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

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


Sub problem: 
guided: 

DP termination of:
<Marked_f(s(x)) , Marked_g(x,s(x))>
<Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))>
<Marked_g(s(x),y) , Marked_+(y,s(x))>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))>
<Marked_g(s(x),y) , Marked_+(y,x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))> 
      --> <Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))>
  <Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))> 
     --> <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))>
  <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))> 
     --> <Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))>
  <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))> 
     --> <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))>
}

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

 ]} 
{
 
DP termination of:
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { 1  <  f ; f  >  1 ; f  >  g ; f  >  s ;
                                   f  >  + ; g  <  f ; g  >  s ; g  >  + ;
                                   s  <  f ; s  <  g ; s  <  + ; +  <  f ;
                                   +  <  g ; +  >  s ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.063020 seconds (real time)
Cime Exit Status: 0