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

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


Sub problem: 
guided: 

DP termination of:
<Marked_f(s(0),y,z) , Marked_f(0,s(y),s(z))>
<Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))>
<Marked_f(s(x),0,s(z)) , Marked_f(x,s(0),z)>
<Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))>
<Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)>
<Marked_f(0,s(s(y)),s(0)) , Marked_f(0,y,s(0))>
<Marked_f(0,s(0),s(s(z))) , Marked_f(0,s(0),z)>
<Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,y,f(0,s(s(y)),s(z)))>
<Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,s(s(y)),s(z))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)> 
      --> <Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)>
  <Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)> 
     --> <Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))>
  <Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)> 
     --> <Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))>
  <Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))> 
     --> <Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)>
  <Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))> 
     --> <Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))>
  <Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))> 
     --> <Marked_f(s(x),0,s(z)) , Marked_f(x,s(0),z)>
  <Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))> 
     --> <Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))>
  <Marked_f(s(x),0,s(z)) , Marked_f(x,s(0),z)> 
     --> <Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)>
  <Marked_f(s(x),0,s(z)) , Marked_f(x,s(0),z)> 
     --> <Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))>
  <Marked_f(s(x),0,s(z)) , Marked_f(x,s(0),z)> 
     --> <Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))>
  <Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))> 
     --> <Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)>
  <Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))> 
     --> <Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))>
  <Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))> 
     --> <Marked_f(s(x),0,s(z)) , Marked_f(x,s(0),z)>
}

{  <Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,s(s(y)),s(z))> 
      --> <Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,s(s(y)),s(z))>
  <Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,s(s(y)),s(z))> 
     --> <Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,y,f(0,s(s(y)),s(z)))>
  <Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,y,f(0,s(s(y)),s(z)))> 
     --> <Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,s(s(y)),s(z))>
  <Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,y,f(0,s(s(y)),s(z)))> 
     --> <Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,y,f(0,s(s(y)),s(z)))>
}

{  <Marked_f(0,s(s(y)),s(0)) , Marked_f(0,y,s(0))> 
      --> <Marked_f(0,s(s(y)),s(0)) , Marked_f(0,y,s(0))>
}

