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

TRS termination of:
[1] U11(tt,N,XS) -> U12(tt,activate(N),activate(XS))
[2] U12(tt,N,XS) -> snd(splitAt(activate(N),activate(XS)))
[3] U21(tt,X) -> U22(tt,activate(X))
[4] U22(tt,X) -> activate(X)
[5] U31(tt,N) -> U32(tt,activate(N))
[6] U32(tt,N) -> activate(N)
[7] U41(tt,N,XS) -> U42(tt,activate(N),activate(XS))
[8] U42(tt,N,XS) -> head(afterNth(activate(N),activate(XS)))
[9] U51(tt,Y) -> U52(tt,activate(Y))
[10] U52(tt,Y) -> activate(Y)
[11] U61(tt,N,X,XS) -> U62(tt,activate(N),activate(X),activate(XS))
[12] U62(tt,N,X,XS) -> U63(tt,activate(N),activate(X),activate(XS))
[13] U63(tt,N,X,XS) -> U64(splitAt(activate(N),activate(XS)),activate(X))
[14] U64(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
[15] U71(tt,XS) -> U72(tt,activate(XS))
[16] U72(tt,XS) -> activate(XS)
[17] U81(tt,N,XS) -> U82(tt,activate(N),activate(XS))
[18] U82(tt,N,XS) -> fst(splitAt(activate(N),activate(XS)))
[19] afterNth(N,XS) -> U11(tt,N,XS)
[20] fst(pair(X,Y)) -> U21(tt,X)
[21] head(cons(N,XS)) -> U31(tt,N)
[22] natsFrom(N) -> cons(N,n__natsFrom(s(N)))
[23] sel(N,XS) -> U41(tt,N,XS)
[24] snd(pair(X,Y)) -> U51(tt,Y)
[25] splitAt(0,XS) -> pair(nil,XS)
[26] splitAt(s(N),cons(X,XS)) -> U61(tt,N,X,activate(XS))
[27] tail(cons(N,XS)) -> U71(tt,activate(XS))
[28] take(N,XS) -> U81(tt,N,XS)
[29] natsFrom(X) -> n__natsFrom(X)
[30] activate(n__natsFrom(X)) -> natsFrom(X)
[31] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_U11(tt,N,XS) , Marked_U12(tt,activate(N),activate(XS))>
<Marked_U11(tt,N,XS) , Marked_activate(N)>
<Marked_U11(tt,N,XS) , Marked_activate(XS)>
<Marked_U12(tt,N,XS) , Marked_snd(splitAt(activate(N),activate(XS)))>
<Marked_U12(tt,N,XS) , Marked_splitAt(activate(N),activate(XS))>
<Marked_U12(tt,N,XS) , Marked_activate(N)>
<Marked_U12(tt,N,XS) , Marked_activate(XS)>
<Marked_U21(tt,X) , Marked_U22(tt,activate(X))>
<Marked_U21(tt,X) , Marked_activate(X)>
<Marked_U22(tt,X) , Marked_activate(X)>
<Marked_U31(tt,N) , Marked_U32(tt,activate(N))>
<Marked_U31(tt,N) , Marked_activate(N)>
<Marked_U32(tt,N) , Marked_activate(N)>
<Marked_U41(tt,N,XS) , Marked_U42(tt,activate(N),activate(XS))>
<Marked_U41(tt,N,XS) , Marked_activate(N)>
<Marked_U41(tt,N,XS) , Marked_activate(XS)>
<Marked_U42(tt,N,XS) , Marked_head(afterNth(activate(N),activate(XS)))>
<Marked_U42(tt,N,XS) , Marked_afterNth(activate(N),activate(XS))>
<Marked_U42(tt,N,XS) , Marked_activate(N)>
<Marked_U42(tt,N,XS) , Marked_activate(XS)>
<Marked_U51(tt,Y) , Marked_U52(tt,activate(Y))>
<Marked_U51(tt,Y) , Marked_activate(Y)>
<Marked_U52(tt,Y) , Marked_activate(Y)>
<Marked_U61(tt,N,X,XS) , Marked_U62(tt,activate(N),activate(X),activate(XS))>
<Marked_U61(tt,N,X,XS) , Marked_activate(N)>
<Marked_U61(tt,N,X,XS) , Marked_activate(X)>
