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

TRS termination of:
[1] if(true,x,y) -> x
[2] if(false,x,y) -> y
[3] eq(0,0) -> true
[4] eq(0,s(x)) -> false
[5] eq(s(x),0) -> false
[6] eq(s(x),s(y)) -> eq(x,y)
[7] app(nil,l) -> l
[8] app(cons(x,l1),l2) -> cons(x,app(l1,l2))
[9] app(app(l1,l2),l3) -> app(l1,app(l2,l3))
[10] mem(x,nil) -> false
[11] mem(x,cons(y,l)) -> ifmem(eq(x,y),x,l)
[12] ifmem(true,x,l) -> true
[13] ifmem(false,x,l) -> mem(x,l)
[14] inter(x,nil) -> nil
[15] inter(nil,x) -> nil
[16] inter(app(l1,l2),l3) -> app(inter(l1,l3),inter(l2,l3))
[17] inter(l1,app(l2,l3)) -> app(inter(l1,l2),inter(l1,l3))
[18] inter(cons(x,l1),l2) -> ifinter(mem(x,l2),x,l1,l2)
[19] inter(l1,cons(x,l2)) -> ifinter(mem(x,l1),x,l2,l1)
[20] ifinter(true,x,l1,l2) -> cons(x,inter(l1,l2))
[21] ifinter(false,x,l1,l2) -> inter(l1,l2)


Sub problem: 
guided: 

DP termination of:
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)>
<Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))>
<Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)>
<Marked_mem(x,cons(y,l)) , Marked_ifmem(eq(x,y),x,l)>
<Marked_mem(x,cons(y,l)) , Marked_eq(x,y)>
<Marked_ifmem(false,x,l) , Marked_mem(x,l)>
<Marked_inter(app(l1,l2),l3) , Marked_app(inter(l1,l3),inter(l2,l3))>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
<Marked_inter(l1,app(l2,l3)) , Marked_app(inter(l1,l2),inter(l1,l3))>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
<Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
<Marked_inter(cons(x,l1),l2) , Marked_mem(x,l2)>
<Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
<Marked_inter(l1,cons(x,l2)) , Marked_mem(x,l1)>
<Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
<Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
      --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)> 
     --> <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)> 
     --> <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)> 
     --> <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)> 
     --> <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
}

{  <Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)> 
      --> <Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)>
  <Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)> 
     --> <Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))>
  <Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)> 
     --> <Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)>
  <Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))> 
     --> <Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)>
  <Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))> 
     --> <Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))>
  <Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))> 
     --> <Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)>
  <Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)> 
     --> <Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)>
  <Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)> 
     --> <Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))>
  <Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)> 
     --> <Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)>
}

{  <Marked_ifmem(false,x,l) , Marked_mem(x,l)> 
      --> <Marked_mem(x,cons(y,l)) , Marked_ifmem(eq(x,y),x,l)>
  <Marked_mem(x,cons(y,l)) , Marked_ifmem(eq(x,y),x,l)> 
     --> <Marked_ifmem(false,x,l) , Marked_mem(x,l)>
}