{  <Marked_f(0,s(0),s(s(z))) , Marked_f(0,s(0),z)> 
      --> <Marked_f(0,s(0),s(s(z))) , Marked_f(0,s(0),z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(0),y,z) >= f(0,s(y),s(z)) ;
  f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) ;
  f(s(x),s(y),0) >= f(x,y,s(0)) ;
  f(s(x),0,s(z)) >= f(x,s(0),z) ;
  f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) ;
  f(0,s(s(y)),s(0)) >= f(0,y,s(0)) ;
  f(0,s(0),s(s(z))) >= f(0,s(0),z) ;
  f(0,s(0),s(0)) >= s(s(0)) ;
  f(0,0,z) >= s(z) ;
  f(0,y,0) >= s(y) ;
  f(x,0,0) >= s(x) ;
  Marked_f(s(x),s(y),s(z)) >= Marked_f(s(x),s(y),z) ;
  Marked_f(s(x),s(y),s(z)) >= Marked_f(x,y,f(s(x),s(y),z)) ;
  Marked_f(s(x),s(y),0) >= Marked_f(x,y,s(0)) ;
  Marked_f(s(x),0,s(z)) >= Marked_f(x,s(0),z) ;
 }
 + Disjunctions:{ 
{
  Marked_f(s(x),s(y),s(z)) > Marked_f(s(x),s(y),z) ;
 }
{
  Marked_f(s(x),s(y),s(z)) > Marked_f(x,y,f(s(x),s(y),z)) ;
 }
{
  Marked_f(s(x),s(y),0) > Marked_f(x,y,s(0)) ;
 }
{
  Marked_f(s(x),0,s(z)) > Marked_f(x,s(0),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
=== 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 ===
=== STOPING TIMER virtual ===
constraint: f(s(0),y,z) >= f(0,s(y),s(z))
constraint: f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z))
constraint: f(s(x),s(y),0) >= f(x,y,s(0))
constraint: f(s(x),0,s(z)) >= f(x,s(0),z)
constraint: f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z)))
constraint: f(0,s(s(y)),s(0)) >= f(0,y,s(0))
constraint: f(0,s(0),s(s(z))) >= f(0,s(0),z)
constraint: f(0,s(0),s(0)) >= s(s(0))
constraint: f(0,0,z) >= s(z)
constraint: f(0,y,0) >= s(y)
constraint: f(x,0,0) >= s(x)
constraint: Marked_f(s(x),s(y),s(z)) >= Marked_f(s(x),s(y),z)
constraint: Marked_f(s(x),s(y),s(z)) >= Marked_f(x,y,f(s(x),s(y),z))
constraint: Marked_f(s(x),s(y),0) >= Marked_f(x,y,s(0))
constraint: Marked_f(s(x),0,s(z)) >= Marked_f(x,s(0),z)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(0),y,z) >= f(0,s(y),s(z)) ;
  f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) ;
  f(s(x),s(y),0) >= f(x,y,s(0)) ;
  f(s(x),0,s(z)) >= f(x,s(0),z) ;
  f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) ;
  f(0,s(s(y)),s(0)) >= f(0,y,s(0)) ;
  f(0,s(0),s(s(z))) >= f(0,s(0),z) ;
  f(0,s(0),s(0)) >= s(s(0)) ;
  f(0,0,z) >= s(z) ;
  f(0,y,0) >= s(y) ;
  f(x,0,0) >= s(x) ;
  Marked_f(0,s(s(y)),s(s(z))) >= Marked_f(0,s(s(y)),s(z)) ;
  Marked_f(0,s(s(y)),s(s(z))) >= Marked_f(0,y,f(0,s(s(y)),s(z))) ;
 }
 + Disjunctions:{ 
{
  Marked_f(0,s(s(y)),s(s(z))) > Marked_f(0,s(s(y)),s(z)) ;
 }
{
  Marked_f(0,s(s(y)),s(s(z))) > Marked_f(0,y,f(0,s(s(y)),s(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
=== 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 ===
=== STOPING TIMER virtual ===
constraint: f(s(0),y,z) >= f(0,s(y),s(z))
constraint: f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z))
constraint: f(s(x),s(y),0) >= f(x,y,s(0))
constraint: f(s(x),0,s(z)) >= f(x,s(0),z)
constraint: f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z)))
constraint: f(0,s(s(y)),s(0)) >= f(0,y,s(0))
constraint: f(0,s(0),s(s(z))) >= f(0,s(0),z)
constraint: f(0,s(0),s(0)) >= s(s(0))
constraint: f(0,0,z) >= s(z)
constraint: f(0,y,0) >= s(y)
constraint: f(x,0,0) >= s(x)
constraint: Marked_f(0,s(s(y)),s(s(z))) >= Marked_f(0,s(s(y)),s(z))
constraint: Marked_f(0,s(s(y)),s(s(z))) >= Marked_f(0,y,f(0,s(s(y)),s(z)))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(0),y,z) >= f(0,s(y),s(z)) ;
  f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) ;
  f(s(x),s(y),0) >= f(x,y,s(0)) ;
  f(s(x),0,s(z)) >= f(x,s(0),z) ;
  f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) ;
  f(0,s(s(y)),s(0)) >= f(0,y,s(0)) ;
  f(0,s(0),s(s(z))) >= f(0,s(0),z) ;
  f(0,s(0),s(0)) >= s(s(0)) ;
  f(0,0,z) >= s(z) ;
  f(0,y,0) >= s(y) ;
  f(x,0,0) >= s(x) ;
  Marked_f(0,s(s(y)),s(0)) >= Marked_f(0,y,s(0)) ;
 }
 + Disjunctions:{ 
{
  Marked_f(0,s(s(y)),s(0)) > Marked_f(0,y,s(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 ===
=== STOPING TIMER virtual ===
constraint: f(s(0),y,z) >= f(0,s(y),s(z))
