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

TRS termination of:
[1] prod(xs) -> prodIter(xs,s(0))
[2] prodIter(xs,x) -> ifProd(isempty(xs),xs,x)
[3] ifProd(true,xs,x) -> x
[4] ifProd(false,xs,x) -> prodIter(tail(xs),times(x,head(xs)))
[5] plus(0,y) -> y
[6] plus(s(x),y) -> s(plus(x,y))
[7] times(x,y) -> timesIter(x,y,0,0)
[8] timesIter(x,y,z,u) -> ifTimes(ge(u,x),x,y,z,u)
[9] ifTimes(true,x,y,z,u) -> z
[10] ifTimes(false,x,y,z,u) -> timesIter(x,y,plus(y,z),s(u))
[11] isempty(nil) -> true
[12] isempty(cons(x,xs)) -> false
[13] head(nil) -> error
[14] head(cons(x,xs)) -> x
[15] tail(nil) -> nil
[16] tail(cons(x,xs)) -> xs
[17] ge(x,0) -> true
[18] ge(0,s(y)) -> false
[19] ge(s(x),s(y)) -> ge(x,y)
[20] a -> b
[21] a -> c


Sub problem: 
guided: 

DP termination of:
<Marked_prod(xs) , Marked_prodIter(xs,s(0))>
<Marked_prodIter(xs,x) , Marked_ifProd(isempty(xs),xs,x)>
<Marked_prodIter(xs,x) , Marked_isempty(xs)>
<Marked_ifProd(false,xs,x) , Marked_prodIter(tail(xs),times(x,head(xs)))>
<Marked_ifProd(false,xs,x) , Marked_tail(xs)>
<Marked_ifProd(false,xs,x) , Marked_times(x,head(xs))>
<Marked_ifProd(false,xs,x) , Marked_head(xs)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_times(x,y) , Marked_timesIter(x,y,0,0)>
<Marked_timesIter(x,y,z,u) , Marked_ifTimes(ge(u,x),x,y,z,u)>
<Marked_timesIter(x,y,z,u) , Marked_ge(u,x)>
<Marked_ifTimes(false,x,y,z,u) , Marked_timesIter(x,y,plus(y,z),s(u))>
<Marked_ifTimes(false,x,y,z,u) , Marked_plus(y,z)>
<Marked_ge(s(x),s(y)) , Marked_ge(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_ifProd(false,xs,x) , Marked_prodIter(tail(xs),times(x,head(xs)))> 
      --> <Marked_prodIter(xs,x) , Marked_ifProd(isempty(xs),xs,x)>
  <Marked_prodIter(xs,x) , Marked_ifProd(isempty(xs),xs,x)> 
     --> <Marked_ifProd(false,xs,x) , Marked_prodIter(tail(xs),
                                       times(x,head(xs)))>
}

{  <Marked_ifTimes(false,x,y,z,u) , Marked_timesIter(x,y,plus(y,z),s(u))> 
      --> <Marked_timesIter(x,y,z,u) , Marked_ifTimes(ge(u,x),x,y,z,u)>
  <Marked_timesIter(x,y,z,u) , Marked_ifTimes(ge(u,x),x,y,z,u)> 
     --> <Marked_ifTimes(false,x,y,z,u) , Marked_timesIter(x,y,plus(y,z),s(u))>
}

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

{  <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:
{
  prodIter(xs,x) >= ifProd(isempty(xs),xs,x) ;
  prod(xs) >= prodIter(xs,s(0)) ;
  ifProd(true,xs,x) >= x ;
  ifProd(false,xs,x) >= prodIter(tail(xs),times(x,head(xs))) ;
  isempty(nil) >= true ;
  isempty(cons(x,xs)) >= false ;
  tail(nil) >= nil ;
  tail(cons(x,xs)) >= xs ;
  times(x,y) >= timesIter(x,y,0,0) ;
  head(nil) >= error ;
  head(cons(x,xs)) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  plus(0,y) >= y ;
  timesIter(x,y,z,u) >= ifTimes(ge(u,x),x,y,z,u) ;
  ifTimes(true,x,y,z,u) >= z ;
  ifTimes(false,x,y,z,u) >= timesIter(x,y,plus(y,z),s(u)) ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(0,s(y)) >= false ;
  ge(x,0) >= true ;
  a >= b ;
  a >= c ;
  Marked_ifProd(false,xs,x) >= Marked_prodIter(tail(xs),times(x,head(xs))) ;
  Marked_prodIter(xs,x) >= Marked_ifProd(isempty(xs),xs,x) ;
 }
 + Disjunctions:{ 
{
  Marked_ifProd(false,xs,x) > Marked_prodIter(tail(xs),times(x,head(xs))) ;
 }
{
  Marked_prodIter(xs,x) > Marked_ifProd(isempty(xs),xs,x) ;
 }
 } 
=== 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:
{
  prodIter(xs,x) >= ifProd(isempty(xs),xs,x) ;
  prod(xs) >= prodIter(xs,s(0)) ;
  ifProd(true,xs,x) >= x ;
  ifProd(false,xs,x) >= prodIter(tail(xs),times(x,head(xs))) ;
  isempty(nil) >= true ;
  isempty(cons(x,xs)) >= false ;
  tail(nil) >= nil ;
  tail(cons(x,xs)) >= xs ;
  times(x,y) >= timesIter(x,y,0,0) ;
  head(nil) >= error ;
  head(cons(x,xs)) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  plus(0,y) >= y ;
  timesIter(x,y,z,u) >= ifTimes(ge(u,x),x,y,z,u) ;
  ifTimes(true,x,y,z,u) >= z ;
  ifTimes(false,x,y,z,u) >= timesIter(x,y,plus(y,z),s(u)) ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(0,s(y)) >= false ;
  ge(x,0) >= true ;
  a >= b ;
  a >= c ;
  Marked_ifProd(false,xs,x) >= Marked_prodIter(tail(xs),times(x,head(xs))) ;
  Marked_prodIter(xs,x) > Marked_ifProd(isempty(xs),xs,x) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  prodIter(xs,x) >= ifProd(isempty(xs),xs,x) ;
  prod(xs) >= prodIter(xs,s(0)) ;
  ifProd(true,xs,x) >= x ;
  ifProd(false,xs,x) >= prodIter(tail(xs),times(x,head(xs))) ;
  isempty(nil) >= true ;
  isempty(cons(x,xs)) >= false ;
  tail(nil) >= nil ;
  tail(cons(x,xs)) >= xs ;
  times(x,y) >= timesIter(x,y,0,0) ;
  head(nil) >= error ;
  head(cons(x,xs)) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  plus(0,y) >= y ;
  timesIter(x,y,z,u) >= ifTimes(ge(u,x),x,y,z,u) ;
  ifTimes(true,x,y,z,u) >= z ;
  ifTimes(false,x,y,z,u) >= timesIter(x,y,plus(y,z),s(u)) ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(0,s(y)) >= false ;
  ge(x,0) >= true ;
  a >= b ;
  a >= c ;
  Marked_ifProd(false,xs,x) >= Marked_prodIter(tail(xs),times(x,head(xs))) ;
  Marked_prodIter(xs,x) > Marked_ifProd(isempty(xs),xs,x) ;
 }
 + 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 51.598605 seconds (real time)
Cime Exit Status: 0