{  <Marked_eq(s(x),s(y)) , Marked_eq(x,y)> 
      --> <Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  if(true,x,y) >= x ;
  if(false,x,y) >= y ;
  eq(0,0) >= true ;
  eq(0,s(x)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  app(app(l1,l2),l3) >= app(l1,app(l2,l3)) ;
  app(nil,l) >= l ;
  app(cons(x,l1),l2) >= cons(x,app(l1,l2)) ;
  mem(x,nil) >= false ;
  mem(x,cons(y,l)) >= ifmem(eq(x,y),x,l) ;
  ifmem(true,x,l) >= true ;
  ifmem(false,x,l) >= mem(x,l) ;
  inter(app(l1,l2),l3) >= app(inter(l1,l3),inter(l2,l3)) ;
  inter(nil,x) >= nil ;
  inter(cons(x,l1),l2) >= ifinter(mem(x,l2),x,l1,l2) ;
  inter(l1,app(l2,l3)) >= app(inter(l1,l2),inter(l1,l3)) ;
  inter(l1,cons(x,l2)) >= ifinter(mem(x,l1),x,l2,l1) ;
  inter(x,nil) >= nil ;
  ifinter(true,x,l1,l2) >= cons(x,inter(l1,l2)) ;
  ifinter(false,x,l1,l2) >= inter(l1,l2) ;
  Marked_ifinter(true,x,l1,l2) >= Marked_inter(l1,l2) ;
  Marked_ifinter(false,x,l1,l2) >= Marked_inter(l1,l2) ;
  Marked_inter(app(l1,l2),l3) >= Marked_inter(l2,l3) ;
  Marked_inter(app(l1,l2),l3) >= Marked_inter(l1,l3) ;
  Marked_inter(cons(x,l1),l2) >= Marked_ifinter(mem(x,l2),x,l1,l2) ;
  Marked_inter(l1,app(l2,l3)) >= Marked_inter(l1,l3) ;
  Marked_inter(l1,app(l2,l3)) >= Marked_inter(l1,l2) ;
  Marked_inter(l1,cons(x,l2)) >= Marked_ifinter(mem(x,l1),x,l2,l1) ;
 }
 + Disjunctions:{ 
{
  Marked_ifinter(true,x,l1,l2) > Marked_inter(l1,l2) ;
 }
{
  Marked_ifinter(false,x,l1,l2) > Marked_inter(l1,l2) ;
 }
{
  Marked_inter(app(l1,l2),l3) > Marked_inter(l2,l3) ;
 }
{
  Marked_inter(app(l1,l2),l3) > Marked_inter(l1,l3) ;
 }
{
  Marked_inter(cons(x,l1),l2) > Marked_ifinter(mem(x,l2),x,l1,l2) ;
 }
{
  Marked_inter(l1,app(l2,l3)) > Marked_inter(l1,l3) ;
 }
{
  Marked_inter(l1,app(l2,l3)) > Marked_inter(l1,l2) ;
 }
{
  Marked_inter(l1,cons(x,l2)) > Marked_ifinter(mem(x,l1),x,l2,l1) ;
 }
 } 
=== 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 : 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: if(true,x,y) >= x
constraint: if(false,x,y) >= y
constraint: eq(0,0) >= true
constraint: eq(0,s(x)) >= false
constraint: eq(s(x),0) >= false
constraint: eq(s(x),s(y)) >= eq(x,y)
constraint: app(app(l1,l2),l3) >= app(l1,app(l2,l3))
constraint: app(nil,l) >= l
constraint: app(cons(x,l1),l2) >= cons(x,app(l1,l2))
constraint: mem(x,nil) >= false
constraint: mem(x,cons(y,l)) >= ifmem(eq(x,y),x,l)
constraint: ifmem(true,x,l) >= true
constraint: ifmem(false,x,l) >= mem(x,l)
constraint: inter(app(l1,l2),l3) >= app(inter(l1,l3),inter(l2,l3))
constraint: inter(nil,x) >= nil
constraint: inter(cons(x,l1),l2) >= ifinter(mem(x,l2),x,l1,l2)
constraint: inter(l1,app(l2,l3)) >= app(inter(l1,l2),inter(l1,l3))
constraint: inter(l1,cons(x,l2)) >= ifinter(mem(x,l1),x,l2,l1)
constraint: inter(x,nil) >= nil
constraint: ifinter(true,x,l1,l2) >= cons(x,inter(l1,l2))
constraint: ifinter(false,x,l1,l2) >= inter(l1,l2)
constraint: Marked_ifinter(true,x,l1,l2) >= Marked_inter(l1,l2)
constraint: Marked_ifinter(false,x,l1,l2) >= Marked_inter(l1,l2)
constraint: Marked_inter(app(l1,l2),l3) >= Marked_inter(l2,l3)
constraint: Marked_inter(app(l1,l2),l3) >= Marked_inter(l1,l3)
constraint: Marked_inter(cons(x,l1),l2) >= Marked_ifinter(mem(x,l2),x,l1,l2)
constraint: Marked_inter(l1,app(l2,l3)) >= Marked_inter(l1,l3)
constraint: Marked_inter(l1,app(l2,l3)) >= Marked_inter(l1,l2)
constraint: Marked_inter(l1,cons(x,l2)) >= Marked_ifinter(mem(x,l1),x,l2,l1)
APPLY CRITERIA (Subterm criterion)

