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

TRS termination of:
[1] times(x,y) -> sum(generate(x,y))
[2] generate(x,y) -> gen(x,y,0)
[3] gen(x,y,z) -> if(ge(z,x),x,y,z)
[4] if(true,x,y,z) -> nil
[5] if(false,x,y,z) -> cons(y,gen(x,y,s(z)))
[6] sum(xs) -> sum2(xs,0)
[7] sum2(xs,y) -> ifsum(isNil(xs),isZero(head(xs)),xs,y)
[8] ifsum(true,b,xs,y) -> y
[9] ifsum(false,b,xs,y) -> ifsum2(b,xs,y)
[10] ifsum2(true,xs,y) -> sum2(tail(xs),y)
[11] ifsum2(false,xs,y) -> sum2(cons(p(head(xs)),tail(xs)),s(y))
[12] isNil(nil) -> true
[13] isNil(cons(x,xs)) -> false
[14] tail(nil) -> nil
[15] tail(cons(x,xs)) -> xs
[16] head(cons(x,xs)) -> x
[17] head(nil) -> error
[18] isZero(0) -> true
[19] isZero(s(0)) -> false
[20] isZero(s(s(x))) -> isZero(s(x))
[21] p(0) -> s(s(0))
[22] p(s(0)) -> 0
[23] p(s(s(x))) -> s(p(s(x)))
[24] ge(x,0) -> true
[25] ge(0,s(y)) -> false
[26] ge(s(x),s(y)) -> ge(x,y)
[27] a -> c
[28] a -> d


Sub problem: 
guided: 

DP termination of:
<Marked_times(x,y) , Marked_sum(generate(x,y))>
<Marked_times(x,y) , Marked_generate(x,y)>
<Marked_generate(x,y) , Marked_gen(x,y,0)>
<Marked_gen(x,y,z) , Marked_if(ge(z,x),x,y,z)>
<Marked_gen(x,y,z) , Marked_ge(z,x)>
<Marked_if(false,x,y,z) , Marked_gen(x,y,s(z))>
<Marked_sum(xs) , Marked_sum2(xs,0)>
<Marked_sum2(xs,y) , Marked_ifsum(isNil(xs),isZero(head(xs)),xs,y)>
<Marked_sum2(xs,y) , Marked_isNil(xs)>
<Marked_sum2(xs,y) , Marked_isZero(head(xs))>
<Marked_sum2(xs,y) , Marked_head(xs)>
<Marked_ifsum(false,b,xs,y) , Marked_ifsum2(b,xs,y)>
<Marked_ifsum2(true,xs,y) , Marked_sum2(tail(xs),y)>
<Marked_ifsum2(true,xs,y) , Marked_tail(xs)>
<Marked_ifsum2(false,xs,y) , Marked_sum2(cons(p(head(xs)),tail(xs)),s(y))>
<Marked_ifsum2(false,xs,y) , Marked_p(head(xs))>
<Marked_ifsum2(false,xs,y) , Marked_head(xs)>
<Marked_ifsum2(false,xs,y) , Marked_tail(xs)>
<Marked_isZero(s(s(x))) , Marked_isZero(s(x))>
<Marked_p(s(s(x))) , Marked_p(s(x))>
<Marked_ge(s(x),s(y)) , Marked_ge(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

{  <Marked_if(false,x,y,z) , Marked_gen(x,y,s(z))> 
      --> <Marked_gen(x,y,z) , Marked_if(ge(z,x),x,y,z)>
  <Marked_gen(x,y,z) , Marked_if(ge(z,x),x,y,z)> 
     --> <Marked_if(false,x,y,z) , Marked_gen(x,y,s(z))>
}

{  <Marked_ifsum2(false,xs,y) , Marked_sum2(cons(p(head(xs)),tail(xs)),s(y))> 
      --> <Marked_sum2(xs,y) , Marked_ifsum(isNil(xs),isZero(head(xs)),xs,y)>
  <Marked_ifsum2(true,xs,y) , Marked_sum2(tail(xs),y)> 
     --> <Marked_sum2(xs,y) , Marked_ifsum(isNil(xs),isZero(head(xs)),xs,y)>
  <Marked_ifsum(false,b,xs,y) , Marked_ifsum2(b,xs,y)> 
     --> <Marked_ifsum2(false,xs,y) , Marked_sum2(cons(p(head(xs)),tail(xs)),
                                       s(y))>
  <Marked_ifsum(false,b,xs,y) , Marked_ifsum2(b,xs,y)> 
     --> <Marked_ifsum2(true,xs,y) , Marked_sum2(tail(xs),y)>
  <Marked_sum2(xs,y) , Marked_ifsum(isNil(xs),isZero(head(xs)),xs,y)> 
     --> <Marked_ifsum(false,b,xs,y) , Marked_ifsum2(b,xs,y)>
}

