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

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


Sub problem: 
guided: 

DP termination of:
<Marked_+(x,minus(y)) , Marked_minus(+(minus(x),y))>
<Marked_+(x,minus(y)) , Marked_+(minus(x),y)>
<Marked_+(x,minus(y)) , Marked_minus(x)>
<Marked_+(x,+(y,z)) , Marked_+(+(x,y),z)>
<Marked_+(x,+(y,z)) , Marked_+(x,y)>
<Marked_+(minus(+(x,1)),1) , Marked_minus(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

Cime worked for 0.039457 seconds (real time)
Cime Exit Status: 0