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

TRS termination of:
[1] +(x,0) -> x
[2] +(0,x) -> x
[3] +(s(x),s(y)) -> s(s(+(x,y)))
[4]  *(x,0) -> 0
[5]  *(0,x) -> 0
[6]  *(s(x),s(y)) -> s(+( *(x,y),+(x,y)))
[7] sum(nil) -> 0
[8] sum(cons(x,l)) -> +(x,sum(l))
[9] prod(nil) -> s(0)
[10] prod(cons(x,l)) ->  *(x,prod(l))


Sub problem: 
guided: 

DP termination of:
<Marked_+(s(x),s(y)) , Marked_+(x,y)>
<Marked_*(s(x),s(y)) , Marked_+( *(x,y),+(x,y))>
<Marked_*(s(x),s(y)) , Marked_*(x,y)>
<Marked_*(s(x),s(y)) , Marked_+(x,y)>
<Marked_sum(cons(x,l)) , Marked_+(x,sum(l))>
<Marked_sum(cons(x,l)) , Marked_sum(l)>
<Marked_prod(cons(x,l)) , Marked_*(x,prod(l))>
<Marked_prod(cons(x,l)) , Marked_prod(l)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_sum(cons(x,l)) , Marked_sum(l)> 
      --> <Marked_sum(cons(x,l)) , Marked_sum(l)>
}

{  <Marked_prod(cons(x,l)) , Marked_prod(l)> 
      --> <Marked_prod(cons(x,l)) , Marked_prod(l)>
}

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

{  <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:
{
  +(0,x) >= x ;
  +(s(x),s(y)) >= s(s(+(x,y))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(s(x),s(y)) >= s(+( *(x,y),+(x,y))) ;
   *(x,0) >= 0 ;
  sum(nil) >= 0 ;
  sum(cons(x,l)) >= +(x,sum(l)) ;
  prod(nil) >= s(0) ;
  prod(cons(x,l)) >=  *(x,prod(l)) ;
  Marked_sum(cons(x,l)) >= Marked_sum(l) ;
 }
 + Disjunctions:{ 
{
  Marked_sum(cons(x,l)) > Marked_sum(l) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: +(0,x) >= x
constraint: +(s(x),s(y)) >= s(s(+(x,y)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(s(x),s(y)) >= s(+( *(x,y),+(x,y)))
constraint:  *(x,0) >= 0
constraint: sum(nil) >= 0
constraint: sum(cons(x,l)) >= +(x,sum(l))
constraint: prod(nil) >= s(0)
constraint: prod(cons(x,l)) >=  *(x,prod(l))
constraint: Marked_sum(cons(x,l)) >= Marked_sum(l)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  +(0,x) >= x ;
  +(s(x),s(y)) >= s(s(+(x,y))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(s(x),s(y)) >= s(+( *(x,y),+(x,y))) ;
   *(x,0) >= 0 ;
  sum(nil) >= 0 ;
  sum(cons(x,l)) >= +(x,sum(l)) ;
  prod(nil) >= s(0) ;
  prod(cons(x,l)) >=  *(x,prod(l)) ;
  Marked_prod(cons(x,l)) >= Marked_prod(l) ;
 }
 + Disjunctions:{ 
{
  Marked_prod(cons(x,l)) > Marked_prod(l) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: +(0,x) >= x
constraint: +(s(x),s(y)) >= s(s(+(x,y)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(s(x),s(y)) >= s(+( *(x,y),+(x,y)))
constraint:  *(x,0) >= 0
constraint: sum(nil) >= 0
constraint: sum(cons(x,l)) >= +(x,sum(l))
constraint: prod(nil) >= s(0)
constraint: prod(cons(x,l)) >=  *(x,prod(l))
constraint: Marked_prod(cons(x,l)) >= Marked_prod(l)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  +(0,x) >= x ;
  +(s(x),s(y)) >= s(s(+(x,y))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(s(x),s(y)) >= s(+( *(x,y),+(x,y))) ;
   *(x,0) >= 0 ;
  sum(nil) >= 0 ;
  sum(cons(x,l)) >= +(x,sum(l)) ;
  prod(nil) >= s(0) ;
  prod(cons(x,l)) >=  *(x,prod(l)) ;
  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: +(0,x) >= x
constraint: +(s(x),s(y)) >= s(s(+(x,y)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(s(x),s(y)) >= s(+( *(x,y),+(x,y)))
constraint:  *(x,0) >= 0
constraint: sum(nil) >= 0
constraint: sum(cons(x,l)) >= +(x,sum(l))
constraint: prod(nil) >= s(0)
constraint: prod(cons(x,l)) >=  *(x,prod(l))
constraint: Marked_*(s(x),s(y)) >= Marked_*(x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  +(0,x) >= x ;
  +(s(x),s(y)) >= s(s(+(x,y))) ;
  +(x,0) >= x ;
   *(0,x) >= 0 ;
   *(s(x),s(y)) >= s(+( *(x,y),+(x,y))) ;
   *(x,0) >= 0 ;
  sum(nil) >= 0 ;
  sum(cons(x,l)) >= +(x,sum(l)) ;
  prod(nil) >= s(0) ;
  prod(cons(x,l)) >=  *(x,prod(l)) ;
  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: +(0,x) >= x
constraint: +(s(x),s(y)) >= s(s(+(x,y)))
constraint: +(x,0) >= x
constraint:  *(0,x) >= 0
constraint:  *(s(x),s(y)) >= s(+( *(x,y),+(x,y)))
constraint:  *(x,0) >= 0
constraint: sum(nil) >= 0
constraint: sum(cons(x,l)) >= +(x,sum(l))
constraint: prod(nil) >= s(0)
constraint: prod(cons(x,l)) >=  *(x,prod(l))
constraint: Marked_+(s(x),s(y)) >= Marked_+(x,y)
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] +(x,0) -> x
[2] +(0,x) -> x
[3] +(s(x),s(y)) -> s(s(+(x,y)))
[4]  *(x,0) -> 0
[5]  *(0,x) -> 0
[6]  *(s(x),s(y)) -> s(+( *(x,y),+(x,y)))
[7] sum(nil) -> 0
[8] sum(cons(x,l)) -> +(x,sum(l))
[9] prod(nil) -> s(0)
[10] prod(cons(x,l)) ->  *(x,prod(l))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_+(s(x),s(y)) , Marked_+(x,y)>
<Marked_*(s(x),s(y)) , Marked_+( *(x,y),+(x,y))>
<Marked_*(s(x),s(y)) , Marked_*(x,y)>
<Marked_*(s(x),s(y)) , Marked_+(x,y)>
<Marked_sum(cons(x,l)) , Marked_+(x,sum(l))>
<Marked_sum(cons(x,l)) , Marked_sum(l)>
<Marked_prod(cons(x,l)) , Marked_*(x,prod(l))>
<Marked_prod(cons(x,l)) , Marked_prod(l)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sum(cons(x,l)) , Marked_sum(l)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ + ] (X0,X1) = 2*X0 + 1*X1 + 0; 
 [ sum ] (X0) = 3*X0 + 0; 
 [ s ] (X0) = 2 + 0; 
 [ Marked_sum ] (X0) = 3*X0 + 0; 
 [ cons ] (X0,X1) = 1 + 3*X0 + 3*X1 + 0; 
 [ 0 ] () = 0; 
 [ nil ] () = 0; 
 [ * ] (X0,X1) = 2 + 3*X0 + 0; 
 [ prod ] (X0) = 2 + 3*X0 + 0; 
 ]} 
{
 
