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

TRS termination of:
[1] lessElements(l,t) -> lessE(l,t,0)
[2] lessE(l,t,n) -> if(le(length(l),n),le(length(toList(t)),n),l,t,n)
[3] if(true,b,l,t,n) -> l
[4] if(false,true,l,t,n) -> t
[5] if(false,false,l,t,n) -> lessE(l,t,s(n))
[6] length(nil) -> 0
[7] length(cons(n,l)) -> s(length(l))
[8] toList(leaf) -> nil
[9] toList(node(t1,n,t2)) -> append(toList(t1),cons(n,toList(t2)))
[10] append(nil,l2) -> l2
[11] append(cons(n,l1),l2) -> cons(n,append(l1,l2))
[12] le(s(n),0) -> false
[13] le(0,m) -> true
[14] le(s(n),s(m)) -> le(n,m)
[15] a -> c
[16] a -> d


Sub problem: 
guided: 

DP termination of:
<Marked_lessElements(l,t) , Marked_lessE(l,t,0)>
<Marked_lessE(l,t,n) , Marked_if(le(length(l),n),le(length(toList(t)),n),l,t,n)>
<Marked_lessE(l,t,n) , Marked_le(length(l),n)>
<Marked_lessE(l,t,n) , Marked_length(l)>
<Marked_lessE(l,t,n) , Marked_le(length(toList(t)),n)>
<Marked_lessE(l,t,n) , Marked_length(toList(t))>
<Marked_lessE(l,t,n) , Marked_toList(t)>
<Marked_if(false,false,l,t,n) , Marked_lessE(l,t,s(n))>
<Marked_length(cons(n,l)) , Marked_length(l)>
<Marked_toList(node(t1,n,t2)) , Marked_append(toList(t1),cons(n,toList(t2)))>
<Marked_toList(node(t1,n,t2)) , Marked_toList(t1)>
<Marked_toList(node(t1,n,t2)) , Marked_toList(t2)>
<Marked_append(cons(n,l1),l2) , Marked_append(l1,l2)>
<Marked_le(s(n),s(m)) , Marked_le(n,m)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

{  <Marked_if(false,false,l,t,n) , Marked_lessE(l,t,s(n))> 
      --> <Marked_lessE(l,t,n) , Marked_if(le(length(l),n),
                                  le(length(toList(t)),n),l,t,n)>
  <Marked_lessE(l,t,n) , Marked_if(le(length(l),n),le(length(toList(t)),n),
                          l,t,n)> 
     --> <Marked_if(false,false,l,t,n) , Marked_lessE(l,t,s(n))>
}

{  <Marked_length(cons(n,l)) , Marked_length(l)> 
      --> <Marked_length(cons(n,l)) , Marked_length(l)>
}

{  <Marked_toList(node(t1,n,t2)) , Marked_toList(t2)> 
      --> <Marked_toList(node(t1,n,t2)) , Marked_toList(t2)>
  <Marked_toList(node(t1,n,t2)) , Marked_toList(t2)> 
     --> <Marked_toList(node(t1,n,t2)) , Marked_toList(t1)>
  <Marked_toList(node(t1,n,t2)) , Marked_toList(t1)> 
     --> <Marked_toList(node(t1,n,t2)) , Marked_toList(t2)>
  <Marked_toList(node(t1,n,t2)) , Marked_toList(t1)> 
     --> <Marked_toList(node(t1,n,t2)) , Marked_toList(t1)>
}

{  <Marked_append(cons(n,l1),l2) , Marked_append(l1,l2)> 
      --> <Marked_append(cons(n,l1),l2) , Marked_append(l1,l2)>
}

{  <Marked_le(s(n),s(m)) , Marked_le(n,m)> 
      --> <Marked_le(s(n),s(m)) , Marked_le(n,m)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  lessE(l,t,n) >= if(le(length(l),n),le(length(toList(t)),n),l,t,n) ;
  lessElements(l,t) >= lessE(l,t,0) ;
  if(true,b,l,t,n) >= l ;
  if(false,true,l,t,n) >= t ;
  if(false,false,l,t,n) >= lessE(l,t,s(n)) ;
  le(0,m) >= true ;
  le(s(n),0) >= false ;
  le(s(n),s(m)) >= le(n,m) ;
  length(nil) >= 0 ;
  length(cons(n,l)) >= s(length(l)) ;
  toList(leaf) >= nil ;
  toList(node(t1,n,t2)) >= append(toList(t1),cons(n,toList(t2))) ;
  append(nil,l2) >= l2 ;
  append(cons(n,l1),l2) >= cons(n,append(l1,l2)) ;
  a >= c ;
  a >= d ;
  Marked_if(false,false,l,t,n) >= Marked_lessE(l,t,s(n)) ;
  Marked_lessE(l,t,n) >= Marked_if(le(length(l),n),le(length(toList(t)),n),
                          l,t,n) ;
 }
 + Disjunctions:{ 
{
  Marked_if(false,false,l,t,n) > Marked_lessE(l,t,s(n)) ;
 }
{
  Marked_lessE(l,t,n) > Marked_if(le(length(l),n),le(length(toList(t)),n),
                         l,t,n) ;
 }
 } 
=== 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 : 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  lessE(l,t,n) >= if(le(length(l),n),le(length(toList(t)),n),l,t,n) ;
  lessElements(l,t) >= lessE(l,t,0) ;
  if(true,b,l,t,n) >= l ;
  if(false,true,l,t,n) >= t ;
  if(false,false,l,t,n) >= lessE(l,t,s(n)) ;
  le(0,m) >= true ;
  le(s(n),0) >= false ;
  le(s(n),s(m)) >= le(n,m) ;
  length(nil) >= 0 ;
  length(cons(n,l)) >= s(length(l)) ;
  toList(leaf) >= nil ;
  toList(node(t1,n,t2)) >= append(toList(t1),cons(n,toList(t2))) ;
  append(nil,l2) >= l2 ;
  append(cons(n,l1),l2) >= cons(n,append(l1,l2)) ;
  a >= c ;
  a >= d ;
  Marked_if(false,false,l,t,n) >= Marked_lessE(l,t,s(n)) ;
  Marked_lessE(l,t,n) > Marked_if(le(length(l),n),le(length(toList(t)),n),
                         l,t,n) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  lessE(l,t,n) >= if(le(length(l),n),le(length(toList(t)),n),l,t,n) ;
  lessElements(l,t) >= lessE(l,t,0) ;
  if(true,b,l,t,n) >= l ;
  if(false,true,l,t,n) >= t ;
  if(false,false,l,t,n) >= lessE(l,t,s(n)) ;
  le(0,m) >= true ;
  le(s(n),0) >= false ;
  le(s(n),s(m)) >= le(n,m) ;
  length(nil) >= 0 ;
  length(cons(n,l)) >= s(length(l)) ;
  toList(leaf) >= nil ;
  toList(node(t1,n,t2)) >= append(toList(t1),cons(n,toList(t2))) ;
  append(nil,l2) >= l2 ;
  append(cons(n,l1),l2) >= cons(n,append(l1,l2)) ;
  a >= c ;
  a >= d ;
  Marked_if(false,false,l,t,n) >= Marked_lessE(l,t,s(n)) ;
  Marked_lessE(l,t,n) > Marked_if(le(length(l),n),le(length(toList(t)),n),
                         l,t,n) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
No solution found for these parameters.(423876 bt (437096) [28981])
=== 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 64.223156 seconds (real time)
Cime Exit Status: 0