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

TRS termination of:
[1] minus(minus(x)) -> x
[2] minus(h(x)) -> h(minus(x))
[3] minus(f(x,y)) -> f(minus(y),minus(x))


Sub problem: 
guided: 

DP termination of:
<Marked_minus(h(x)) , Marked_minus(x)>
<Marked_minus(f(x,y)) , Marked_minus(y)>
<Marked_minus(f(x,y)) , Marked_minus(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_minus(f(x,y)) , Marked_minus(x)> 
      --> <Marked_minus(f(x,y)) , Marked_minus(x)>
  <Marked_minus(f(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(f(x,y)) , Marked_minus(y)>
  <Marked_minus(f(x,y)) , Marked_minus(x)> 
     --> <Marked_minus(h(x)) , Marked_minus(x)>
  <Marked_minus(f(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(f(x,y)) , Marked_minus(x)>
  <Marked_minus(f(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(f(x,y)) , Marked_minus(y)>
  <Marked_minus(f(x,y)) , Marked_minus(y)> 
     --> <Marked_minus(h(x)) , Marked_minus(x)>
  <Marked_minus(h(x)) , Marked_minus(x)> 
     --> <Marked_minus(f(x,y)) , Marked_minus(x)>
  <Marked_minus(h(x)) , Marked_minus(x)> 
     --> <Marked_minus(f(x,y)) , Marked_minus(y)>
  <Marked_minus(h(x)) , Marked_minus(x)> 
     --> <Marked_minus(h(x)) , Marked_minus(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(minus(x)) >= x ;
  minus(h(x)) >= h(minus(x)) ;
  minus(f(x,y)) >= f(minus(y),minus(x)) ;
  Marked_minus(h(x)) >= Marked_minus(x) ;
  Marked_minus(f(x,y)) >= Marked_minus(x) ;
  Marked_minus(f(x,y)) >= Marked_minus(y) ;
 }
 + Disjunctions:{ 
{
  Marked_minus(h(x)) > Marked_minus(x) ;
 }
{
  Marked_minus(f(x,y)) > Marked_minus(x) ;
 }
{
  Marked_minus(f(x,y)) > Marked_minus(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: minus(minus(x)) >= x
constraint: minus(h(x)) >= h(minus(x))
constraint: minus(f(x,y)) >= f(minus(y),minus(x))
constraint: Marked_minus(h(x)) >= Marked_minus(x)
constraint: Marked_minus(f(x,y)) >= Marked_minus(x)
constraint: Marked_minus(f(x,y)) >= Marked_minus(y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_minus(h(x)) , Marked_minus(x)> 
      --> <Marked_minus(h(x)) , Marked_minus(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(minus(x)) >= x ;
  minus(h(x)) >= h(minus(x)) ;
  minus(f(x,y)) >= f(minus(y),minus(x)) ;
  Marked_minus(h(x)) >= Marked_minus(x) ;
 }
 + Disjunctions:{ 
{
  Marked_minus(h(x)) > Marked_minus(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: minus(minus(x)) >= x
constraint: minus(h(x)) >= h(minus(x))
constraint: minus(f(x,y)) >= f(minus(y),minus(x))
constraint: Marked_minus(h(x)) >= Marked_minus(x)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] minus(minus(x)) -> x
[2] minus(h(x)) -> h(minus(x))
[3] minus(f(x,y)) -> f(minus(y),minus(x))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_minus(h(x)) , Marked_minus(x)>
<Marked_minus(f(x,y)) , Marked_minus(y)>
<Marked_minus(f(x,y)) , Marked_minus(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_minus(h(x)) , Marked_minus(x)>
<Marked_minus(f(x,y)) , Marked_minus(y)>
<Marked_minus(f(x,y)) , Marked_minus(x)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ minus ] (X0) = 2*X0; 
 [ f ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 [ h ] (X0) = 1*X0; 
 [ Marked_minus ] (X0) = 3*X0; 
 removing <Marked_minus(f(x,y)),Marked_minus(y)><Marked_minus(f(x,y)),
Marked_minus(x)>
 [ {
      
     DP termination of:
     <Marked_minus(h(x)) , Marked_minus(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_minus(h(x)) , Marked_minus(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ minus ] (X0) = 2 + 2*X0 + 0; 
 [ f ] (X0,X1) = 0; 
 [ h ] (X0) = 2 + 1*X0 + 0; 
 [ Marked_minus ] (X0) = 3*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.038207 seconds (real time)
Cime Exit Status: 0