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

TRS termination of:
[1] flatten(nil) -> nil
[2] flatten(unit(x)) -> flatten(x)
[3] flatten(++(x,y)) -> ++(flatten(x),flatten(y))
[4] flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
[5] flatten(flatten(x)) -> flatten(x)
[6] rev(nil) -> nil
[7] rev(unit(x)) -> unit(x)
[8] rev(++(x,y)) -> ++(rev(y),rev(x))
[9] rev(rev(x)) -> x
[10] ++(x,nil) -> x
[11] ++(nil,y) -> y
[12] ++(++(x,y),z) -> ++(x,++(y,z))


Sub problem: 
guided: 

DP termination of:
<Marked_flatten(unit(x)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_++(flatten(x),flatten(y))>
<Marked_flatten(++(x,y)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_flatten(y)>
<Marked_flatten(++(unit(x),y)) , Marked_++(flatten(x),flatten(y))>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
<Marked_rev(++(x,y)) , Marked_++(rev(y),rev(x))>
<Marked_rev(++(x,y)) , Marked_rev(y)>
<Marked_rev(++(x,y)) , Marked_rev(x)>
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
      --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(y)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(++(x,y)) , Marked_flatten(x)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(y)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(++(x,y)) , Marked_flatten(x)>
  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
     --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
}

{  <Marked_rev(++(x,y)) , Marked_rev(x)> 
      --> <Marked_rev(++(x,y)) , Marked_rev(x)>
  <Marked_rev(++(x,y)) , Marked_rev(x)> 
     --> <Marked_rev(++(x,y)) , Marked_rev(y)>
  <Marked_rev(++(x,y)) , Marked_rev(y)> 
     --> <Marked_rev(++(x,y)) , Marked_rev(x)>
  <Marked_rev(++(x,y)) , Marked_rev(y)> 
     --> <Marked_rev(++(x,y)) , Marked_rev(y)>
}