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

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

{  <Marked_ge(s(x),s(y)) , Marked_ge(x,y)> 
      --> <Marked_ge(s(x),s(y)) , Marked_ge(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sum(xs) >= sum2(xs,0) ;
  generate(x,y) >= gen(x,y,0) ;
  times(x,y) >= sum(generate(x,y)) ;
  gen(x,y,z) >= if(ge(z,x),x,y,z) ;
  if(true,x,y,z) >= nil ;
  if(false,x,y,z) >= cons(y,gen(x,y,s(z))) ;
  ge(0,s(y)) >= false ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(x,0) >= true ;
  sum2(xs,y) >= ifsum(isNil(xs),isZero(head(xs)),xs,y) ;
  ifsum(true,b,xs,y) >= y ;
  ifsum(false,b,xs,y) >= ifsum2(b,xs,y) ;
  isNil(nil) >= true ;
  isNil(cons(x,xs)) >= false ;
  isZero(0) >= true ;
  isZero(s(0)) >= false ;
  isZero(s(s(x))) >= isZero(s(x)) ;
  head(nil) >= error ;
  head(cons(x,xs)) >= x ;
  ifsum2(true,xs,y) >= sum2(tail(xs),y) ;
  ifsum2(false,xs,y) >= sum2(cons(p(head(xs)),tail(xs)),s(y)) ;
  tail(nil) >= nil ;
  tail(cons(x,xs)) >= xs ;
  p(0) >= s(s(0)) ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  a >= c ;
  a >= d ;
  Marked_if(false,x,y,z) >= Marked_gen(x,y,s(z)) ;
  Marked_gen(x,y,z) >= Marked_if(ge(z,x),x,y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_if(false,x,y,z) > Marked_gen(x,y,s(z)) ;
 }
{
  Marked_gen(x,y,z) > Marked_if(ge(z,x),x,y,z) ;
 }
 } 
=== 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:
{
  sum(xs) >= sum2(xs,0) ;
  generate(x,y) >= gen(x,y,0) ;
  times(x,y) >= sum(generate(x,y)) ;
  gen(x,y,z) >= if(ge(z,x),x,y,z) ;
  if(true,x,y,z) >= nil ;
  if(false,x,y,z) >= cons(y,gen(x,y,s(z))) ;
  ge(0,s(y)) >= false ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(x,0) >= true ;
  sum2(xs,y) >= ifsum(isNil(xs),isZero(head(xs)),xs,y) ;
  ifsum(true,b,xs,y) >= y ;
  ifsum(false,b,xs,y) >= ifsum2(b,xs,y) ;
  isNil(nil) >= true ;
  isNil(cons(x,xs)) >= false ;
  isZero(0) >= true ;
  isZero(s(0)) >= false ;
  isZero(s(s(x))) >= isZero(s(x)) ;
  head(nil) >= error ;
  head(cons(x,xs)) >= x ;
  ifsum2(true,xs,y) >= sum2(tail(xs),y) ;
  ifsum2(false,xs,y) >= sum2(cons(p(head(xs)),tail(xs)),s(y)) ;
  tail(nil) >= nil ;
  tail(cons(x,xs)) >= xs ;
  p(0) >= s(s(0)) ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  a >= c ;
  a >= d ;
  Marked_if(false,x,y,z) >= Marked_gen(x,y,s(z)) ;
  Marked_gen(x,y,z) > Marked_if(ge(z,x),x,y,z) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  sum(xs) >= sum2(xs,0) ;
  generate(x,y) >= gen(x,y,0) ;
  times(x,y) >= sum(generate(x,y)) ;
  gen(x,y,z) >= if(ge(z,x),x,y,z) ;
  if(true,x,y,z) >= nil ;
  if(false,x,y,z) >= cons(y,gen(x,y,s(z))) ;
  ge(0,s(y)) >= false ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(x,0) >= true ;
  sum2(xs,y) >= ifsum(isNil(xs),isZero(head(xs)),xs,y) ;
  ifsum(true,b,xs,y) >= y ;
  ifsum(false,b,xs,y) >= ifsum2(b,xs,y) ;
  isNil(nil) >= true ;
  isNil(cons(x,xs)) >= false ;
  isZero(0) >= true ;
  isZero(s(0)) >= false ;
  isZero(s(s(x))) >= isZero(s(x)) ;
  head(nil) >= error ;
  head(cons(x,xs)) >= x ;
  ifsum2(true,xs,y) >= sum2(tail(xs),y) ;
  ifsum2(false,xs,y) >= sum2(cons(p(head(xs)),tail(xs)),s(y)) ;
  tail(nil) >= nil ;
  tail(cons(x,xs)) >= xs ;
  p(0) >= s(s(0)) ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  a >= c ;
  a >= d ;
  Marked_if(false,x,y,z) >= Marked_gen(x,y,s(z)) ;
  Marked_gen(x,y,z) > Marked_if(ge(z,x),x,y,z) ;
 }
 + 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 53.599439 seconds (real time)
Cime Exit Status: 0