<Marked_U61(tt,N,X,XS) , Marked_activate(XS)>
<Marked_U62(tt,N,X,XS) , Marked_U63(tt,activate(N),activate(X),activate(XS))>
<Marked_U62(tt,N,X,XS) , Marked_activate(N)>
<Marked_U62(tt,N,X,XS) , Marked_activate(X)>
<Marked_U62(tt,N,X,XS) , Marked_activate(XS)>
<Marked_U63(tt,N,X,XS) , Marked_U64(splitAt(activate(N),activate(XS)),
                          activate(X))>
<Marked_U63(tt,N,X,XS) , Marked_splitAt(activate(N),activate(XS))>
<Marked_U63(tt,N,X,XS) , Marked_activate(N)>
<Marked_U63(tt,N,X,XS) , Marked_activate(XS)>
<Marked_U63(tt,N,X,XS) , Marked_activate(X)>
<Marked_U64(pair(YS,ZS),X) , Marked_activate(X)>
<Marked_U71(tt,XS) , Marked_U72(tt,activate(XS))>
<Marked_U71(tt,XS) , Marked_activate(XS)>
<Marked_U72(tt,XS) , Marked_activate(XS)>
<Marked_U81(tt,N,XS) , Marked_U82(tt,activate(N),activate(XS))>
<Marked_U81(tt,N,XS) , Marked_activate(N)>
<Marked_U81(tt,N,XS) , Marked_activate(XS)>
<Marked_U82(tt,N,XS) , Marked_fst(splitAt(activate(N),activate(XS)))>
<Marked_U82(tt,N,XS) , Marked_splitAt(activate(N),activate(XS))>
<Marked_U82(tt,N,XS) , Marked_activate(N)>
<Marked_U82(tt,N,XS) , Marked_activate(XS)>
<Marked_afterNth(N,XS) , Marked_U11(tt,N,XS)>
<Marked_fst(pair(X,Y)) , Marked_U21(tt,X)>
<Marked_head(cons(N,XS)) , Marked_U31(tt,N)>
<Marked_sel(N,XS) , Marked_U41(tt,N,XS)>
<Marked_snd(pair(X,Y)) , Marked_U51(tt,Y)>
<Marked_splitAt(s(N),cons(X,XS)) , Marked_U61(tt,N,X,activate(XS))>
<Marked_splitAt(s(N),cons(X,XS)) , Marked_activate(XS)>
<Marked_tail(cons(N,XS)) , Marked_U71(tt,activate(XS))>
<Marked_tail(cons(N,XS)) , Marked_activate(XS)>
<Marked_take(N,XS) , Marked_U81(tt,N,XS)>
<Marked_activate(n__natsFrom(X)) , Marked_natsFrom(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_splitAt(s(N),cons(X,XS)) , Marked_U61(tt,N,X,activate(XS))> 
      --> <Marked_U61(tt,N,X,XS) , Marked_U62(tt,activate(N),activate(X),
                                    activate(XS))>
  <Marked_U63(tt,N,X,XS) , Marked_splitAt(activate(N),activate(XS))> 
     --> <Marked_splitAt(s(N),cons(X,XS)) , Marked_U61(tt,N,X,activate(XS))>
  <Marked_U62(tt,N,X,XS) , Marked_U63(tt,activate(N),activate(X),activate(XS))> 
     --> <Marked_U63(tt,N,X,XS) , Marked_splitAt(activate(N),activate(XS))>
  <Marked_U61(tt,N,X,XS) , Marked_U62(tt,activate(N),activate(X),activate(XS))> 
     --> <Marked_U62(tt,N,X,XS) , Marked_U63(tt,activate(N),activate(X),
                                   activate(XS))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  U12(tt,N,XS) >= snd(splitAt(activate(N),activate(XS))) ;
  activate(n__natsFrom(X)) >= natsFrom(X) ;
  activate(X) >= X ;
  U11(tt,N,XS) >= U12(tt,activate(N),activate(XS)) ;
  snd(pair(X,Y)) >= U51(tt,Y) ;
  splitAt(s(N),cons(X,XS)) >= U61(tt,N,X,activate(XS)) ;