ST: Marked_app -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_ifmem -> 3
Marked_mem -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_eq -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
      --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)> 
     --> <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)> 
     --> <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  if(true,x,y) >= x ;
  if(false,x,y) >= y ;
  eq(0,0) >= true ;
  eq(0,s(x)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  app(app(l1,l2),l3) >= app(l1,app(l2,l3)) ;
  app(nil,l) >= l ;
  app(cons(x,l1),l2) >= cons(x,app(l1,l2)) ;
  mem(x,nil) >= false ;
  mem(x,cons(y,l)) >= ifmem(eq(x,y),x,l) ;
  ifmem(true,x,l) >= true ;
  ifmem(false,x,l) >= mem(x,l) ;
  inter(app(l1,l2),l3) >= app(inter(l1,l3),inter(l2,l3)) ;
  inter(nil,x) >= nil ;
  inter(cons(x,l1),l2) >= ifinter(mem(x,l2),x,l1,l2) ;
  inter(l1,app(l2,l3)) >= app(inter(l1,l2),inter(l1,l3)) ;
  inter(l1,cons(x,l2)) >= ifinter(mem(x,l1),x,l2,l1) ;
  inter(x,nil) >= nil ;
  ifinter(true,x,l1,l2) >= cons(x,inter(l1,l2)) ;
  ifinter(false,x,l1,l2) >= inter(l1,l2) ;
  Marked_ifinter(true,x,l1,l2) >= Marked_inter(l1,l2) ;
  Marked_inter(app(l1,l2),l3) >= Marked_inter(l2,l3) ;
  Marked_inter(app(l1,l2),l3) >= Marked_inter(l1,l3) ;
  Marked_inter(cons(x,l1),l2) >= Marked_ifinter(mem(x,l2),x,l1,l2) ;
  Marked_inter(l1,app(l2,l3)) >= Marked_inter(l1,l3) ;
  Marked_inter(l1,app(l2,l3)) >= Marked_inter(l1,l2) ;
  Marked_inter(l1,cons(x,l2)) >= Marked_ifinter(mem(x,l1),x,l2,l1) ;
 }
 + Disjunctions:{ 
{
  Marked_ifinter(true,x,l1,l2) > Marked_inter(l1,l2) ;
 }
{
  Marked_inter(app(l1,l2),l3) > Marked_inter(l2,l3) ;
 }
{
  Marked_inter(app(l1,l2),l3) > Marked_inter(l1,l3) ;
 }
{
  Marked_inter(cons(x,l1),l2) > Marked_ifinter(mem(x,l2),x,l1,l2) ;
 }
{
  Marked_inter(l1,app(l2,l3)) > Marked_inter(l1,l3) ;
 }
{
  Marked_inter(l1,app(l2,l3)) > Marked_inter(l1,l2) ;
 }
{
  Marked_inter(l1,cons(x,l2)) > Marked_ifinter(mem(x,l1),x,l2,l1) ;
 }
 } 
=== 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: if(true,x,y) >= x
constraint: if(false,x,y) >= y
constraint: eq(0,0) >= true
constraint: eq(0,s(x)) >= false
constraint: eq(s(x),0) >= false
constraint: eq(s(x),s(y)) >= eq(x,y)
constraint: app(app(l1,l2),l3) >= app(l1,app(l2,l3))
constraint: app(nil,l) >= l
constraint: app(cons(x,l1),l2) >= cons(x,app(l1,l2))
constraint: mem(x,nil) >= false
constraint: mem(x,cons(y,l)) >= ifmem(eq(x,y),x,l)
constraint: ifmem(true,x,l) >= true
constraint: ifmem(false,x,l) >= mem(x,l)
constraint: inter(app(l1,l2),l3) >= app(inter(l1,l3),inter(l2,l3))
constraint: inter(nil,x) >= nil
constraint: inter(cons(x,l1),l2) >= ifinter(mem(x,l2),x,l1,l2)
constraint: inter(l1,app(l2,l3)) >= app(inter(l1,l2),inter(l1,l3))
constraint: inter(l1,cons(x,l2)) >= ifinter(mem(x,l1),x,l2,l1)
constraint: inter(x,nil) >= nil
constraint: ifinter(true,x,l1,l2) >= cons(x,inter(l1,l2))
constraint: ifinter(false,x,l1,l2) >= inter(l1,l2)
constraint: Marked_ifinter(true,x,l1,l2) >= Marked_inter(l1,l2)
constraint: Marked_inter(app(l1,l2),l3) >= Marked_inter(l2,l3)
constraint: Marked_inter(app(l1,l2),l3) >= Marked_inter(l1,l3)
constraint: Marked_inter(cons(x,l1),l2) >= Marked_ifinter(mem(x,l2),x,l1,l2)
constraint: Marked_inter(l1,app(l2,l3)) >= Marked_inter(l1,l3)
constraint: Marked_inter(l1,app(l2,l3)) >= Marked_inter(l1,l2)
constraint: Marked_inter(l1,cons(x,l2)) >= Marked_ifinter(mem(x,l1),x,l2,l1)
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] if(true,x,y) -> x
[2] if(false,x,y) -> y
[3] eq(0,0) -> true
[4] eq(0,s(x)) -> false
[5] eq(s(x),0) -> false
[6] eq(s(x),s(y)) -> eq(x,y)
[7] app(nil,l) -> l
[8] app(cons(x,l1),l2) -> cons(x,app(l1,l2))
[9] app(app(l1,l2),l3) -> app(l1,app(l2,l3))
[10] mem(x,nil) -> false
[11] mem(x,cons(y,l)) -> ifmem(eq(x,y),x,l)
[12] ifmem(true,x,l) -> true
[13] ifmem(false,x,l) -> mem(x,l)
[14] inter(x,nil) -> nil
[15] inter(nil,x) -> nil
[16] inter(app(l1,l2),l3) -> app(inter(l1,l3),inter(l2,l3))
[17] inter(l1,app(l2,l3)) -> app(inter(l1,l2),inter(l1,l3))
[18] inter(cons(x,l1),l2) -> ifinter(mem(x,l2),x,l1,l2)
[19] inter(l1,cons(x,l2)) -> ifinter(mem(x,l1),x,l2,l1)
[20] ifinter(true,x,l1,l2) -> cons(x,inter(l1,l2))
[21] ifinter(false,x,l1,l2) -> inter(l1,l2)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)>
<Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))>
<Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)>
<Marked_mem(x,cons(y,l)) , Marked_ifmem(eq(x,y),x,l)>
<Marked_mem(x,cons(y,l)) , Marked_eq(x,y)>
<Marked_ifmem(false,x,l) , Marked_mem(x,l)>
<Marked_inter(app(l1,l2),l3) , Marked_app(inter(l1,l3),inter(l2,l3))>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
<Marked_inter(l1,app(l2,l3)) , Marked_app(inter(l1,l2),inter(l1,l3))>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
<Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
<Marked_inter(cons(x,l1),l2) , Marked_mem(x,l2)>
<Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
<Marked_inter(l1,cons(x,l2)) , Marked_mem(x,l1)>
<Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
<Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
<Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
<Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
<Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
<Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ if ] (X0,X1,X2) = 2*X2*X1*X0 + 2*X2*X1 + 2*X2*X0 + 2*X1*X0 + 1*X1 + 2*X0 + 2; 
 [ cons ] (X0,X1) = 1*X1 + 2; 
 [ 0 ] () = 0; 
 [ ifinter ] (X0,X1,X2,X3) = 2*X3*X2 + 2*X3 + 2*X2 + 2; 
 [ false ] () = 2; 
 [ ifmem ] (X0,X1,X2) = 2*X2; 
 [ app ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 [ Marked_inter ] (X0,X1) = 2*X1*X0; 
 [ true ] () = 0; 
 [ mem ] (X0,X1) = 2*X1; 
 [ s ] (X0) = 1*X0 + 2; 
 [ Marked_ifinter ] (X0,X1,X2,X3) = 2*X3*X2 + 2*X0; 
 [ eq ] (X0,X1) = 1*X1 + 2*X0; 
 [ inter ] (X0,X1) = 2*X1*X0 + 2*X1 + 2*X0; 
 [ nil ] () = 1; 
 removing <Marked_ifinter(false,x,l1,l2),Marked_inter(l1,l2)>
 [ {
      
