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

TRS termination of:
[1] ack_in(0,n) -> ack_out(s(n))
[2] ack_in(s(m),0) -> u11(ack_in(m,s(0)))
[3] u11(ack_out(n)) -> ack_out(n)
[4] ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
[5] u21(ack_out(n),m) -> u22(ack_in(m,n))
[6] u22(ack_out(n)) -> ack_out(n)


Sub problem: 
guided: 

DP termination of:
<Marked_ack_in(s(m),0) , Marked_u11(ack_in(m,s(0)))>
<Marked_ack_in(s(m),0) , Marked_ack_in(m,s(0))>
<Marked_ack_in(s(m),s(n)) , Marked_u21(ack_in(s(m),n),m)>
<Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
<Marked_u21(ack_out(n),m) , Marked_u22(ack_in(m,n))>
<Marked_u21(ack_out(n),m) , Marked_ack_in(m,n)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_u21(ack_out(n),m) , Marked_ack_in(m,n)> 
      --> <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
  <Marked_u21(ack_out(n),m) , Marked_ack_in(m,n)> 
     --> <Marked_ack_in(s(m),s(n)) , Marked_u21(ack_in(s(m),n),m)>
  <Marked_u21(ack_out(n),m) , Marked_ack_in(m,n)> 
     --> <Marked_ack_in(s(m),0) , Marked_ack_in(m,s(0))>
  <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)> 
     --> <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
  <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)> 
     --> <Marked_ack_in(s(m),s(n)) , Marked_u21(ack_in(s(m),n),m)>
  <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)> 
     --> <Marked_ack_in(s(m),0) , Marked_ack_in(m,s(0))>
  <Marked_ack_in(s(m),s(n)) , Marked_u21(ack_in(s(m),n),m)> 
     --> <Marked_u21(ack_out(n),m) , Marked_ack_in(m,n)>
  <Marked_ack_in(s(m),0) , Marked_ack_in(m,s(0))> 
     --> <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
  <Marked_ack_in(s(m),0) , Marked_ack_in(m,s(0))> 
     --> <Marked_ack_in(s(m),s(n)) , Marked_u21(ack_in(s(m),n),m)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ack_in(s(m),s(n)) >= u21(ack_in(s(m),n),m) ;
  ack_in(s(m),0) >= u11(ack_in(m,s(0))) ;
  ack_in(0,n) >= ack_out(s(n)) ;
  u11(ack_out(n)) >= ack_out(n) ;
  u21(ack_out(n),m) >= u22(ack_in(m,n)) ;
  u22(ack_out(n)) >= ack_out(n) ;
  Marked_u21(ack_out(n),m) >= Marked_ack_in(m,n) ;
  Marked_ack_in(s(m),s(n)) >= Marked_u21(ack_in(s(m),n),m) ;
  Marked_ack_in(s(m),s(n)) >= Marked_ack_in(s(m),n) ;
  Marked_ack_in(s(m),0) >= Marked_ack_in(m,s(0)) ;
 }
 + Disjunctions:{ 
{
  Marked_u21(ack_out(n),m) > Marked_ack_in(m,n) ;
 }
{
  Marked_ack_in(s(m),s(n)) > Marked_u21(ack_in(s(m),n),m) ;
 }
{
  Marked_ack_in(s(m),s(n)) > Marked_ack_in(s(m),n) ;
 }
{
  Marked_ack_in(s(m),0) > Marked_ack_in(m,s(0)) ;
 }
 } 
=== 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: ack_in(s(m),s(n)) >= u21(ack_in(s(m),n),m)
constraint: ack_in(s(m),0) >= u11(ack_in(m,s(0)))
constraint: ack_in(0,n) >= ack_out(s(n))
constraint: u11(ack_out(n)) >= ack_out(n)
constraint: u21(ack_out(n),m) >= u22(ack_in(m,n))
constraint: u22(ack_out(n)) >= ack_out(n)
constraint: Marked_u21(ack_out(n),m) >= Marked_ack_in(m,n)
constraint: Marked_ack_in(s(m),s(n)) >= Marked_u21(ack_in(s(m),n),m)
constraint: Marked_ack_in(s(m),s(n)) >= Marked_ack_in(s(m),n)