constraint: f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z))
constraint: f(s(x),s(y),0) >= f(x,y,s(0))
constraint: f(s(x),0,s(z)) >= f(x,s(0),z)
constraint: f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z)))
constraint: f(0,s(s(y)),s(0)) >= f(0,y,s(0))
constraint: f(0,s(0),s(s(z))) >= f(0,s(0),z)
constraint: f(0,s(0),s(0)) >= s(s(0))
constraint: f(0,0,z) >= s(z)
constraint: f(0,y,0) >= s(y)
constraint: f(x,0,0) >= s(x)
constraint: Marked_f(0,s(s(y)),s(0)) >= Marked_f(0,y,s(0))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(0),y,z) >= f(0,s(y),s(z)) ;
  f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) ;
  f(s(x),s(y),0) >= f(x,y,s(0)) ;
  f(s(x),0,s(z)) >= f(x,s(0),z) ;
  f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) ;
  f(0,s(s(y)),s(0)) >= f(0,y,s(0)) ;
  f(0,s(0),s(s(z))) >= f(0,s(0),z) ;
  f(0,s(0),s(0)) >= s(s(0)) ;
  f(0,0,z) >= s(z) ;
  f(0,y,0) >= s(y) ;
  f(x,0,0) >= s(x) ;
  Marked_f(0,s(0),s(s(z))) >= Marked_f(0,s(0),z) ;
 }
 + Disjunctions:{ 
{
  Marked_f(0,s(0),s(s(z))) > Marked_f(0,s(0),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
=== 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 ===
=== STOPING TIMER virtual ===
constraint: f(s(0),y,z) >= f(0,s(y),s(z))
constraint: f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z))
constraint: f(s(x),s(y),0) >= f(x,y,s(0))
constraint: f(s(x),0,s(z)) >= f(x,s(0),z)
constraint: f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z)))
constraint: f(0,s(s(y)),s(0)) >= f(0,y,s(0))
constraint: f(0,s(0),s(s(z))) >= f(0,s(0),z)
constraint: f(0,s(0),s(0)) >= s(s(0))
constraint: f(0,0,z) >= s(z)
constraint: f(0,y,0) >= s(y)
constraint: f(x,0,0) >= s(x)
constraint: Marked_f(0,s(0),s(s(z))) >= Marked_f(0,s(0),z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
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] f(x,0,0) -> s(x)
[2] f(0,y,0) -> s(y)
[3] f(0,0,z) -> s(z)
[4] f(s(0),y,z) -> f(0,s(y),s(z))
[5] f(s(x),s(y),0) -> f(x,y,s(0))
[6] f(s(x),0,s(z)) -> f(x,s(0),z)
[7] f(0,s(0),s(0)) -> s(s(0))
[8] f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
[9] f(0,s(s(y)),s(0)) -> f(0,y,s(0))
[10] f(0,s(0),s(s(z))) -> f(0,s(0),z)
[11] f(0,s(s(y)),s(s(z))) -> f(0,y,f(0,s(s(y)),s(z)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(0),y,z) , Marked_f(0,s(y),s(z))>
<Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))>
<Marked_f(s(x),0,s(z)) , Marked_f(x,s(0),z)>
<Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))>
<Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)>
<Marked_f(0,s(s(y)),s(0)) , Marked_f(0,y,s(0))>
<Marked_f(0,s(0),s(s(z))) , Marked_f(0,s(0),z)>
<Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,y,f(0,s(s(y)),s(z)))>
<Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,s(s(y)),s(z))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(x),s(y),0) , Marked_f(x,y,s(0))>
<Marked_f(s(x),0,s(z)) , Marked_f(x,s(0),z)>
<Marked_f(s(x),s(y),s(z)) , Marked_f(x,y,f(s(x),s(y),z))>
<Marked_f(s(x),s(y),s(z)) , Marked_f(s(x),s(y),z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { s  <  f ; s  <  Marked_f ; f  >  s ;
                                   f  <  Marked_f ; Marked_f  >  s ;
                                   Marked_f  >  f ; }

 ]} 
{
 
DP termination of:
<Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,y,f(0,s(s(y)),s(z)))>
<Marked_f(0,s(s(y)),s(s(z))) , Marked_f(0,s(s(y)),s(z))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { s  <  f ; s  <  Marked_f ; f  >  s ;
                                   f  <  Marked_f ; Marked_f  >  s ;
                                   Marked_f  >  f ; }

 ]} 
{
 
DP termination of:
<Marked_f(0,s(s(y)),s(0)) , Marked_f(0,y,s(0))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { s  <  f ; f  >  s ; }

 ]} 
{
 
DP termination of:
<Marked_f(0,s(0),s(s(z))) , Marked_f(0,s(0),z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { s  <  f ; f  >  s ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.309521 seconds (real time)
Cime Exit Status: 0