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

ST: Marked_mark -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_a__eq -> 1

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

Cime worked for 0.010240 seconds (real time)
Cime Exit Status: 0