     DP termination of:
     <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
<Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
<Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
<Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
<Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
<Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
<Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ if ] (X0,X1,X2) = 2 + 2*X0 + 2*X1 + 1*X1*X0 + 1*X2 + 2*X2*X1 + 2*X2*X1*X0 + 0; 
 [ cons ] (X0,X1) = 2 + 1*X1 + 0; 
 [ 0 ] () = 0; 
 [ ifinter ] (X0,X1,X2,X3) = 2 + 1*X2 + 2*X3 + 1*X3*X2 + 0; 
 [ false ] () = 0; 
 [ ifmem ] (X0,X1,X2) = 2*X2 + 0; 
 [ app ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 [ Marked_inter ] (X0,X1) = 2*X0 + 2*X1 + 2*X1*X0 + 0; 
 [ true ] () = 0; 
 [ mem ] (X0,X1) = 2*X1 + 0; 
 [ s ] (X0) = 0; 
 [ Marked_ifinter ] (X0,X1,X2,X3) = 2 + 1*X0 + 2*X2 + 2*X3 + 2*X3*X2 + 0; 
 [ eq ] (X0,X1) = 0; 
 [ inter ] (X0,X1) = 1*X0 + 2*X1 + 1*X1*X0 + 0; 
 [ nil ] () = 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)>
<Marked_app(app(l1,l2),l3) , Marked_app(l1,app(l2,l3))>
<Marked_app(app(l1,l2),l3) , Marked_app(l2,l3)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_mem(x,cons(y,l)) , Marked_ifmem(eq(x,y),x,l)>
<Marked_ifmem(false,x,l) , Marked_mem(x,l)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_ifmem(false,x,l) , Marked_mem(x,l)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
{
 
DP termination of:
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 32.319549 seconds (real time)
Cime Exit Status: 0