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

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


Sub problem: 
guided: 

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

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

{  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
      --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] +(+(x,y),z) -> +(x,+(y,z))
[2] +(f(x),f(y)) -> f(+(x,y))
[3] +(f(x),+(f(y),z)) -> +(f(+(x,y)),z)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_+(f(x),f(y)) , Marked_+(x,y)>
<Marked_+(f(x),+(f(y),z)) , Marked_+(f(+(x,y)),z)>
<Marked_+(f(x),+(f(y),z)) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_+(f(x),f(y)) , Marked_+(x,y)>
<Marked_+(f(x),+(f(y),z)) , Marked_+(f(+(x,y)),z)>
<Marked_+(f(x),+(f(y),z)) , Marked_+(x,y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ + ] (X0,X1) = 1*X1 + 1*X0; 
 [ Marked_+ ] (X0,X1) = 1*X1 + 1*X0; 
 [ f ] (X0) = 1*X0 + 2; 
 removing <Marked_+(f(x),f(y)),Marked_+(x,y)><Marked_+(f(x),+(f(y),z)),
Marked_+(f(+(x,y)),z)><Marked_+(f(x),+(f(y),z)),Marked_+(x,y)>
 [ {
      
     DP termination of:
     <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.048047 seconds (real time)
Cime Exit Status: 0