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

TRS termination of:
[1] rev(nil) -> nil
[2] rev(.(x,y)) -> ++(rev(y),.(x,nil))
[3] car(.(x,y)) -> x
[4] cdr(.(x,y)) -> y
[5] null(nil) -> true
[6] null(.(x,y)) -> false
[7] ++(nil,y) -> y
[8] ++(.(x,y),z) -> .(x,++(y,z))


Sub problem: 
guided: 

DP termination of:
<Marked_rev(.(x,y)) , Marked_++(rev(y),.(x,nil))>
<Marked_rev(.(x,y)) , Marked_rev(y)>
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <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)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  rev(nil) >= nil ;
  rev(.(x,y)) >= ++(rev(y),.(x,nil)) ;
  ++(nil,y) >= y ;
  ++(.(x,y),z) >= .(x,++(y,z)) ;
  car(.(x,y)) >= x ;
  cdr(.(x,y)) >= y ;
  null(nil) >= true ;
  null(.(x,y)) >= false ;
  Marked_rev(.(x,y)) >= Marked_rev(y) ;
 }
 + Disjunctions:{ 
{
  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: rev(nil) >= nil
constraint: rev(.(x,y)) >= ++(rev(y),.(x,nil))
constraint: ++(nil,y) >= y
constraint: ++(.(x,y),z) >= .(x,++(y,z))
constraint: car(.(x,y)) >= x
constraint: cdr(.(x,y)) >= y
constraint: null(nil) >= true
constraint: null(.(x,y)) >= false
constraint: Marked_rev(.(x,y)) >= Marked_rev(y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  rev(nil) >= nil ;
  rev(.(x,y)) >= ++(rev(y),.(x,nil)) ;
  ++(nil,y) >= y ;
  ++(.(x,y),z) >= .(x,++(y,z)) ;
  car(.(x,y)) >= x ;
  cdr(.(x,y)) >= y ;
  null(nil) >= true ;
  null(.(x,y)) >= false ;
  Marked_++(.(x,y),z) >= Marked_++(y,z) ;
 }
 + Disjunctions:{ 
{
  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: rev(nil) >= nil
constraint: rev(.(x,y)) >= ++(rev(y),.(x,nil))
constraint: ++(nil,y) >= y
constraint: ++(.(x,y),z) >= .(x,++(y,z))
constraint: car(.(x,y)) >= x
constraint: cdr(.(x,y)) >= y
constraint: null(nil) >= true
constraint: null(.(x,y)) >= false
constraint: Marked_++(.(x,y),z) >= Marked_++(y,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] rev(nil) -> nil
[2] rev(.(x,y)) -> ++(rev(y),.(x,nil))
[3] car(.(x,y)) -> x
[4] cdr(.(x,y)) -> y
[5] null(nil) -> true
[6] null(.(x,y)) -> false
[7] ++(nil,y) -> y
[8] ++(.(x,y),z) -> .(x,++(y,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_rev(.(x,y)) , Marked_++(rev(y),.(x,nil))>
<Marked_rev(.(x,y)) , Marked_rev(y)>
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_rev(.(x,y)) , Marked_rev(y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ false ] () = 0; 
 [ car ] (X0) = 3 + 3*X0 + 0; 
 [ ++ ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ true ] () = 3 + 0; 
 [ rev ] (X0) = 2*X0 + 0; 
 [ cdr ] (X0) = 3 + 3*X0 + 0; 
 [ Marked_rev ] (X0) = 3*X0 + 0; 
 [ . ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; 
 [ null ] (X0) = 3 + 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_++(.(x,y),z) , Marked_++(y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ false ] () = 3 + 0; 
 [ car ] (X0) = 2 + 3*X0 + 0; 
 [ ++ ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ true ] () = 3 + 0; 
 [ rev ] (X0) = 2*X0 + 0; 
 [ Marked_++ ] (X0,X1) = 3*X0 + 0; 
 [ cdr ] (X0) = 2 + 3*X0 + 0; 
 [ . ] (X0,X1) = 1 + 1*X0 + 1*X1 + 0; 
 [ null ] (X0) = 3 + 3*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.042649 seconds (real time)
Cime Exit Status: 0