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

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


Sub problem: 
guided: 

DP termination of:
<Marked_+(s(x),y) , Marked_s(+(x,y))>
<Marked_+(s(x),y) , Marked_+(x,y)>
<Marked_+(p(x),y) , Marked_p(+(x,y))>
<Marked_+(p(x),y) , Marked_+(x,y)>
<Marked_minus(s(x)) , Marked_p(minus(x))>
<Marked_minus(s(x)) , Marked_minus(x)>
<Marked_minus(p(x)) , Marked_s(minus(x))>
<Marked_minus(p(x)) , Marked_minus(x)>
<Marked_*(s(x),y) , Marked_+( *(x,y),y)>
<Marked_*(s(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_+( *(x,y),minus(y))>
<Marked_*(p(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_minus(y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_*(p(x),y) , Marked_*(x,y)> --> <Marked_*(p(x),y) , Marked_*(x,y)>
  <Marked_*(p(x),y) , Marked_*(x,y)> --> <Marked_*(s(x),y) , Marked_*(x,y)>
  <Marked_*(s(x),y) , Marked_*(x,y)> --> <Marked_*(p(x),y) , Marked_*(x,y)>
  <Marked_*(s(x),y) , Marked_*(x,y)> --> <Marked_*(s(x),y) , Marked_*(x,y)>
}

