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

TRS termination of:
[1] 0(#) -> #
[2] +(x,#) -> x
[3] +(#,x) -> x
[4] +(0(x),0(y)) -> 0(+(x,y))
[5] +(0(x),1(y)) -> 1(+(x,y))
[6] +(1(x),0(y)) -> 1(+(x,y))
[7] +(1(x),1(y)) -> 0(+(+(x,y),1(#)))
[8] +(+(x,y),z) -> +(x,+(y,z))
[9]  *(#,x) -> #
[10]  *(0(x),y) -> 0( *(x,y))
[11]  *(1(x),y) -> +(0( *(x,y)),y)
[12]  *( *(x,y),z) ->  *(x, *(y,z))
[13] sum(nil) -> 0(#)
[14] sum(cons(x,l)) -> +(x,sum(l))
[15] prod(nil) -> 1(#)
[16] prod(cons(x,l)) ->  *(x,prod(l))


Sub problem: 
guided: 

DP termination of:
<Marked_+(0(x),0(y)) , Marked_0(+(x,y))>
<Marked_+(0(x),0(y)) , Marked_+(x,y)>
<Marked_+(0(x),1(y)) , Marked_+(x,y)>
<Marked_+(1(x),0(y)) , Marked_+(x,y)>
<Marked_+(1(x),1(y)) , Marked_0(+(+(x,y),1(#)))>
<Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
<Marked_+(1(x),1(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_*(0(x),y) , Marked_0( *(x,y))>
<Marked_*(0(x),y) , Marked_*(x,y)>
<Marked_*(1(x),y) , Marked_+(0( *(x,y)),y)>
<Marked_*(1(x),y) , Marked_0( *(x,y))>
<Marked_*(1(x),y) , Marked_*(x,y)>
<Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
<Marked_*( *(x,y),z) , Marked_*(y,z)>
<Marked_sum(nil) , Marked_0(#)>
<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_*( *(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_*(1(x),y) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> --> <Marked_*(0(x),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_*(1(x),y) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(1(x),y) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(0(x),y) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(0(x),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_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(0(x),0(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_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_sum -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_prod -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_* -> 1

APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0(#) >= # ;
  +(#,x) >= x ;
  +(0(x),0(y)) >= 0(+(x,y)) ;
  +(0(x),1(y)) >= 1(+(x,y)) ;
  +(+(x,y),z) >= +(x,+(y,z)) ;
  +(1(x),0(y)) >= 1(+(x,y)) ;
  +(1(x),1(y)) >= 0(+(+(x,y),1(#))) ;
  +(x,#) >= x ;
   *(#,x) >= # ;
   *(0(x),y) >= 0( *(x,y)) ;
   *(1(x),y) >= +(0( *(x,y)),y) ;
   *( *(x,y),z) >=  *(x, *(y,z)) ;
  sum(nil) >= 0(#) ;
  sum(cons(x,l)) >= +(x,sum(l)) ;
  prod(nil) >= 1(#) ;
  prod(cons(x,l)) >=  *(x,prod(l)) ;
  Marked_+(0(x),0(y)) >= Marked_+(x,y) ;
  Marked_+(0(x),1(y)) >= Marked_+(x,y) ;
  Marked_+(+(x,y),z) >= Marked_+(y,z) ;
  Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) ;
  Marked_+(1(x),0(y)) >= Marked_+(x,y) ;
  Marked_+(1(x),1(y)) >= Marked_+(+(x,y),1(#)) ;
  Marked_+(1(x),1(y)) >= Marked_+(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_+(0(x),0(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(0(x),1(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(+(x,y),z) > Marked_+(y,z) ;
 }
{
  Marked_+(+(x,y),z) > Marked_+(x,+(y,z)) ;
 }
{
  Marked_+(1(x),0(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(1(x),1(y)) > Marked_+(+(x,y),1(#)) ;
 }
{
  Marked_+(1(x),1(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 ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: 0(#) >= #
constraint: +(#,x) >= x
constraint: +(0(x),0(y)) >= 0(+(x,y))
constraint: +(0(x),1(y)) >= 1(+(x,y))
constraint: +(+(x,y),z) >= +(x,+(y,z))
constraint: +(1(x),0(y)) >= 1(+(x,y))
constraint: +(1(x),1(y)) >= 0(+(+(x,y),1(#)))
constraint: +(x,#) >= x
constraint:  *(#,x) >= #
constraint:  *(0(x),y) >= 0( *(x,y))
constraint:  *(1(x),y) >= +(0( *(x,y)),y)
constraint:  *( *(x,y),z) >=  *(x, *(y,z))
constraint: sum(nil) >= 0(#)
constraint: sum(cons(x,l)) >= +(x,sum(l))
constraint: prod(nil) >= 1(#)
constraint: prod(cons(x,l)) >=  *(x,prod(l))
constraint: Marked_+(0(x),0(y)) >= Marked_+(x,y)
constraint: Marked_+(0(x),1(y)) >= Marked_+(x,y)
constraint: Marked_+(+(x,y),z) >= Marked_+(y,z)
constraint: Marked_+(+(x,y),z) >= Marked_+(x,+(y,z))
constraint: Marked_+(1(x),0(y)) >= Marked_+(x,y)
constraint: Marked_+(1(x),1(y)) >= Marked_+(+(x,y),1(#))
constraint: Marked_+(1(x),1(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 1 components:

