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

TRS termination of:
[1] a(h,h,h,x) -> s(x)
[2] a(l,x,s(y),h) -> a(l,x,y,s(h))
[3] a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
[4] a(l,s(x),h,z) -> a(l,x,z,z)
[5] a(s(l),h,h,z) -> a(l,z,h,z)
[6] +(x,h) -> x
[7] +(h,x) -> x
[8] +(s(x),s(y)) -> s(s(+(x,y)))
[9] +(+(x,y),z) -> +(x,+(y,z))
[10] s(h) -> 1
[11]  *(h,x) -> h
[12]  *(x,h) -> h
[13]  *(s(x),s(y)) -> s(+(+( *(x,y),x),y))


Sub problem: 
guided: 

DP termination of:
<Marked_a(h,h,h,x) , Marked_s(x)>
<Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
<Marked_a(l,x,s(y),h) , Marked_s(h)>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
<Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
<Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
<Marked_+(s(x),s(y)) , Marked_s(s(+(x,y)))>
<Marked_+(s(x),s(y)) , Marked_s(+(x,y))>
<Marked_+(s(x),s(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_*(s(x),s(y)) , Marked_s(+(+( *(x,y),x),y))>
<Marked_*(s(x),s(y)) , Marked_+(+( *(x,y),x),y)>
<Marked_*(s(x),s(y)) , Marked_+( *(x,y),x)>
<Marked_*(s(x),s(y)) , Marked_*(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)> 
      --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
  <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))> 
     --> <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
}

