- : 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] bits(0) -> 0
[5] bits(s(x)) -> s(bits(half(s(x))))


Sub problem: 
guided: 

DP termination of:
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_bits(s(x)) , Marked_bits(half(s(x)))>
<Marked_bits(s(x)) , Marked_half(s(x))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

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

{  <Marked_half(s(s(x))) , Marked_half(x)> 
      --> <Marked_half(s(s(x))) , Marked_half(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)) ;
  bits(0) >= 0 ;
  bits(s(x)) >= s(bits(half(s(x)))) ;
  Marked_bits(s(x)) >= Marked_bits(half(s(x))) ;
 }
 + Disjunctions:{ 
{
  Marked_bits(s(x)) > Marked_bits(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: bits(0) >= 0
constraint: bits(s(x)) >= s(bits(half(s(x))))
constraint: Marked_bits(s(x)) >= Marked_bits(half(s(x)))
APPLY CRITERIA (Subterm criterion)

ST: Marked_half -> 1

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] bits(0) -> 0
[5] bits(s(x)) -> s(bits(half(s(x))))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_half(s(s(x))) , Marked_half(x)>
<Marked_bits(s(x)) , Marked_bits(half(s(x)))>
<Marked_bits(s(x)) , Marked_half(s(x))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_bits(s(x)) , Marked_bits(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 ] ]; 
 [ Marked_bits ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ s ] (X0) = [ [ 0 , 1 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ half ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 1 , 0 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ bits ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 ]} 
{
 
DP termination of:
<Marked_half(s(s(x))) , Marked_half(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.524023 seconds (real time)
Cime Exit Status: 0