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

TRS termination of:
[1] O(0) -> 0
[2] +(0,x) -> x
[3] +(x,0) -> x
[4] +(O(x),O(y)) -> O(+(x,y))
[5] +(O(x),I(y)) -> I(+(x,y))
[6] +(I(x),O(y)) -> I(+(x,y))
[7] +(I(x),I(y)) -> O(+(+(x,y),I(0)))
[8]  *(0,x) -> 0
[9]  *(x,0) -> 0
[10]  *(O(x),y) -> O( *(x,y))
[11]  *(I(x),y) -> +(O( *(x,y)),y)


Sub problem: 
guided: 

DP termination of:
<Marked_+(O(x),O(y)) , Marked_O(+(x,y))>
<Marked_+(O(x),O(y)) , Marked_+(x,y)>
<Marked_+(O(x),I(y)) , Marked_+(x,y)>
<Marked_+(I(x),O(y)) , Marked_+(x,y)>
<Marked_+(I(x),I(y)) , Marked_O(+(+(x,y),I(0)))>
<Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
<Marked_+(I(x),I(y)) , Marked_+(x,y)>
<Marked_*(O(x),y) , Marked_O( *(x,y))>
<Marked_*(O(x),y) , Marked_*(x,y)>
<Marked_*(I(x),y) , Marked_+(O( *(x,y)),y)>
<Marked_*(I(x),y) , Marked_O( *(x,y))>
<Marked_*(I(x),y) , Marked_*(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_*(I(x),y) , Marked_*(x,y)> --> <Marked_*(I(x),y) , Marked_*(x,y)>
  <Marked_*(I(x),y) , Marked_*(x,y)> --> <Marked_*(O(x),y) , Marked_*(x,y)>
  <Marked_*(O(x),y) , Marked_*(x,y)> --> <Marked_*(I(x),y) , Marked_*(x,y)>
  <Marked_*(O(x),y) , Marked_*(x,y)> --> <Marked_*(O(x),y) , Marked_*(x,y)>
}