{  <Marked_++(++(x,y),z) , Marked_++(y,z)> 
      --> <Marked_++(++(x,y),z) , Marked_++(y,z)>
  <Marked_++(++(x,y),z) , Marked_++(y,z)> 
     --> <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
  <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))> 
     --> <Marked_++(++(x,y),z) , Marked_++(y,z)>
  <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))> 
     --> <Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  flatten(nil) >= nil ;
  flatten(flatten(x)) >= flatten(x) ;
  flatten(unit(x)) >= flatten(x) ;
  flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) ;
  flatten(++(x,y)) >= ++(flatten(x),flatten(y)) ;
  ++(nil,y) >= y ;
  ++(++(x,y),z) >= ++(x,++(y,z)) ;
  ++(x,nil) >= x ;
  rev(nil) >= nil ;
  rev(unit(x)) >= unit(x) ;
  rev(++(x,y)) >= ++(rev(y),rev(x)) ;
  rev(rev(x)) >= x ;
  Marked_flatten(unit(x)) >= Marked_flatten(x) ;
  Marked_flatten(++(unit(x),y)) >= Marked_flatten(x) ;
  Marked_flatten(++(unit(x),y)) >= Marked_flatten(y) ;
  Marked_flatten(++(x,y)) >= Marked_flatten(x) ;
  Marked_flatten(++(x,y)) >= Marked_flatten(y) ;
 }
 + Disjunctions:{ 
{
  Marked_flatten(unit(x)) > Marked_flatten(x) ;
 }
{
  Marked_flatten(++(unit(x),y)) > Marked_flatten(x) ;
 }
{
  Marked_flatten(++(unit(x),y)) > Marked_flatten(y) ;
 }
{
  Marked_flatten(++(x,y)) > Marked_flatten(x) ;
 }
{
  Marked_flatten(++(x,y)) > Marked_flatten(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: flatten(nil) >= nil
constraint: flatten(flatten(x)) >= flatten(x)
constraint: flatten(unit(x)) >= flatten(x)
constraint: flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y))
constraint: flatten(++(x,y)) >= ++(flatten(x),flatten(y))
constraint: ++(nil,y) >= y
constraint: ++(++(x,y),z) >= ++(x,++(y,z))
constraint: ++(x,nil) >= x
constraint: rev(nil) >= nil
constraint: rev(unit(x)) >= unit(x)
constraint: rev(++(x,y)) >= ++(rev(y),rev(x))
constraint: rev(rev(x)) >= x
constraint: Marked_flatten(unit(x)) >= Marked_flatten(x)
constraint: Marked_flatten(++(unit(x),y)) >= Marked_flatten(x)
constraint: Marked_flatten(++(unit(x),y)) >= Marked_flatten(y)
constraint: Marked_flatten(++(x,y)) >= Marked_flatten(x)
constraint: Marked_flatten(++(x,y)) >= Marked_flatten(y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  flatten(nil) >= nil ;
  flatten(flatten(x)) >= flatten(x) ;
  flatten(unit(x)) >= flatten(x) ;
  flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) ;
  flatten(++(x,y)) >= ++(flatten(x),flatten(y)) ;
  ++(nil,y) >= y ;
  ++(++(x,y),z) >= ++(x,++(y,z)) ;
  ++(x,nil) >= x ;
  rev(nil) >= nil ;
  rev(unit(x)) >= unit(x) ;
  rev(++(x,y)) >= ++(rev(y),rev(x)) ;
  rev(rev(x)) >= x ;
  Marked_rev(++(x,y)) >= Marked_rev(x) ;
  Marked_rev(++(x,y)) >= Marked_rev(y) ;
 }
 + Disjunctions:{ 
{
  Marked_rev(++(x,y)) > Marked_rev(x) ;
 }
{
  Marked_rev(++(x,y)) > Marked_rev(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: flatten(nil) >= nil
constraint: flatten(flatten(x)) >= flatten(x)
constraint: flatten(unit(x)) >= flatten(x)
constraint: flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y))
constraint: flatten(++(x,y)) >= ++(flatten(x),flatten(y))
constraint: ++(nil,y) >= y
constraint: ++(++(x,y),z) >= ++(x,++(y,z))
constraint: ++(x,nil) >= x
constraint: rev(nil) >= nil
constraint: rev(unit(x)) >= unit(x)
constraint: rev(++(x,y)) >= ++(rev(y),rev(x))
constraint: rev(rev(x)) >= x
constraint: Marked_rev(++(x,y)) >= Marked_rev(x)
constraint: Marked_rev(++(x,y)) >= Marked_rev(y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  flatten(nil) >= nil ;
  flatten(flatten(x)) >= flatten(x) ;
  flatten(unit(x)) >= flatten(x) ;
  flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) ;
  flatten(++(x,y)) >= ++(flatten(x),flatten(y)) ;
  ++(nil,y) >= y ;
  ++(++(x,y),z) >= ++(x,++(y,z)) ;
  ++(x,nil) >= x ;
  rev(nil) >= nil ;
  rev(unit(x)) >= unit(x) ;
  rev(++(x,y)) >= ++(rev(y),rev(x)) ;
  rev(rev(x)) >= x ;
  Marked_++(++(x,y),z) >= Marked_++(x,++(y,z)) ;
  Marked_++(++(x,y),z) >= Marked_++(y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_++(++(x,y),z) > Marked_++(x,++(y,z)) ;
 }
{
  Marked_++(++(x,y),z) > Marked_++(y,z) ;
 }
 } 
=== 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: flatten(nil) >= nil
constraint: flatten(flatten(x)) >= flatten(x)
constraint: flatten(unit(x)) >= flatten(x)
constraint: flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y))
constraint: flatten(++(x,y)) >= ++(flatten(x),flatten(y))
constraint: ++(nil,y) >= y
constraint: ++(++(x,y),z) >= ++(x,++(y,z))
