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

TRS termination of:
[1] eq(0,0) -> true
[2] eq(0,s(y)) -> false
[3] eq(s(x),0) -> false
[4] eq(s(x),s(y)) -> eq(x,y)
[5] lt(0,s(y)) -> true
[6] lt(x,0) -> false
[7] lt(s(x),s(y)) -> lt(x,y)
[8] bin2s(nil) -> 0
[9] bin2s(cons(x,xs)) -> bin2ss(x,xs)
[10] bin2ss(x,nil) -> x
[11] bin2ss(x,cons(0,xs)) -> bin2ss(double(x),xs)
[12] bin2ss(x,cons(1,xs)) -> bin2ss(s(double(x)),xs)
[13] half(0) -> 0
[14] half(s(0)) -> 0
[15] half(s(s(x))) -> s(half(x))
[16] log(0) -> 0
[17] log(s(0)) -> 0
[18] log(s(s(x))) -> s(log(half(s(s(x)))))
[19] more(nil) -> nil
[20] more(cons(xs,ys)) -> cons(cons(0,xs),cons(cons(1,xs),cons(xs,ys)))
[21] s2bin(x) -> s2bin1(x,0,cons(nil,nil))
[22] s2bin1(x,y,lists) -> if1(lt(y,log(x)),x,y,lists)
[23] if1(true,x,y,lists) -> s2bin1(x,s(y),more(lists))
[24] if1(false,x,y,lists) -> s2bin2(x,lists)
[25] s2bin2(x,nil) -> bug_list_not
[26] s2bin2(x,cons(xs,ys)) -> if2(eq(x,bin2s(xs)),x,xs,ys)
[27] if2(true,x,xs,ys) -> xs
[28] if2(false,x,xs,ys) -> s2bin2(x,ys)


Sub problem: 
guided: 

DP termination of:
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
<Marked_bin2s(cons(x,xs)) , Marked_bin2ss(x,xs)>
<Marked_bin2ss(x,cons(0,xs)) , Marked_bin2ss(double(x),xs)>
<Marked_bin2ss(x,cons(1,xs)) , Marked_bin2ss(s(double(x)),xs)>
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_log(s(s(x))) , Marked_log(half(s(s(x))))>
<Marked_log(s(s(x))) , Marked_half(s(s(x)))>
<Marked_s2bin(x) , Marked_s2bin1(x,0,cons(nil,nil))>
<Marked_s2bin1(x,y,lists) , Marked_if1(lt(y,log(x)),x,y,lists)>
<Marked_s2bin1(x,y,lists) , Marked_lt(y,log(x))>
<Marked_s2bin1(x,y,lists) , Marked_log(x)>
<Marked_if1(true,x,y,lists) , Marked_s2bin1(x,s(y),more(lists))>
<Marked_if1(true,x,y,lists) , Marked_more(lists)>
<Marked_if1(false,x,y,lists) , Marked_s2bin2(x,lists)>
<Marked_s2bin2(x,cons(xs,ys)) , Marked_if2(eq(x,bin2s(xs)),x,xs,ys)>
<Marked_s2bin2(x,cons(xs,ys)) , Marked_eq(x,bin2s(xs))>
<Marked_s2bin2(x,cons(xs,ys)) , Marked_bin2s(xs)>
<Marked_if2(false,x,xs,ys) , Marked_s2bin2(x,ys)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 7 components:

{  <Marked_if1(true,x,y,lists) , Marked_s2bin1(x,s(y),more(lists))> 
      --> <Marked_s2bin1(x,y,lists) , Marked_if1(lt(y,log(x)),x,y,lists)>
  <Marked_s2bin1(x,y,lists) , Marked_if1(lt(y,log(x)),x,y,lists)> 
     --> <Marked_if1(true,x,y,lists) , Marked_s2bin1(x,s(y),more(lists))>
}

{  <Marked_lt(s(x),s(y)) , Marked_lt(x,y)> 
      --> <Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
}

{  <Marked_log(s(s(x))) , Marked_log(half(s(s(x))))> 
      --> <Marked_log(s(s(x))) , Marked_log(half(s(s(x))))>
}

{  <Marked_half(s(s(x))) , Marked_half(x)> 
      --> <Marked_half(s(s(x))) , Marked_half(x)>
}

{  <Marked_if2(false,x,xs,ys) , Marked_s2bin2(x,ys)> 
      --> <Marked_s2bin2(x,cons(xs,ys)) , Marked_if2(eq(x,bin2s(xs)),x,xs,ys)>
  <Marked_s2bin2(x,cons(xs,ys)) , Marked_if2(eq(x,bin2s(xs)),x,xs,ys)> 
     --> <Marked_if2(false,x,xs,ys) , Marked_s2bin2(x,ys)>
}

{  <Marked_eq(s(x),s(y)) , Marked_eq(x,y)> 
      --> <Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
}