{  <Marked_+(I(x),I(y)) , Marked_+(x,y)> 
      --> <Marked_+(I(x),I(y)) , Marked_+(x,y)>
  <Marked_+(I(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
  <Marked_+(I(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),O(y)) , Marked_+(x,y)>
  <Marked_+(I(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),I(y)) , Marked_+(x,y)>
  <Marked_+(I(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),O(y)) , Marked_+(x,y)>
  <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))> 
     --> <Marked_+(I(x),I(y)) , Marked_+(x,y)>
  <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))> 
     --> <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
  <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))> 
     --> <Marked_+(O(x),I(y)) , Marked_+(x,y)>
  <Marked_+(I(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),I(y)) , Marked_+(x,y)>
  <Marked_+(I(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
  <Marked_+(I(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),O(y)) , Marked_+(x,y)>
  <Marked_+(I(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),I(y)) , Marked_+(x,y)>
  <Marked_+(I(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),O(y)) , Marked_+(x,y)>
  <Marked_+(O(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),I(y)) , Marked_+(x,y)>
  <Marked_+(O(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
  <Marked_+(O(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),O(y)) , Marked_+(x,y)>
  <Marked_+(O(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),I(y)) , Marked_+(x,y)>
  <Marked_+(O(x),I(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),O(y)) , Marked_+(x,y)>
  <Marked_+(O(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),I(y)) , Marked_+(x,y)>
  <Marked_+(O(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
  <Marked_+(O(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),O(y)) , Marked_+(x,y)>
  <Marked_+(O(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),I(y)) , Marked_+(x,y)>
  <Marked_+(O(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),O(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  O(0) >= 0 ;
  +(0,x) >= x ;
  +(O(x),O(y)) >= O(+(x,y)) ;
  +(O(x),I(y)) >= I(+(x,y)) ;
  +(I(x),O(y)) >= I(+(x,y)) ;
  +(I(x),I(y)) >= O(+(+(x,y),I(0))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(O(x),y) >= O( *(x,y)) ;
   *(I(x),y) >= +(O( *(x,y)),y) ;
   *(x,0) >= 0 ;
  Marked_*(O(x),y) >= Marked_*(x,y) ;
  Marked_*(I(x),y) >= Marked_*(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_*(O(x),y) > Marked_*(x,y) ;
 }
{
  Marked_*(I(x),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
=== 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 : 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: O(0) >= 0
constraint: +(0,x) >= x
constraint: +(O(x),O(y)) >= O(+(x,y))
constraint: +(O(x),I(y)) >= I(+(x,y))
constraint: +(I(x),O(y)) >= I(+(x,y))
constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(O(x),y) >= O( *(x,y))
constraint:  *(I(x),y) >= +(O( *(x,y)),y)
constraint:  *(x,0) >= 0
constraint: Marked_*(O(x),y) >= Marked_*(x,y)
constraint: Marked_*(I(x),y) >= Marked_*(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  O(0) >= 0 ;
  +(0,x) >= x ;
  +(O(x),O(y)) >= O(+(x,y)) ;
  +(O(x),I(y)) >= I(+(x,y)) ;
  +(I(x),O(y)) >= I(+(x,y)) ;
  +(I(x),I(y)) >= O(+(+(x,y),I(0))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(O(x),y) >= O( *(x,y)) ;
   *(I(x),y) >= +(O( *(x,y)),y) ;
   *(x,0) >= 0 ;
  Marked_+(O(x),O(y)) >= Marked_+(x,y) ;
  Marked_+(O(x),I(y)) >= Marked_+(x,y) ;
  Marked_+(I(x),O(y)) >= Marked_+(x,y) ;
  Marked_+(I(x),I(y)) >= Marked_+(+(x,y),I(0)) ;
  Marked_+(I(x),I(y)) >= Marked_+(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_+(O(x),O(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(O(x),I(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(I(x),O(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(I(x),I(y)) > Marked_+(+(x,y),I(0)) ;
 }
{
  Marked_+(I(x),I(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
=== 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 : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: O(0) >= 0
constraint: +(0,x) >= x
constraint: +(O(x),O(y)) >= O(+(x,y))
constraint: +(O(x),I(y)) >= I(+(x,y))
constraint: +(I(x),O(y)) >= I(+(x,y))
constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(O(x),y) >= O( *(x,y))
constraint:  *(I(x),y) >= +(O( *(x,y)),y)
constraint:  *(x,0) >= 0
constraint: Marked_+(O(x),O(y)) >= Marked_+(x,y)
constraint: Marked_+(O(x),I(y)) >= Marked_+(x,y)
constraint: Marked_+(I(x),O(y)) >= Marked_+(x,y)
constraint: Marked_+(I(x),I(y)) >= Marked_+(+(x,y),I(0))
constraint: Marked_+(I(x),I(y)) >= Marked_+(x,y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_*(O(x),y) , Marked_*(x,y)> --> <Marked_*(O(x),y) , Marked_*(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  O(0) >= 0 ;
  +(0,x) >= x ;
  +(O(x),O(y)) >= O(+(x,y)) ;
  +(O(x),I(y)) >= I(+(x,y)) ;
  +(I(x),O(y)) >= I(+(x,y)) ;
  +(I(x),I(y)) >= O(+(+(x,y),I(0))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(O(x),y) >= O( *(x,y)) ;
   *(I(x),y) >= +(O( *(x,y)),y) ;
   *(x,0) >= 0 ;
  Marked_*(O(x),y) >= Marked_*(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_*(O(x),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
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: O(0) >= 0
constraint: +(0,x) >= x
constraint: +(O(x),O(y)) >= O(+(x,y))
constraint: +(O(x),I(y)) >= I(+(x,y))
constraint: +(I(x),O(y)) >= I(+(x,y))
constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(O(x),y) >= O( *(x,y))
constraint:  *(I(x),y) >= +(O( *(x,y)),y)
constraint:  *(x,0) >= 0
constraint: Marked_*(O(x),y) >= Marked_*(x,y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_+(I(x),O(y)) , Marked_+(x,y)> 
      --> <Marked_+(I(x),O(y)) , Marked_+(x,y)>
  <Marked_+(I(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),O(y)) , Marked_+(x,y)>
  <Marked_+(O(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(I(x),O(y)) , Marked_+(x,y)>
  <Marked_+(O(x),O(y)) , Marked_+(x,y)> 
     --> <Marked_+(O(x),O(y)) , Marked_+(x,y)>
}

