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

TRS termination of:
[1] ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
[2] u21(ackout(X),Y) -> u22(ackin(Y,X))


Sub problem: 
guided: 

DP termination of:
<Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
<Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
<Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)> 
      --> <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
  <Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)> 
     --> <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
  <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)> 
     --> <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
  <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)> 
     --> <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
  <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)> 
     --> <Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  u21(ackout(X),Y) >= u22(ackin(Y,X)) ;
  ackin(s(X),s(Y)) >= u21(ackin(s(X),Y),X) ;
  Marked_u21(ackout(X),Y) >= Marked_ackin(Y,X) ;
  Marked_ackin(s(X),s(Y)) >= Marked_u21(ackin(s(X),Y),X) ;
  Marked_ackin(s(X),s(Y)) >= Marked_ackin(s(X),Y) ;
 }
 + Disjunctions:{ 
{
  Marked_u21(ackout(X),Y) > Marked_ackin(Y,X) ;
 }
{
  Marked_ackin(s(X),s(Y)) > Marked_u21(ackin(s(X),Y),X) ;
 }
{
  Marked_ackin(s(X),s(Y)) > Marked_ackin(s(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: u21(ackout(X),Y) >= u22(ackin(Y,X))
constraint: ackin(s(X),s(Y)) >= u21(ackin(s(X),Y),X)
constraint: Marked_u21(ackout(X),Y) >= Marked_ackin(Y,X)
constraint: Marked_ackin(s(X),s(Y)) >= Marked_u21(ackin(s(X),Y),X)
constraint: Marked_ackin(s(X),s(Y)) >= Marked_ackin(s(X),Y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)> 
      --> <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  u21(ackout(X),Y) >= u22(ackin(Y,X)) ;
  ackin(s(X),s(Y)) >= u21(ackin(s(X),Y),X) ;
  Marked_ackin(s(X),s(Y)) >= Marked_ackin(s(X),Y) ;
 }
 + Disjunctions:{ 
{
  Marked_ackin(s(X),s(Y)) > Marked_ackin(s(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: u21(ackout(X),Y) >= u22(ackin(Y,X))
constraint: ackin(s(X),s(Y)) >= u21(ackin(s(X),Y),X)
constraint: Marked_ackin(s(X),s(Y)) >= Marked_ackin(s(X),Y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
[2] u21(ackout(X),Y) -> u22(ackin(Y,X))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
<Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
<Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ackin(s(X),s(Y)) , Marked_u21(ackin(s(X),Y),X)>
<Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
<Marked_u21(ackout(X),Y) , Marked_ackin(Y,X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ u21 ] (X0,X1) = 2; 
 [ ackout ] (X0) = 0; 
 [ s ] (X0) = 3*X0 + 2; 
 [ Marked_ackin ] (X0,X1) = 2*X0; 
 [ ackin ] (X0,X1) = 2*X0; 
 [ Marked_u21 ] (X0,X1) = 2*X1 + 2; 
 [ u22 ] (X0) = 0; 
 removing <Marked_ackin(s(X),s(Y)),Marked_u21(ackin(s(X),Y),X)><Marked_u21(
                                                                 ackout(
                                                                  X),
                                                                 Y),Marked_ackin(
                                                                    Y,
                                                                    X)>
 [ {
      
     DP termination of:
     <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ackin(s(X),s(Y)) , Marked_ackin(s(X),Y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ u21 ] (X0,X1) = 2 + 2*X0 + 0; 
 [ ackout ] (X0) = 2 + 3*X0 + 0; 
 [ s ] (X0) = 2 + 3*X0 + 0; 
 [ Marked_ackin ] (X0,X1) = 3*X1 + 0; 
 [ ackin ] (X0,X1) = 2*X1 + 0; 
 [ u22 ] (X0) = 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.056321 seconds (real time)
Cime Exit Status: 0