{  <Marked_*(s(x),s(y)) , Marked_*(x,y)> 
      --> <Marked_*(s(x),s(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_+(y,z)> 
     --> <Marked_+(s(x),s(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))>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(s(x),s(y)) , Marked_+(x,y)>
  <Marked_+(s(x),s(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(s(x),s(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(s(x),s(y)) , Marked_+(x,y)> 
     --> <Marked_+(s(x),s(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  s(h) >= 1 ;
  a(s(l),h,h,z) >= a(l,z,h,z) ;
  a(h,h,h,x) >= s(x) ;
  a(l,s(x),h,z) >= a(l,x,z,z) ;
  a(l,x,s(y),s(z)) >= a(l,x,y,a(l,x,s(y),z)) ;
  a(l,x,s(y),h) >= a(l,x,y,s(h)) ;
  +(s(x),s(y)) >= s(s(+(x,y))) ;
  +(h,x) >= x ;
  +(+(x,y),z) >= +(x,+(y,z)) ;
  +(x,h) >= x ;
   *(s(x),s(y)) >= s(+(+( *(x,y),x),y)) ;
   *(h,x) >= h ;
   *(x,h) >= h ;
  Marked_a(s(l),h,h,z) >= Marked_a(l,z,h,z) ;
  Marked_a(l,s(x),h,z) >= Marked_a(l,x,z,z) ;
  Marked_a(l,x,s(y),s(z)) >= Marked_a(l,x,s(y),z) ;
  Marked_a(l,x,s(y),s(z)) >= Marked_a(l,x,y,a(l,x,s(y),z)) ;
  Marked_a(l,x,s(y),h) >= Marked_a(l,x,y,s(h)) ;
 }
 + Disjunctions:{ 
{
  Marked_a(s(l),h,h,z) > Marked_a(l,z,h,z) ;
 }
{
  Marked_a(l,s(x),h,z) > Marked_a(l,x,z,z) ;
 }
{
  Marked_a(l,x,s(y),s(z)) > Marked_a(l,x,s(y),z) ;
 }
{
  Marked_a(l,x,s(y),s(z)) > Marked_a(l,x,y,a(l,x,s(y),z)) ;
 }
{
  Marked_a(l,x,s(y),h) > Marked_a(l,x,y,s(h)) ;
 }
 } 
=== 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: s(h) >= 1
constraint: a(s(l),h,h,z) >= a(l,z,h,z)
constraint: a(h,h,h,x) >= s(x)
constraint: a(l,s(x),h,z) >= a(l,x,z,z)
constraint: a(l,x,s(y),s(z)) >= a(l,x,y,a(l,x,s(y),z))
constraint: a(l,x,s(y),h) >= a(l,x,y,s(h))
constraint: +(s(x),s(y)) >= s(s(+(x,y)))
constraint: +(h,x) >= x
constraint: +(+(x,y),z) >= +(x,+(y,z))
constraint: +(x,h) >= x
constraint:  *(s(x),s(y)) >= s(+(+( *(x,y),x),y))
constraint:  *(h,x) >= h
constraint:  *(x,h) >= h
constraint: Marked_a(s(l),h,h,z) >= Marked_a(l,z,h,z)
constraint: Marked_a(l,s(x),h,z) >= Marked_a(l,x,z,z)
constraint: Marked_a(l,x,s(y),s(z)) >= Marked_a(l,x,s(y),z)
constraint: Marked_a(l,x,s(y),s(z)) >= Marked_a(l,x,y,a(l,x,s(y),z))
constraint: Marked_a(l,x,s(y),h) >= Marked_a(l,x,y,s(h))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  s(h) >= 1 ;
  a(s(l),h,h,z) >= a(l,z,h,z) ;
  a(h,h,h,x) >= s(x) ;
  a(l,s(x),h,z) >= a(l,x,z,z) ;
  a(l,x,s(y),s(z)) >= a(l,x,y,a(l,x,s(y),z)) ;
  a(l,x,s(y),h) >= a(l,x,y,s(h)) ;
  +(s(x),s(y)) >= s(s(+(x,y))) ;
  +(h,x) >= x ;
  +(+(x,y),z) >= +(x,+(y,z)) ;
  +(x,h) >= x ;
   *(s(x),s(y)) >= s(+(+( *(x,y),x),y)) ;
   *(h,x) >= h ;
   *(x,h) >= h ;
  Marked_*(s(x),s(y)) >= Marked_*(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_*(s(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: s(h) >= 1
constraint: a(s(l),h,h,z) >= a(l,z,h,z)
constraint: a(h,h,h,x) >= s(x)
constraint: a(l,s(x),h,z) >= a(l,x,z,z)
constraint: a(l,x,s(y),s(z)) >= a(l,x,y,a(l,x,s(y),z))
constraint: a(l,x,s(y),h) >= a(l,x,y,s(h))
constraint: +(s(x),s(y)) >= s(s(+(x,y)))
constraint: +(h,x) >= x
constraint: +(+(x,y),z) >= +(x,+(y,z))
constraint: +(x,h) >= x
constraint:  *(s(x),s(y)) >= s(+(+( *(x,y),x),y))
constraint:  *(h,x) >= h
constraint:  *(x,h) >= h
constraint: Marked_*(s(x),s(y)) >= Marked_*(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  s(h) >= 1 ;
  a(s(l),h,h,z) >= a(l,z,h,z) ;
  a(h,h,h,x) >= s(x) ;
  a(l,s(x),h,z) >= a(l,x,z,z) ;
  a(l,x,s(y),s(z)) >= a(l,x,y,a(l,x,s(y),z)) ;
  a(l,x,s(y),h) >= a(l,x,y,s(h)) ;
  +(s(x),s(y)) >= s(s(+(x,y))) ;
  +(h,x) >= x ;
  +(+(x,y),z) >= +(x,+(y,z)) ;
  +(x,h) >= x ;
   *(s(x),s(y)) >= s(+(+( *(x,y),x),y)) ;
   *(h,x) >= h ;
   *(x,h) >= h ;
  Marked_+(s(x),s(y)) >= Marked_+(x,y) ;
  Marked_+(+(x,y),z) >= Marked_+(y,z) ;
  Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) ;
 }
 + Disjunctions:{ 
{
  Marked_+(s(x),s(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(+(x,y),z) > Marked_+(y,z) ;
 }
{
  Marked_+(+(x,y),z) > Marked_+(x,+(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: s(h) >= 1
constraint: a(s(l),h,h,z) >= a(l,z,h,z)
constraint: a(h,h,h,x) >= s(x)
constraint: a(l,s(x),h,z) >= a(l,x,z,z)
constraint: a(l,x,s(y),s(z)) >= a(l,x,y,a(l,x,s(y),z))
constraint: a(l,x,s(y),h) >= a(l,x,y,s(h))
constraint: +(s(x),s(y)) >= s(s(+(x,y)))
constraint: +(h,x) >= x
constraint: +(+(x,y),z) >= +(x,+(y,z))
constraint: +(x,h) >= x
constraint:  *(s(x),s(y)) >= s(+(+( *(x,y),x),y))
constraint:  *(h,x) >= h
constraint:  *(x,h) >= h
constraint: Marked_+(s(x),s(y)) >= Marked_+(x,y)
constraint: Marked_+(+(x,y),z) >= Marked_+(y,z)
constraint: Marked_+(+(x,y),z) >= Marked_+(x,+(y,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(h,h,h,x) -> s(x)
[2] a(l,x,s(y),h) -> a(l,x,y,s(h))
[3] a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
[4] a(l,s(x),h,z) -> a(l,x,z,z)
[5] a(s(l),h,h,z) -> a(l,z,h,z)
[6] +(x,h) -> x
[7] +(h,x) -> x
[8] +(s(x),s(y)) -> s(s(+(x,y)))
[9] +(+(x,y),z) -> +(x,+(y,z))
[10] s(h) -> 1
[11]  *(h,x) -> h
[12]  *(x,h) -> h
[13]  *(s(x),s(y)) -> s(+(+( *(x,y),x),y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a(h,h,h,x) , Marked_s(x)>
<Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
<Marked_a(l,x,s(y),h) , Marked_s(h)>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
<Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
<Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
<Marked_+(s(x),s(y)) , Marked_s(s(+(x,y)))>
<Marked_+(s(x),s(y)) , Marked_s(+(x,y))>
<Marked_+(s(x),s(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_*(s(x),s(y)) , Marked_s(+(+( *(x,y),x),y))>
<Marked_*(s(x),s(y)) , Marked_+(+( *(x,y),x),y)>
<Marked_*(s(x),s(y)) , Marked_+( *(x,y),x)>
<Marked_*(s(x),s(y)) , Marked_*(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a(l,x,s(y),h) , Marked_a(l,x,y,s(h))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,y,a(l,x,s(y),z))>
<Marked_a(l,x,s(y),s(z)) , Marked_a(l,x,s(y),z)>
<Marked_a(l,s(x),h,z) , Marked_a(l,x,z,z)>
<Marked_a(s(l),h,h,z) , Marked_a(l,z,h,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { s  <  a ; s  <  + ; s  >  1 ; s  <   * ;
                                   s  <  Marked_a ; a  >  s ; a  >  1 ;
                                   a  <  Marked_a ; +  >  s ; +  >  1 ;
                                   +  <   * ; 1  <  s ; 1  <  a ; 1  <  + ;
                                   1  <   * ; 1  <  Marked_a ;  *  >  s ;
                                    *  >  + ;  *  >  1 ; Marked_a  >  s ;
                                   Marked_a  >  a ; Marked_a  >  1 ; }

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

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

 ]} 
 ]} 
 ]} 

Cime worked for 0.227988 seconds (real time)
Cime Exit Status: 0