 2 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.177920 seconds (real time)
Cime Exit Status: 0