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

TRS termination of:
[1] +(a,b) -> +(b,a)
[2] +(a,+(b,z)) -> +(b,+(a,z))
[3] +(+(x,y),z) -> +(x,+(y,z))
[4] f(a,y) -> a
[5] f(b,y) -> b
[6] f(+(x,y),z) -> +(f(x,z),f(y,z))


Sub problem: 
guided: 

DP termination of:
<Marked_+(a,b) , Marked_+(b,a)>
<Marked_+(a,+(b,z)) , Marked_+(b,+(a,z))>
<Marked_+(a,+(b,z)) , Marked_+(a,z)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_f(+(x,y),z) , Marked_+(f(x,z),f(y,z))>
<Marked_f(+(x,y),z) , Marked_f(x,z)>
<Marked_f(+(x,y),z) , Marked_f(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_f(+(x,y),z) , Marked_f(y,z)> 
      --> <Marked_f(+(x,y),z) , Marked_f(y,z)>
  <Marked_f(+(x,y),z) , Marked_f(y,z)> --> <Marked_f(+(x,y),z) , Marked_f(x,z)>
  <Marked_f(+(x,y),z) , Marked_f(x,z)> --> <Marked_f(+(x,y),z) , Marked_f(y,z)>
  <Marked_f(+(x,y),z) , Marked_f(x,z)> --> <Marked_f(+(x,y),z) , Marked_f(x,z)>
}

{  <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))>
}

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

Cime worked for 0.078303 seconds (real time)
Cime Exit Status: 0