constraint: Marked_ack_in(s(m),0) >= Marked_ack_in(m,s(0))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)> 
      --> <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ack_in(s(m),s(n)) >= u21(ack_in(s(m),n),m) ;
  ack_in(s(m),0) >= u11(ack_in(m,s(0))) ;
  ack_in(0,n) >= ack_out(s(n)) ;
  u11(ack_out(n)) >= ack_out(n) ;
  u21(ack_out(n),m) >= u22(ack_in(m,n)) ;
  u22(ack_out(n)) >= ack_out(n) ;
  Marked_ack_in(s(m),s(n)) >= Marked_ack_in(s(m),n) ;
 }
 + Disjunctions:{ 
{
  Marked_ack_in(s(m),s(n)) > Marked_ack_in(s(m),n) ;
 }
 } 
=== 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: ack_in(s(m),s(n)) >= u21(ack_in(s(m),n),m)
constraint: ack_in(s(m),0) >= u11(ack_in(m,s(0)))
constraint: ack_in(0,n) >= ack_out(s(n))
constraint: u11(ack_out(n)) >= ack_out(n)
constraint: u21(ack_out(n),m) >= u22(ack_in(m,n))
constraint: u22(ack_out(n)) >= ack_out(n)
constraint: Marked_ack_in(s(m),s(n)) >= Marked_ack_in(s(m),n)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] ack_in(0,n) -> ack_out(s(n))
[2] ack_in(s(m),0) -> u11(ack_in(m,s(0)))
[3] u11(ack_out(n)) -> ack_out(n)
[4] ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
[5] u21(ack_out(n),m) -> u22(ack_in(m,n))
[6] u22(ack_out(n)) -> ack_out(n)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_ack_in(s(m),0) , Marked_u11(ack_in(m,s(0)))>
<Marked_ack_in(s(m),0) , Marked_ack_in(m,s(0))>
<Marked_ack_in(s(m),s(n)) , Marked_u21(ack_in(s(m),n),m)>
<Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
<Marked_u21(ack_out(n),m) , Marked_u22(ack_in(m,n))>
<Marked_u21(ack_out(n),m) , Marked_ack_in(m,n)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ack_in(s(m),0) , Marked_ack_in(m,s(0))>
<Marked_ack_in(s(m),s(n)) , Marked_u21(ack_in(s(m),n),m)>
<Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
<Marked_u21(ack_out(n),m) , Marked_ack_in(m,n)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ ack_out ] (X0) = 0; 
 [ Marked_u21 ] (X0,X1) = 2*X1; 
 [ u11 ] (X0) = 0; 
 [ ack_in ] (X0,X1) = 0; 
 [ u22 ] (X0) = 0; 
 [ s ] (X0) = 2*X0 + 2; 
 [ Marked_ack_in ] (X0,X1) = 1*X0; 
 [ u21 ] (X0,X1) = 0; 
 [ 0 ] () = 0; 
 removing <Marked_ack_in(s(m),0),Marked_ack_in(m,s(0))><Marked_ack_in(
                                                         s(m),s(n)),Marked_u21(
                                                                    ack_in(
                                                                    s(m),
                                                                    n),
                                                                    m)>
 [ {
      
     DP termination of:
     <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
<Marked_u21(ack_out(n),m) , Marked_ack_in(m,n)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_ack_in(s(m),s(n)) , Marked_ack_in(s(m),n)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ ack_out ] (X0) = 0; 
 [ u11 ] (X0) = 2 + 0; 
 [ ack_in ] (X0,X1) = 2*X0 + 2*X1 + 0; 
 [ u22 ] (X0) = 0; 
 [ s ] (X0) = 1 + 3*X0 + 0; 
 [ Marked_ack_in ] (X0,X1) = 3*X1 + 0; 
 [ u21 ] (X0,X1) = 2 + 0; 
 [ 0 ] () = 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.102754 seconds (real time)
Cime Exit Status: 0