constraint: ++(x,nil) >= x
constraint: rev(nil) >= nil
constraint: rev(unit(x)) >= unit(x)
constraint: rev(++(x,y)) >= ++(rev(y),rev(x))
constraint: rev(rev(x)) >= x
constraint: Marked_++(++(x,y),z) >= Marked_++(x,++(y,z))
constraint: Marked_++(++(x,y),z) >= Marked_++(y,z)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_flatten(unit(x)) , Marked_flatten(x)> 
      --> <Marked_flatten(unit(x)) , Marked_flatten(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  flatten(nil) >= nil ;
  flatten(flatten(x)) >= flatten(x) ;
  flatten(unit(x)) >= flatten(x) ;
  flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y)) ;
  flatten(++(x,y)) >= ++(flatten(x),flatten(y)) ;
  ++(nil,y) >= y ;
  ++(++(x,y),z) >= ++(x,++(y,z)) ;
  ++(x,nil) >= x ;
  rev(nil) >= nil ;
  rev(unit(x)) >= unit(x) ;
  rev(++(x,y)) >= ++(rev(y),rev(x)) ;
  rev(rev(x)) >= x ;
  Marked_flatten(unit(x)) >= Marked_flatten(x) ;
 }
 + Disjunctions:{ 
{
  Marked_flatten(unit(x)) > Marked_flatten(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: flatten(nil) >= nil
constraint: flatten(flatten(x)) >= flatten(x)
constraint: flatten(unit(x)) >= flatten(x)
constraint: flatten(++(unit(x),y)) >= ++(flatten(x),flatten(y))
constraint: flatten(++(x,y)) >= ++(flatten(x),flatten(y))
constraint: ++(nil,y) >= y
constraint: ++(++(x,y),z) >= ++(x,++(y,z))
constraint: ++(x,nil) >= x
constraint: rev(nil) >= nil
constraint: rev(unit(x)) >= unit(x)
constraint: rev(++(x,y)) >= ++(rev(y),rev(x))
constraint: rev(rev(x)) >= x
constraint: Marked_flatten(unit(x)) >= Marked_flatten(x)
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] flatten(nil) -> nil
[2] flatten(unit(x)) -> flatten(x)
[3] flatten(++(x,y)) -> ++(flatten(x),flatten(y))
[4] flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
[5] flatten(flatten(x)) -> flatten(x)
[6] rev(nil) -> nil
[7] rev(unit(x)) -> unit(x)
[8] rev(++(x,y)) -> ++(rev(y),rev(x))
[9] rev(rev(x)) -> x
[10] ++(x,nil) -> x
[11] ++(nil,y) -> y
[12] ++(++(x,y),z) -> ++(x,++(y,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_flatten(unit(x)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_++(flatten(x),flatten(y))>
<Marked_flatten(++(x,y)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_flatten(y)>
<Marked_flatten(++(unit(x),y)) , Marked_++(flatten(x),flatten(y))>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
<Marked_rev(++(x,y)) , Marked_++(rev(y),rev(x))>
<Marked_rev(++(x,y)) , Marked_rev(y)>
<Marked_rev(++(x,y)) , Marked_rev(x)>
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_flatten(unit(x)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_flatten(x)>
<Marked_flatten(++(x,y)) , Marked_flatten(y)>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(x)>
<Marked_flatten(++(unit(x),y)) , Marked_flatten(y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ nil ] () = 0; 
 [ rev ] (X0) = 2*X0; 
 [ unit ] (X0) = 1*X0; 
 [ flatten ] (X0) = 2*X0; 
 [ ++ ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 [ Marked_flatten ] (X0) = 2*X0; 
 removing <Marked_flatten(++(x,y)),Marked_flatten(x)><Marked_flatten(++(x,y)),
Marked_flatten(y)><Marked_flatten(++(unit(x),y)),Marked_flatten(x)><Marked_flatten(
                                                                    ++(
                                                                    unit(x),
                                                                    y)),
Marked_flatten(y)>
 [ {
      
     DP termination of:
     <Marked_flatten(unit(x)) , Marked_flatten(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_flatten(unit(x)) , Marked_flatten(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ rev ] (X0) = 1*X0 + 0; 
 [ unit ] (X0) = 2 + 3*X0 + 0; 
 [ flatten ] (X0) = 3*X0 + 0; 
 [ ++ ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ Marked_flatten ] (X0) = 3*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_rev(++(x,y)) , Marked_rev(y)>
<Marked_rev(++(x,y)) , Marked_rev(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ rev ] (X0) = 2*X0 + 0; 
 [ unit ] (X0) = 1*X0 + 0; 
 [ Marked_rev ] (X0) = 3*X0 + 0; 
 [ flatten ] (X0) = 2*X0 + 0; 
 [ ++ ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_++(++(x,y),z) , Marked_++(x,++(y,z))>
<Marked_++(++(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ rev ] (X0) = 2*X0 + 0; 
 [ unit ] (X0) = 1*X0 + 0; 
 [ flatten ] (X0) = 2*X0 + 0; 
 [ Marked_++ ] (X0,X1) = 3*X0 + 0; 
 [ ++ ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.120934 seconds (real time)
Cime Exit Status: 0