{  <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_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(0(x),0(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_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0(#) >= # ;
  +(#,x) >= x ;
  +(0(x),0(y)) >= 0(+(x,y)) ;
  +(0(x),1(y)) >= 1(+(x,y)) ;
  +(+(x,y),z) >= +(x,+(y,z)) ;
  +(1(x),0(y)) >= 1(+(x,y)) ;
  +(1(x),1(y)) >= 0(+(+(x,y),1(#))) ;
  +(x,#) >= x ;
   *(#,x) >= # ;
   *(0(x),y) >= 0( *(x,y)) ;
   *(1(x),y) >= +(0( *(x,y)),y) ;
   *( *(x,y),z) >=  *(x, *(y,z)) ;
  sum(nil) >= 0(#) ;
  sum(cons(x,l)) >= +(x,sum(l)) ;
  prod(nil) >= 1(#) ;
  prod(cons(x,l)) >=  *(x,prod(l)) ;
  Marked_+(0(x),0(y)) >= Marked_+(x,y) ;
  Marked_+(+(x,y),z) >= Marked_+(y,z) ;
  Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) ;
  Marked_+(1(x),1(y)) >= Marked_+(+(x,y),1(#)) ;
 }
 + Disjunctions:{ 
{
  Marked_+(0(x),0(y)) > Marked_+(x,y) ;
 }
{
  Marked_+(+(x,y),z) > Marked_+(y,z) ;
 }
{
  Marked_+(+(x,y),z) > Marked_+(x,+(y,z)) ;
 }
{
  Marked_+(1(x),1(y)) > Marked_+(+(x,y),1(#)) ;
 }
 } 
=== 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 ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: 0(#) >= #
constraint: +(#,x) >= x
constraint: +(0(x),0(y)) >= 0(+(x,y))
constraint: +(0(x),1(y)) >= 1(+(x,y))
constraint: +(+(x,y),z) >= +(x,+(y,z))
constraint: +(1(x),0(y)) >= 1(+(x,y))
constraint: +(1(x),1(y)) >= 0(+(+(x,y),1(#)))
constraint: +(x,#) >= x
constraint:  *(#,x) >= #
constraint:  *(0(x),y) >= 0( *(x,y))
constraint:  *(1(x),y) >= +(0( *(x,y)),y)
constraint:  *( *(x,y),z) >=  *(x, *(y,z))
constraint: sum(nil) >= 0(#)
constraint: sum(cons(x,l)) >= +(x,sum(l))
constraint: prod(nil) >= 1(#)
constraint: prod(cons(x,l)) >=  *(x,prod(l))
constraint: Marked_+(0(x),0(y)) >= Marked_+(x,y)
constraint: Marked_+(+(x,y),z) >= Marked_+(y,z)
constraint: Marked_+(+(x,y),z) >= Marked_+(x,+(y,z))
constraint: Marked_+(1(x),1(y)) >= Marked_+(+(x,y),1(#))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <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_+(0(x),0(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_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] 0(#) -> #
[2] +(x,#) -> x
[3] +(#,x) -> x
[4] +(0(x),0(y)) -> 0(+(x,y))
[5] +(0(x),1(y)) -> 1(+(x,y))
[6] +(1(x),0(y)) -> 1(+(x,y))
[7] +(1(x),1(y)) -> 0(+(+(x,y),1(#)))
[8] +(+(x,y),z) -> +(x,+(y,z))
[9]  *(#,x) -> #
[10]  *(0(x),y) -> 0( *(x,y))
[11]  *(1(x),y) -> +(0( *(x,y)),y)
[12]  *( *(x,y),z) ->  *(x, *(y,z))
[13] sum(nil) -> 0(#)
[14] sum(cons(x,l)) -> +(x,sum(l))
