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

TRS termination of:
[1] f(0,y) -> y
[2] f(x,0) -> x
[3] f(i(x),y) -> i(x)
[4] f(f(x,y),z) -> f(x,f(y,z))
[5] f(g(x,y),z) -> g(f(x,z),f(y,z))
[6] f(1,g(x,y)) -> x
[7] f(2,g(x,y)) -> y


Sub problem: 
guided: 

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

{  <Marked_f(g(x,y),z) , Marked_f(y,z)> 
      --> <Marked_f(g(x,y),z) , Marked_f(y,z)>
  <Marked_f(g(x,y),z) , Marked_f(y,z)> --> <Marked_f(g(x,y),z) , Marked_f(x,z)>
  <Marked_f(g(x,y),z) , Marked_f(y,z)> --> <Marked_f(f(x,y),z) , Marked_f(y,z)>
  <Marked_f(g(x,y),z) , Marked_f(y,z)> 
     --> <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))>
  <Marked_f(g(x,y),z) , Marked_f(x,z)> --> <Marked_f(g(x,y),z) , Marked_f(y,z)>
  <Marked_f(g(x,y),z) , Marked_f(x,z)> --> <Marked_f(g(x,y),z) , Marked_f(x,z)>
  <Marked_f(g(x,y),z) , Marked_f(x,z)> --> <Marked_f(f(x,y),z) , Marked_f(y,z)>
  <Marked_f(g(x,y),z) , Marked_f(x,z)> 
     --> <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))>
  <Marked_f(f(x,y),z) , Marked_f(y,z)> --> <Marked_f(g(x,y),z) , Marked_f(y,z)>
  <Marked_f(f(x,y),z) , Marked_f(y,z)> --> <Marked_f(g(x,y),z) , Marked_f(x,z)>
  <Marked_f(f(x,y),z) , Marked_f(y,z)> --> <Marked_f(f(x,y),z) , Marked_f(y,z)>
  <Marked_f(f(x,y),z) , Marked_f(y,z)> 
     --> <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))>
  <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))> 
     --> <Marked_f(g(x,y),z) , Marked_f(y,z)>
  <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))> 
     --> <Marked_f(g(x,y),z) , Marked_f(x,z)>
  <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))> 
     --> <Marked_f(f(x,y),z) , Marked_f(y,z)>
  <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))> 
     --> <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(f(x,y),z) >= f(x,f(y,z)) ;
  f(0,y) >= y ;
  f(i(x),y) >= i(x) ;
  f(g(x,y),z) >= g(f(x,z),f(y,z)) ;
  f(1,g(x,y)) >= x ;
  f(2,g(x,y)) >= y ;
  f(x,0) >= x ;
  Marked_f(f(x,y),z) >= Marked_f(x,f(y,z)) ;
  Marked_f(f(x,y),z) >= Marked_f(y,z) ;
  Marked_f(g(x,y),z) >= Marked_f(x,z) ;
  Marked_f(g(x,y),z) >= Marked_f(y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_f(f(x,y),z) > Marked_f(x,f(y,z)) ;
 }
{
  Marked_f(f(x,y),z) > Marked_f(y,z) ;
 }
{
  Marked_f(g(x,y),z) > Marked_f(x,z) ;
 }
{
  Marked_f(g(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
=== 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(f(x,y),z) >= f(x,f(y,z))
constraint: f(0,y) >= y
constraint: f(i(x),y) >= i(x)
constraint: f(g(x,y),z) >= g(f(x,z),f(y,z))
constraint: f(1,g(x,y)) >= x
constraint: f(2,g(x,y)) >= y
constraint: f(x,0) >= x
constraint: Marked_f(f(x,y),z) >= Marked_f(x,f(y,z))
constraint: Marked_f(f(x,y),z) >= Marked_f(y,z)
constraint: Marked_f(g(x,y),z) >= Marked_f(x,z)
constraint: Marked_f(g(x,y),z) >= Marked_f(y,z)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(0,y) -> y
[2] f(x,0) -> x
[3] f(i(x),y) -> i(x)
[4] f(f(x,y),z) -> f(x,f(y,z))
[5] f(g(x,y),z) -> g(f(x,z),f(y,z))
[6] f(1,g(x,y)) -> x
[7] f(2,g(x,y)) -> y
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))>
<Marked_f(f(x,y),z) , Marked_f(y,z)>
<Marked_f(g(x,y),z) , Marked_f(x,z)>
<Marked_f(g(x,y),z) , Marked_f(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(f(x,y),z) , Marked_f(x,f(y,z))>
<Marked_f(f(x,y),z) , Marked_f(y,z)>
<Marked_f(g(x,y),z) , Marked_f(x,z)>
<Marked_f(g(x,y),z) , Marked_f(y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { f  >  g ; f  <  Marked_f ; g  <  f ;
                                   g  <  Marked_f ; Marked_f  >  f ;
                                   Marked_f  >  g ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.028137 seconds (real time)
Cime Exit Status: 0