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

TRS termination of:
[1] half(0) -> 0
[2] half(s(s(x))) -> s(half(x))
[3] log(s(0)) -> 0
[4] log(s(s(x))) -> s(log(s(half(x))))


Sub problem: 
guided: 

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

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

{  <Marked_half(s(s(x))) , Marked_half(x)> 
      --> <Marked_half(s(s(x))) , Marked_half(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  half(0) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  log(s(0)) >= 0 ;
  log(s(s(x))) >= s(log(s(half(x)))) ;
  Marked_log(s(s(x))) >= Marked_log(s(half(x))) ;
 }
 + Disjunctions:{ 
{
  Marked_log(s(s(x))) > Marked_log(s(half(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: half(0) >= 0
constraint: half(s(s(x))) >= s(half(x))
constraint: log(s(0)) >= 0
constraint: log(s(s(x))) >= s(log(s(half(x))))
constraint: Marked_log(s(s(x))) >= Marked_log(s(half(x)))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  half(0) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  log(s(0)) >= 0 ;
  log(s(s(x))) >= s(log(s(half(x)))) ;
  Marked_half(s(s(x))) >= Marked_half(x) ;
 }
 + Disjunctions:{ 
{
  Marked_half(s(s(x))) > Marked_half(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: half(0) >= 0
constraint: half(s(s(x))) >= s(half(x))
constraint: log(s(0)) >= 0
constraint: log(s(s(x))) >= s(log(s(half(x))))
constraint: Marked_half(s(s(x))) >= Marked_half(x)
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(s(x))) -> s(half(x))
[3] log(s(0)) -> 0
[4] log(s(s(x))) -> s(log(s(half(x))))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_half(s(s(x))) , Marked_half(x)>
<Marked_log(s(s(x))) , Marked_log(s(half(x)))>
<Marked_log(s(s(x))) , Marked_half(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_log(s(s(x))) , Marked_log(s(half(x)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ Marked_log ] (X0) = 3*X0 + 0; 
 [ s ] (X0) = 2 + 2*X0 + 0; 
 [ half ] (X0) = 1*X0 + 0; 
 [ log ] (X0) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_half(s(s(x))) , Marked_half(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ half ] (X0) = 1*X0 + 0; 
 [ Marked_half ] (X0) = 1*X0 + 0; 
 [ log ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.066887 seconds (real time)
Cime Exit Status: 0