DP termination of:
<Marked_prod(cons(x,l)) , Marked_prod(l)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ + ] (X0,X1) = 2*X0 + 1*X1 + 0; 
 [ Marked_prod ] (X0) = 3*X0 + 0; 
 [ sum ] (X0) = 3*X0 + 0; 
 [ s ] (X0) = 2 + 0; 
 [ cons ] (X0,X1) = 1 + 3*X0 + 3*X1 + 0; 
 [ 0 ] () = 0; 
 [ nil ] () = 0; 
 [ * ] (X0,X1) = 2 + 3*X0 + 0; 
 [ prod ] (X0) = 2 + 2*X0 + 0; 
 ]} 
{
 
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 ; +  <   * ; +  <  sum ;
                                   +  <  prod ; 0  <  sum ; 0  <  prod ;
                                   s  <  + ; s  <   * ; s  <  sum ;
                                   s  <  prod ;  *  >  + ;  *  >  s ;
                                    *  <  prod ; sum  >  + ; sum  >  0 ;
                                   sum  >  s ; prod  >  + ; prod  >  0 ;
                                   prod  >  s ; prod  >   * ; }

 ]} 
{
 
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 ; +  <   * ; +  <  sum ;
                                   +  <  prod ; 0  <  sum ; 0  <  prod ;
                                   s  <  + ; s  <   * ; s  <  sum ;
                                   s  <  prod ;  *  >  + ;  *  >  s ;
                                    *  <  prod ; sum  >  + ; sum  >  0 ;
                                   sum  >  s ; prod  >  + ; prod  >  0 ;
                                   prod  >  s ; prod  >   * ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.204561 seconds (real time)
Cime Exit Status: 0