{  <Marked_bin2ss(x,cons(1,xs)) , Marked_bin2ss(s(double(x)),xs)> 
      --> <Marked_bin2ss(x,cons(1,xs)) , Marked_bin2ss(s(double(x)),xs)>
  <Marked_bin2ss(x,cons(1,xs)) , Marked_bin2ss(s(double(x)),xs)> 
     --> <Marked_bin2ss(x,cons(0,xs)) , Marked_bin2ss(double(x),xs)>
  <Marked_bin2ss(x,cons(0,xs)) , Marked_bin2ss(double(x),xs)> 
     --> <Marked_bin2ss(x,cons(1,xs)) , Marked_bin2ss(s(double(x)),xs)>
  <Marked_bin2ss(x,cons(0,xs)) , Marked_bin2ss(double(x),xs)> 
     --> <Marked_bin2ss(x,cons(0,xs)) , Marked_bin2ss(double(x),xs)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  eq(0,0) >= true ;
  eq(0,s(y)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  bin2s(nil) >= 0 ;
  bin2s(cons(x,xs)) >= bin2ss(x,xs) ;
  bin2ss(x,nil) >= x ;
  bin2ss(x,cons(0,xs)) >= bin2ss(double(x),xs) ;
  bin2ss(x,cons(1,xs)) >= bin2ss(s(double(x)),xs) ;
  half(0) >= 0 ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  log(0) >= 0 ;
  log(s(0)) >= 0 ;
  log(s(s(x))) >= s(log(half(s(s(x))))) ;
  more(nil) >= nil ;
  more(cons(xs,ys)) >= cons(cons(0,xs),cons(cons(1,xs),cons(xs,ys))) ;
  s2bin1(x,y,lists) >= if1(lt(y,log(x)),x,y,lists) ;
  s2bin(x) >= s2bin1(x,0,cons(nil,nil)) ;
  if1(true,x,y,lists) >= s2bin1(x,s(y),more(lists)) ;
  if1(false,x,y,lists) >= s2bin2(x,lists) ;
  s2bin2(x,nil) >= bug_list_not ;
  s2bin2(x,cons(xs,ys)) >= if2(eq(x,bin2s(xs)),x,xs,ys) ;
  if2(true,x,xs,ys) >= xs ;
  if2(false,x,xs,ys) >= s2bin2(x,ys) ;
  Marked_if1(true,x,y,lists) >= Marked_s2bin1(x,s(y),more(lists)) ;
  Marked_s2bin1(x,y,lists) >= Marked_if1(lt(y,log(x)),x,y,lists) ;
 }
 + Disjunctions:{ 
{
  Marked_if1(true,x,y,lists) > Marked_s2bin1(x,s(y),more(lists)) ;
 }
{
  Marked_s2bin1(x,y,lists) > Marked_if1(lt(y,log(x)),x,y,lists) ;
 }
 } 
=== 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 ===
Time out for these parameters.
=== 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:
{
  eq(0,0) >= true ;
  eq(0,s(y)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  bin2s(nil) >= 0 ;
  bin2s(cons(x,xs)) >= bin2ss(x,xs) ;
  bin2ss(x,nil) >= x ;
  bin2ss(x,cons(0,xs)) >= bin2ss(double(x),xs) ;
  bin2ss(x,cons(1,xs)) >= bin2ss(s(double(x)),xs) ;
  half(0) >= 0 ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  log(0) >= 0 ;
  log(s(0)) >= 0 ;
  log(s(s(x))) >= s(log(half(s(s(x))))) ;
  more(nil) >= nil ;
  more(cons(xs,ys)) >= cons(cons(0,xs),cons(cons(1,xs),cons(xs,ys))) ;
  s2bin1(x,y,lists) >= if1(lt(y,log(x)),x,y,lists) ;
  s2bin(x) >= s2bin1(x,0,cons(nil,nil)) ;
  if1(true,x,y,lists) >= s2bin1(x,s(y),more(lists)) ;
  if1(false,x,y,lists) >= s2bin2(x,lists) ;
  s2bin2(x,nil) >= bug_list_not ;
  s2bin2(x,cons(xs,ys)) >= if2(eq(x,bin2s(xs)),x,xs,ys) ;
  if2(true,x,xs,ys) >= xs ;
  if2(false,x,xs,ys) >= s2bin2(x,ys) ;
  Marked_if1(true,x,y,lists) >= Marked_s2bin1(x,s(y),more(lists)) ;
  Marked_s2bin1(x,y,lists) > Marked_if1(lt(y,log(x)),x,y,lists) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  eq(0,0) >= true ;
  eq(0,s(y)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  bin2s(nil) >= 0 ;
  bin2s(cons(x,xs)) >= bin2ss(x,xs) ;
  bin2ss(x,nil) >= x ;
  bin2ss(x,cons(0,xs)) >= bin2ss(double(x),xs) ;
  bin2ss(x,cons(1,xs)) >= bin2ss(s(double(x)),xs) ;
  half(0) >= 0 ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  log(0) >= 0 ;
  log(s(0)) >= 0 ;
  log(s(s(x))) >= s(log(half(s(s(x))))) ;
  more(nil) >= nil ;
  more(cons(xs,ys)) >= cons(cons(0,xs),cons(cons(1,xs),cons(xs,ys))) ;
  s2bin1(x,y,lists) >= if1(lt(y,log(x)),x,y,lists) ;
  s2bin(x) >= s2bin1(x,0,cons(nil,nil)) ;
  if1(true,x,y,lists) >= s2bin1(x,s(y),more(lists)) ;
  if1(false,x,y,lists) >= s2bin2(x,lists) ;
  s2bin2(x,nil) >= bug_list_not ;
  s2bin2(x,cons(xs,ys)) >= if2(eq(x,bin2s(xs)),x,xs,ys) ;
  if2(true,x,xs,ys) >= xs ;
  if2(false,x,xs,ys) >= s2bin2(x,ys) ;
  Marked_if1(true,x,y,lists) >= Marked_s2bin1(x,s(y),more(lists)) ;
  Marked_s2bin1(x,y,lists) > Marked_if1(lt(y,log(x)),x,y,lists) ;
 }
 + 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 ===
Time out for these parameters.
=== 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 57.908809 seconds (real time)
Cime Exit Status: 0