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

{  <Marked_minus(p(x)) , Marked_minus(x)> 
      --> <Marked_minus(p(x)) , Marked_minus(x)>
  <Marked_minus(p(x)) , Marked_minus(x)> 
     --> <Marked_minus(s(x)) , Marked_minus(x)>
  <Marked_minus(s(x)) , Marked_minus(x)> 
     --> <Marked_minus(p(x)) , Marked_minus(x)>
  <Marked_minus(s(x)) , Marked_minus(x)> 
     --> <Marked_minus(s(x)) , Marked_minus(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  p(s(x)) >= x ;
  s(p(x)) >= x ;
  +(p(x),y) >= p(+(x,y)) ;
  +(s(x),y) >= s(+(x,y)) ;
  +(0,y) >= y ;
  minus(p(x)) >= s(minus(x)) ;
  minus(s(x)) >= p(minus(x)) ;
  minus(0) >= 0 ;
   *(p(x),y) >= +( *(x,y),minus(y)) ;
   *(s(x),y) >= +( *(x,y),y) ;
   *(0,y) >= 0 ;
  Marked_*(p(x),y) >= Marked_*(x,y) ;
  Marked_*(s(x),y) >= Marked_*(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_*(p(x),y) > Marked_*(x,y) ;
 }
{
  Marked_*(s(x),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: p(s(x)) >= x
constraint: s(p(x)) >= x
constraint: +(p(x),y) >= p(+(x,y))
constraint: +(s(x),y) >= s(+(x,y))
constraint: +(0,y) >= y
constraint: minus(p(x)) >= s(minus(x))
constraint: minus(s(x)) >= p(minus(x))
constraint: minus(0) >= 0
constraint:  *(p(x),y) >= +( *(x,y),minus(y))
constraint:  *(s(x),y) >= +( *(x,y),y)
constraint:  *(0,y) >= 0
constraint: Marked_*(p(x),y) >= Marked_*(x,y)
constraint: Marked_*(s(x),y) >= Marked_*(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  p(s(x)) >= x ;
  s(p(x)) >= x ;
  +(p(x),y) >= p(+(x,y)) ;
  +(s(x),y) >= s(+(x,y)) ;
  +(0,y) >= y ;
  minus(p(x)) >= s(minus(x)) ;
  minus(s(x)) >= p(minus(x)) ;
  minus(0) >= 0 ;
   *(p(x),y) >= +( *(x,y),minus(y)) ;
   *(s(x),y) >= +( *(x,y),y) ;
   *(0,y) >= 0 ;
  Marked_+(p(x),y) >= Marked_+(x,y) ;
  Marked_+(s(x),y) >= Marked_+(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_+(p(x),y) > Marked_+(x,y) ;
 }
{
  Marked_+(s(x),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: p(s(x)) >= x
constraint: s(p(x)) >= x
constraint: +(p(x),y) >= p(+(x,y))
constraint: +(s(x),y) >= s(+(x,y))
constraint: +(0,y) >= y
constraint: minus(p(x)) >= s(minus(x))
constraint: minus(s(x)) >= p(minus(x))
constraint: minus(0) >= 0
constraint:  *(p(x),y) >= +( *(x,y),minus(y))
constraint:  *(s(x),y) >= +( *(x,y),y)
constraint:  *(0,y) >= 0
constraint: Marked_+(p(x),y) >= Marked_+(x,y)
constraint: Marked_+(s(x),y) >= Marked_+(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  p(s(x)) >= x ;
  s(p(x)) >= x ;
  +(p(x),y) >= p(+(x,y)) ;
  +(s(x),y) >= s(+(x,y)) ;
  +(0,y) >= y ;
  minus(p(x)) >= s(minus(x)) ;
  minus(s(x)) >= p(minus(x)) ;
  minus(0) >= 0 ;
   *(p(x),y) >= +( *(x,y),minus(y)) ;
   *(s(x),y) >= +( *(x,y),y) ;
   *(0,y) >= 0 ;
  Marked_minus(p(x)) >= Marked_minus(x) ;
  Marked_minus(s(x)) >= Marked_minus(x) ;
 }
 + Disjunctions:{ 
{
  Marked_minus(p(x)) > Marked_minus(x) ;
 }
{
  Marked_minus(s(x)) > Marked_minus(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: p(s(x)) >= x
constraint: s(p(x)) >= x
constraint: +(p(x),y) >= p(+(x,y))
constraint: +(s(x),y) >= s(+(x,y))
constraint: +(0,y) >= y
constraint: minus(p(x)) >= s(minus(x))
constraint: minus(s(x)) >= p(minus(x))
constraint: minus(0) >= 0
constraint:  *(p(x),y) >= +( *(x,y),minus(y))
constraint:  *(s(x),y) >= +( *(x,y),y)
constraint:  *(0,y) >= 0
constraint: Marked_minus(p(x)) >= Marked_minus(x)
constraint: Marked_minus(s(x)) >= Marked_minus(x)
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] p(s(x)) -> x
[2] s(p(x)) -> x
[3] +(0,y) -> y
[4] +(s(x),y) -> s(+(x,y))
[5] +(p(x),y) -> p(+(x,y))
[6] minus(0) -> 0
[7] minus(s(x)) -> p(minus(x))
[8] minus(p(x)) -> s(minus(x))
[9]  *(0,y) -> 0
[10]  *(s(x),y) -> +( *(x,y),y)
[11]  *(p(x),y) -> +( *(x,y),minus(y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_+(s(x),y) , Marked_s(+(x,y))>
<Marked_+(s(x),y) , Marked_+(x,y)>
<Marked_+(p(x),y) , Marked_p(+(x,y))>
<Marked_+(p(x),y) , Marked_+(x,y)>
<Marked_minus(s(x)) , Marked_p(minus(x))>
<Marked_minus(s(x)) , Marked_minus(x)>
<Marked_minus(p(x)) , Marked_s(minus(x))>
<Marked_minus(p(x)) , Marked_minus(x)>
<Marked_*(s(x),y) , Marked_+( *(x,y),y)>
<Marked_*(s(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_+( *(x,y),minus(y))>
<Marked_*(p(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_minus(y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(s(x),y) , Marked_*(x,y)>
<Marked_*(p(x),y) , Marked_*(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { p  <  + ; p  <  minus ; p  <   * ;
                                   s  <  + ; s  <  minus ; s  <   * ; 
                                   +  >  p ; +  >  s ; +  <   * ; minus  >  p ;
                                   minus  >  s ; minus  <   * ;  *  >  p ;
                                    *  >  s ;  *  >  + ;  *  >  minus ; }

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

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

 ]} 
 ]} 
 ]} 

Cime worked for 0.096129 seconds (real time)
Cime Exit Status: 0