[15] prod(nil) -> 1(#)
[16] prod(cons(x,l)) ->  *(x,prod(l))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_+(0(x),0(y)) , Marked_0(+(x,y))>
<Marked_+(0(x),0(y)) , Marked_+(x,y)>
<Marked_+(0(x),1(y)) , Marked_+(x,y)>
<Marked_+(1(x),0(y)) , Marked_+(x,y)>
<Marked_+(1(x),1(y)) , Marked_0(+(+(x,y),1(#)))>
<Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
<Marked_+(1(x),1(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_*(0(x),y) , Marked_0( *(x,y))>
<Marked_*(0(x),y) , Marked_*(x,y)>
<Marked_*(1(x),y) , Marked_+(0( *(x,y)),y)>
<Marked_*(1(x),y) , Marked_0( *(x,y))>
<Marked_*(1(x),y) , Marked_*(x,y)>
<Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
<Marked_*( *(x,y),z) , Marked_*(y,z)>
<Marked_sum(nil) , Marked_0(#)>
<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: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_prod(cons(x,l)) , Marked_prod(l)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_*(0(x),y) , Marked_*(x,y)>
<Marked_*(1(x),y) , Marked_*(x,y)>
<Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
<Marked_*( *(x,y),z) , Marked_*(y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_+(0(x),0(y)) , Marked_+(x,y)>
<Marked_+(0(x),1(y)) , Marked_+(x,y)>
<Marked_+(1(x),0(y)) , Marked_+(x,y)>
<Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
<Marked_+(1(x),1(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ # ] () = 2; 
 [ prod ] (X0) = 2*X0; 
 [ * ] (X0,X1) = 1*X1*X0 + 1*X1 + 2*X0; 
 [ Marked_+ ] (X0,X1) = 2*X1 + 2*X0; 
 [ + ] (X0,X1) = 1*X1 + 1*X0; 
 [ nil ] () = 2; 
 [ 0 ] (X0) = 1*X0; 
 [ sum ] (X0) = 1*X0 + 1; 
 [ 1 ] (X0) = 1*X0 + 2; 
 [ cons ] (X0,X1) = 1*X1*X0 + 2*X1 + 2*X0 + 2; 
 removing <Marked_+(0(x),1(y)),Marked_+(x,y)><Marked_+(1(x),0(y)),Marked_+(x,y)><
Marked_+(1(x),1(y)),Marked_+(x,y)>
 [ {
      
     DP termination of:
     <Marked_+(0(x),0(y)) , Marked_+(x,y)>
<Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_+(0(x),0(y)) , Marked_+(x,y)>
<Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ # ] () = 0; 
 [ prod ] (X0) = 2*X0 + 2; 
 [ * ] (X0,X1) = 1*X1*X0 + 2*X0; 
 [ Marked_+ ] (X0,X1) = 1*X1 + 1*X0; 
 [ + ] (X0,X1) = 1*X1 + 1*X0; 
 [ nil ] () = 0; 
 [ 0 ] (X0) = 2*X0; 
 [ sum ] (X0) = 1*X0; 
 [ 1 ] (X0) = 2*X0 + 2; 
 [ cons ] (X0,X1) = 1*X1*X0 + 1*X1 + 2*X0; 
 removing <Marked_+(1(x),1(y)),Marked_+(+(x,y),1(#))>
 [ {
      
     DP termination of:
     <Marked_+(0(x),0(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_+(0(x),0(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 1.812684 seconds (real time)
Cime Exit Status: 0