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

TRS termination of:
[1] half(0) -> 0
[2] half(s(0)) -> 0
[3] half(s(s(x))) -> s(half(x))
[4] lastbit(0) -> 0
[5] lastbit(s(0)) -> s(0)
[6] lastbit(s(s(x))) -> lastbit(x)
[7] conv(0) -> cons(nil,0)
[8] conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))


Sub problem: 
guided: 

DP termination of:
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_lastbit(s(s(x))) , Marked_lastbit(x)>
<Marked_conv(s(x)) , Marked_conv(half(s(x)))>
<Marked_conv(s(x)) , Marked_half(s(x))>
<Marked_conv(s(x)) , Marked_lastbit(s(x))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_conv(s(x)) , Marked_conv(half(s(x)))> 
      --> <Marked_conv(s(x)) , Marked_conv(half(s(x)))>
}

{  <Marked_half(s(s(x))) , Marked_half(x)> 
      --> <Marked_half(s(s(x))) , Marked_half(x)>
}

{  <Marked_lastbit(s(s(x))) , Marked_lastbit(x)> 
      --> <Marked_lastbit(s(s(x))) , Marked_lastbit(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  half(0) >= 0 ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  lastbit(0) >= 0 ;
  lastbit(s(0)) >= s(0) ;
  lastbit(s(s(x))) >= lastbit(x) ;
  conv(0) >= cons(nil,0) ;
  conv(s(x)) >= cons(conv(half(s(x))),lastbit(s(x))) ;
  Marked_conv(s(x)) >= Marked_conv(half(s(x))) ;
 }
 + Disjunctions:{ 
{
  Marked_conv(s(x)) > Marked_conv(half(s(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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: half(0) >= 0
constraint: half(s(0)) >= 0
constraint: half(s(s(x))) >= s(half(x))
constraint: lastbit(0) >= 0
constraint: lastbit(s(0)) >= s(0)
constraint: lastbit(s(s(x))) >= lastbit(x)
constraint: conv(0) >= cons(nil,0)
constraint: conv(s(x)) >= cons(conv(half(s(x))),lastbit(s(x)))
constraint: Marked_conv(s(x)) >= Marked_conv(half(s(x)))
APPLY CRITERIA (Subterm criterion)

ST: Marked_half -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_lastbit -> 1

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] half(0) -> 0
[2] half(s(0)) -> 0
[3] half(s(s(x))) -> s(half(x))
[4] lastbit(0) -> 0
[5] lastbit(s(0)) -> s(0)
[6] lastbit(s(s(x))) -> lastbit(x)
[7] conv(0) -> cons(nil,0)
[8] conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_half(s(s(x))) , Marked_half(x)>
<Marked_lastbit(s(s(x))) , Marked_lastbit(x)>
<Marked_conv(s(x)) , Marked_conv(half(s(x)))>
<Marked_conv(s(x)) , Marked_half(s(x))>
<Marked_conv(s(x)) , Marked_lastbit(s(x))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_conv(s(x)) , Marked_conv(half(s(x)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ cons ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ s ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ conv ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 1 , 1 , 1 ] [ 1 , 1 , 1 ] [ 1 , 1 , 1 ] ]; 
 [ half ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ nil ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ lastbit ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ Marked_conv ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
{
 
DP termination of:
<Marked_half(s(s(x))) , Marked_half(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_lastbit(s(s(x))) , Marked_lastbit(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.869764 seconds (real time)
Cime Exit Status: 0