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

TRS termination of:
[1] double(0) -> 0
[2] double(s(x)) -> s(s(double(x)))
[3] half(0) -> 0
[4] half(s(0)) -> 0
[5] half(s(s(x))) -> s(half(x))
[6] -(x,0) -> x
[7] -(s(x),s(y)) -> -(x,y)
[8] if(0,y,z) -> y
[9] if(s(x),y,z) -> z
[10] half(double(x)) -> x


Sub problem: 
guided: 

DP termination of:
<Marked_double(s(x)) , Marked_double(x)>
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

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

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

{  <Marked_-(s(x),s(y)) , Marked_-(x,y)> 
      --> <Marked_-(s(x),s(y)) , Marked_-(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  double(0) >= 0 ;
  double(s(x)) >= s(s(double(x))) ;
  half(0) >= 0 ;
  half(double(x)) >= x ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  -(s(x),s(y)) >= -(x,y) ;
  -(x,0) >= x ;
  if(0,y,z) >= y ;
  if(s(x),y,z) >= z ;
  Marked_double(s(x)) >= Marked_double(x) ;
 }
 + Disjunctions:{ 
{
  Marked_double(s(x)) > Marked_double(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: double(0) >= 0
constraint: double(s(x)) >= s(s(double(x)))
constraint: half(0) >= 0
constraint: half(double(x)) >= x
constraint: half(s(0)) >= 0
constraint: half(s(s(x))) >= s(half(x))
constraint: -(s(x),s(y)) >= -(x,y)
constraint: -(x,0) >= x
constraint: if(0,y,z) >= y
constraint: if(s(x),y,z) >= z
constraint: Marked_double(s(x)) >= Marked_double(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  double(0) >= 0 ;
  double(s(x)) >= s(s(double(x))) ;
  half(0) >= 0 ;
  half(double(x)) >= x ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  -(s(x),s(y)) >= -(x,y) ;
  -(x,0) >= x ;
  if(0,y,z) >= y ;
  if(s(x),y,z) >= z ;
  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: double(0) >= 0
constraint: double(s(x)) >= s(s(double(x)))
constraint: half(0) >= 0
constraint: half(double(x)) >= x
constraint: half(s(0)) >= 0
constraint: half(s(s(x))) >= s(half(x))
constraint: -(s(x),s(y)) >= -(x,y)
constraint: -(x,0) >= x
constraint: if(0,y,z) >= y
constraint: if(s(x),y,z) >= z
constraint: Marked_half(s(s(x))) >= Marked_half(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  double(0) >= 0 ;
  double(s(x)) >= s(s(double(x))) ;
  half(0) >= 0 ;
  half(double(x)) >= x ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  -(s(x),s(y)) >= -(x,y) ;
  -(x,0) >= x ;
  if(0,y,z) >= y ;
  if(s(x),y,z) >= z ;
  Marked_-(s(x),s(y)) >= Marked_-(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_-(s(x),s(y)) > Marked_-(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: double(0) >= 0
constraint: double(s(x)) >= s(s(double(x)))
constraint: half(0) >= 0
constraint: half(double(x)) >= x
constraint: half(s(0)) >= 0
constraint: half(s(s(x))) >= s(half(x))
constraint: -(s(x),s(y)) >= -(x,y)
constraint: -(x,0) >= x
constraint: if(0,y,z) >= y
constraint: if(s(x),y,z) >= z
constraint: Marked_-(s(x),s(y)) >= Marked_-(x,y)
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] double(0) -> 0
[2] double(s(x)) -> s(s(double(x)))
[3] half(0) -> 0
[4] half(s(0)) -> 0
[5] half(s(s(x))) -> s(half(x))
[6] -(x,0) -> x
[7] -(s(x),s(y)) -> -(x,y)
[8] if(0,y,z) -> y
[9] if(s(x),y,z) -> z
[10] half(double(x)) -> x
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_double(s(x)) , Marked_double(x)>
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_double(s(x)) , Marked_double(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ - ] (X0,X1) = 3 + 3*X0 + 3*X1 + 0; 
 [ s ] (X0) = 1 + 1*X0 + 0; 
 [ double ] (X0) = 1 + 2*X0 + 0; 
 [ Marked_double ] (X0) = 3*X0 + 0; 
 [ if ] (X0,X1,X2) = 2 + 3*X0 + 2*X1 + 2*X2 + 0; 
 [ half ] (X0) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_half(s(s(x))) , Marked_half(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ - ] (X0,X1) = 2 + 3*X0 + 3*X1 + 0; 
 [ s ] (X0) = 1 + 1*X0 + 0; 
 [ Marked_half ] (X0) = 1*X0 + 0; 
 [ double ] (X0) = 1 + 2*X0 + 0; 
 [ if ] (X0,X1,X2) = 3 + 2*X0 + 3*X1 + 2*X2 + 0; 
 [ half ] (X0) = 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ Marked_- ] (X0,X1) = 1*X0 + 0; 
 [ - ] (X0,X1) = 3 + 3*X0 + 3*X1 + 0; 
 [ s ] (X0) = 1 + 1*X0 + 0; 
 [ double ] (X0) = 1 + 3*X0 + 0; 
 [ if ] (X0,X1,X2) = 2 + 3*X0 + 3*X1 + 3*X2 + 0; 
 [ half ] (X0) = 2 + 1*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.088070 seconds (real time)
Cime Exit Status: 0