{  <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))> 
      --> <Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  O(0) >= 0 ;
  +(0,x) >= x ;
  +(O(x),O(y)) >= O(+(x,y)) ;
  +(O(x),I(y)) >= I(+(x,y)) ;
  +(I(x),O(y)) >= I(+(x,y)) ;
  +(I(x),I(y)) >= O(+(+(x,y),I(0))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(O(x),y) >= O( *(x,y)) ;
   *(I(x),y) >= +(O( *(x,y)),y) ;
   *(x,0) >= 0 ;
  Marked_+(O(x),O(y)) >= Marked_+(x,y) ;
  Marked_+(I(x),O(y)) >= Marked_+(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_+(O(x),O(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(I(x),O(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
=== 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 : 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: O(0) >= 0
constraint: +(0,x) >= x
constraint: +(O(x),O(y)) >= O(+(x,y))
constraint: +(O(x),I(y)) >= I(+(x,y))
constraint: +(I(x),O(y)) >= I(+(x,y))
constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(O(x),y) >= O( *(x,y))
constraint:  *(I(x),y) >= +(O( *(x,y)),y)
constraint:  *(x,0) >= 0
constraint: Marked_+(O(x),O(y)) >= Marked_+(x,y)
constraint: Marked_+(I(x),O(y)) >= Marked_+(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  O(0) >= 0 ;
  +(0,x) >= x ;
  +(O(x),O(y)) >= O(+(x,y)) ;
  +(O(x),I(y)) >= I(+(x,y)) ;
  +(I(x),O(y)) >= I(+(x,y)) ;
  +(I(x),I(y)) >= O(+(+(x,y),I(0))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(O(x),y) >= O( *(x,y)) ;
   *(I(x),y) >= +(O( *(x,y)),y) ;
   *(x,0) >= 0 ;
  Marked_+(I(x),I(y)) >= Marked_+(+(x,y),I(0)) ;
 }
 + Disjunctions:{ 
{
  Marked_+(I(x),I(y)) > Marked_+(+(x,y),I(0)) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: O(0) >= 0
constraint: +(0,x) >= x
constraint: +(O(x),O(y)) >= O(+(x,y))
constraint: +(O(x),I(y)) >= I(+(x,y))
constraint: +(I(x),O(y)) >= I(+(x,y))
constraint: +(I(x),I(y)) >= O(+(+(x,y),I(0)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(O(x),y) >= O( *(x,y))
constraint:  *(I(x),y) >= +(O( *(x,y)),y)
constraint:  *(x,0) >= 0
constraint: Marked_+(I(x),I(y)) >= Marked_+(+(x,y),I(0))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] O(0) -> 0
[2] +(0,x) -> x
[3] +(x,0) -> x
[4] +(O(x),O(y)) -> O(+(x,y))
[5] +(O(x),I(y)) -> I(+(x,y))
[6] +(I(x),O(y)) -> I(+(x,y))
[7] +(I(x),I(y)) -> O(+(+(x,y),I(0)))
[8]  *(0,x) -> 0
[9]  *(x,0) -> 0
[10]  *(O(x),y) -> O( *(x,y))
[11]  *(I(x),y) -> +(O( *(x,y)),y)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_+(O(x),O(y)) , Marked_O(+(x,y))>
<Marked_+(O(x),O(y)) , Marked_+(x,y)>
<Marked_+(O(x),I(y)) , Marked_+(x,y)>
<Marked_+(I(x),O(y)) , Marked_+(x,y)>
<Marked_+(I(x),I(y)) , Marked_O(+(+(x,y),I(0)))>
<Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
<Marked_+(I(x),I(y)) , Marked_+(x,y)>
<Marked_*(O(x),y) , Marked_O( *(x,y))>
<Marked_*(O(x),y) , Marked_*(x,y)>
<Marked_*(I(x),y) , Marked_+(O( *(x,y)),y)>
<Marked_*(I(x),y) , Marked_O( *(x,y))>
<Marked_*(I(x),y) , Marked_*(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(O(x),y) , Marked_*(x,y)>
<Marked_*(I(x),y) , Marked_*(x,y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ 0 ] () = 0; 
 [ * ] (X0,X1) = 1*X1*X0; 
 [ + ] (X0,X1) = 1*X1 + 1*X0; 
 [ O ] (X0) = 2*X0; 
 [ Marked_* ] (X0,X1) = 1*X1*X0 + 2*X0; 
 [ I ] (X0) = 2*X0 + 1; 
 removing <Marked_*(I(x),y),Marked_*(x,y)>
 [ {
      
     DP termination of:
     <Marked_*(O(x),y) , Marked_*(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(O(x),y) , Marked_*(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ * ] (X0,X1) = 2*X0 + 2*X1 + 1*X1*X0 + 0; 
 [ + ] (X0,X1) = 1*X0 + 2*X1 + 0; 
 [ O ] (X0) = 1 + 1*X0 + 0; 
 [ Marked_* ] (X0,X1) = 2*X0 + 2*X1*X0 + 0; 
 [ I ] (X0) = 2 + 1*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_+(O(x),O(y)) , Marked_+(x,y)>
<Marked_+(O(x),I(y)) , Marked_+(x,y)>
<Marked_+(I(x),O(y)) , Marked_+(x,y)>
<Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
<Marked_+(I(x),I(y)) , Marked_+(x,y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ 0 ] () = 0; 
 [ * ] (X0,X1) = 1*X1*X0; 
 [ + ] (X0,X1) = 1*X1 + 1*X0; 
 [ Marked_+ ] (X0,X1) = 2*X1; 
 [ O ] (X0) = 2*X0; 
 [ I ] (X0) = 2*X0 + 1; 
 removing <Marked_+(O(x),I(y)),Marked_+(x,y)><Marked_+(I(x),I(y)),Marked_+(x,y)>
 [ {
      
     DP termination of:
     <Marked_+(O(x),O(y)) , Marked_+(x,y)>
<Marked_+(I(x),O(y)) , Marked_+(x,y)>
<Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_+(O(x),O(y)) , Marked_+(x,y)>
<Marked_+(I(x),O(y)) , Marked_+(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ * ] (X0,X1) = 2*X0 + 2*X1*X0 + 0; 
 [ + ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ Marked_+ ] (X0,X1) = 2*X1 + 0; 
 [ O ] (X0) = 1 + 1*X0 + 0; 
 [ I ] (X0) = 2 + 1*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_+(I(x),I(y)) , Marked_+(+(x,y),I(0))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ * ] (X0,X1) = 1*X1*X0 + 0; 
 [ + ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ Marked_+ ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ O ] (X0) = 2*X0 + 0; 
 [ I ] (X0) = 1 + 2*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 1.153630 seconds (real time)
Cime Exit Status: 0