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

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


Sub problem: 
guided: 

DP termination of:
<Marked_i(+(x,y)) , Marked_+(i(x),i(y))>
<Marked_i(+(x,y)) , Marked_i(x)>
<Marked_i(+(x,y)) , Marked_i(y)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_i(+(x,y)) , Marked_i(y)> --> <Marked_i(+(x,y)) , Marked_i(y)>
  <Marked_i(+(x,y)) , Marked_i(y)> --> <Marked_i(+(x,y)) , Marked_i(x)>
  <Marked_i(+(x,y)) , Marked_i(x)> --> <Marked_i(+(x,y)) , Marked_i(y)>
  <Marked_i(+(x,y)) , Marked_i(x)> --> <Marked_i(+(x,y)) , Marked_i(x)>
}

{  <Marked_+(x,+(y,z)) , Marked_+(x,y)> 
      --> <Marked_+(x,+(y,z)) , Marked_+(x,y)>
  <Marked_+(x,+(y,z)) , Marked_+(x,y)> 
     --> <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
  <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)> 
     --> <Marked_+(x,+(y,z)) , Marked_+(x,y)>
  <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)> 
     --> <Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  i(0) >= 0 ;
  i(i(x)) >= x ;
  i(+(x,y)) >= +(i(x),i(y)) ;
  +(0,y) >= y ;
  +(i(x),x) >= 0 ;
  +(+(x,i(y)),y) >= x ;
  +(+(x,y),i(y)) >= x ;
  +(x,0) >= x ;
  +(x,i(x)) >= 0 ;
  +(x,+(y,z)) >= +(+(x,y),z) ;
  Marked_i(+(x,y)) >= Marked_i(x) ;
  Marked_i(+(x,y)) >= Marked_i(y) ;
 }
 + Disjunctions:{ 
{
  Marked_i(+(x,y)) > Marked_i(x) ;
 }
{
  Marked_i(+(x,y)) > Marked_i(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: i(0) >= 0
constraint: i(i(x)) >= x
constraint: i(+(x,y)) >= +(i(x),i(y))
constraint: +(0,y) >= y
constraint: +(i(x),x) >= 0
constraint: +(+(x,i(y)),y) >= x
constraint: +(+(x,y),i(y)) >= x
constraint: +(x,0) >= x
constraint: +(x,i(x)) >= 0
constraint: +(x,+(y,z)) >= +(+(x,y),z)
constraint: Marked_i(+(x,y)) >= Marked_i(x)
constraint: Marked_i(+(x,y)) >= Marked_i(y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  i(0) >= 0 ;
  i(i(x)) >= x ;
  i(+(x,y)) >= +(i(x),i(y)) ;
  +(0,y) >= y ;
  +(i(x),x) >= 0 ;
  +(+(x,i(y)),y) >= x ;
  +(+(x,y),i(y)) >= x ;
  +(x,0) >= x ;
  +(x,i(x)) >= 0 ;
  +(x,+(y,z)) >= +(+(x,y),z) ;
  Marked_+(x,+(y,z)) >= Marked_+(+(x,y),z) ;
  Marked_+(x,+(y,z)) >= Marked_+(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_+(x,+(y,z)) > Marked_+(+(x,y),z) ;
 }
{
  Marked_+(x,+(y,z)) > 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: i(0) >= 0
constraint: i(i(x)) >= x
constraint: i(+(x,y)) >= +(i(x),i(y))
constraint: +(0,y) >= y
constraint: +(i(x),x) >= 0
constraint: +(+(x,i(y)),y) >= x
constraint: +(+(x,y),i(y)) >= x
constraint: +(x,0) >= x
constraint: +(x,i(x)) >= 0
constraint: +(x,+(y,z)) >= +(+(x,y),z)
constraint: Marked_+(x,+(y,z)) >= Marked_+(+(x,y),z)
constraint: Marked_+(x,+(y,z)) >= Marked_+(x,y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] i(0) -> 0
[2] +(0,y) -> y
[3] +(x,0) -> x
[4] i(i(x)) -> x
[5] +(i(x),x) -> 0
[6] +(x,i(x)) -> 0
[7] i(+(x,y)) -> +(i(x),i(y))
[8] +(x,+(y,z)) -> +(+(x,y),z)
[9] +(+(x,i(y)),y) -> x
[10] +(+(x,y),i(y)) -> x
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_i(+(x,y)) , Marked_+(i(x),i(y))>
<Marked_i(+(x,y)) , Marked_i(x)>
<Marked_i(+(x,y)) , Marked_i(y)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_i(+(x,y)) , Marked_i(x)>
<Marked_i(+(x,y)) , Marked_i(y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ Marked_i ] (X0) = 3*X0 + 0; 
 [ + ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 [ i ] (X0) = 2*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 0; 
 [ + ] (X0,X1) = 2 + 1*X0 + 2*X1 + 0; 
 [ i ] (X0) = 2*X0 + 0; 
 [ Marked_+ ] (X0,X1) = 3*X1 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.044673 seconds (real time)
Cime Exit Status: 0