  splitAt(0,XS) >= pair(nil,XS) ;
  U22(tt,X) >= activate(X) ;
  U21(tt,X) >= U22(tt,activate(X)) ;
  U32(tt,N) >= activate(N) ;
  U31(tt,N) >= U32(tt,activate(N)) ;
  U42(tt,N,XS) >= head(afterNth(activate(N),activate(XS))) ;
  U41(tt,N,XS) >= U42(tt,activate(N),activate(XS)) ;
  head(cons(N,XS)) >= U31(tt,N) ;
  afterNth(N,XS) >= U11(tt,N,XS) ;
  U52(tt,Y) >= activate(Y) ;
  U51(tt,Y) >= U52(tt,activate(Y)) ;
  U62(tt,N,X,XS) >= U63(tt,activate(N),activate(X),activate(XS)) ;
  U61(tt,N,X,XS) >= U62(tt,activate(N),activate(X),activate(XS)) ;
  U63(tt,N,X,XS) >= U64(splitAt(activate(N),activate(XS)),activate(X)) ;
  U64(pair(YS,ZS),X) >= pair(cons(activate(X),YS),ZS) ;
  U72(tt,XS) >= activate(XS) ;
  U71(tt,XS) >= U72(tt,activate(XS)) ;
  U82(tt,N,XS) >= fst(splitAt(activate(N),activate(XS))) ;
  U81(tt,N,XS) >= U82(tt,activate(N),activate(XS)) ;
  fst(pair(X,Y)) >= U21(tt,X) ;
  natsFrom(N) >= cons(N,n__natsFrom(s(N))) ;
  natsFrom(X) >= n__natsFrom(X) ;
  sel(N,XS) >= U41(tt,N,XS) ;
  tail(cons(N,XS)) >= U71(tt,activate(XS)) ;
  take(N,XS) >= U81(tt,N,XS) ;
  Marked_splitAt(s(N),cons(X,XS)) >= Marked_U61(tt,N,X,activate(XS)) ;
  Marked_U61(tt,N,X,XS) >= Marked_U62(tt,activate(N),activate(X),activate(XS)) ;
  Marked_U63(tt,N,X,XS) >= Marked_splitAt(activate(N),activate(XS)) ;
  Marked_U62(tt,N,X,XS) >= Marked_U63(tt,activate(N),activate(X),activate(XS)) ;
 }
 + Disjunctions:{ 
{
  Marked_splitAt(s(N),cons(X,XS)) > Marked_U61(tt,N,X,activate(XS)) ;
 }
{
  Marked_U61(tt,N,X,XS) > Marked_U62(tt,activate(N),activate(X),activate(XS)) ;
 }
{
  Marked_U63(tt,N,X,XS) > Marked_splitAt(activate(N),activate(XS)) ;
 }
{
  Marked_U62(tt,N,X,XS) > Marked_U63(tt,activate(N),activate(X),activate(XS)) ;
 }
 } 
=== 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:
{
  U12(tt,N,XS) >= snd(splitAt(activate(N),activate(XS))) ;
  activate(n__natsFrom(X)) >= natsFrom(X) ;
  activate(X) >= X ;
  U11(tt,N,XS) >= U12(tt,activate(N),activate(XS)) ;
  snd(pair(X,Y)) >= U51(tt,Y) ;
  splitAt(s(N),cons(X,XS)) >= U61(tt,N,X,activate(XS)) ;
  splitAt(0,XS) >= pair(nil,XS) ;
  U22(tt,X) >= activate(X) ;
  U21(tt,X) >= U22(tt,activate(X)) ;
  U32(tt,N) >= activate(N) ;
  U31(tt,N) >= U32(tt,activate(N)) ;
  U42(tt,N,XS) >= head(afterNth(activate(N),activate(XS))) ;
  U41(tt,N,XS) >= U42(tt,activate(N),activate(XS)) ;
  head(cons(N,XS)) >= U31(tt,N) ;
  afterNth(N,XS) >= U11(tt,N,XS) ;
  U52(tt,Y) >= activate(Y) ;
  U51(tt,Y) >= U52(tt,activate(Y)) ;
  U62(tt,N,X,XS) >= U63(tt,activate(N),activate(X),activate(XS)) ;
  U61(tt,N,X,XS) >= U62(tt,activate(N),activate(X),activate(XS)) ;
  U63(tt,N,X,XS) >= U64(splitAt(activate(N),activate(XS)),activate(X)) ;
  U64(pair(YS,ZS),X) >= pair(cons(activate(X),YS),ZS) ;
  U72(tt,XS) >= activate(XS) ;
  U71(tt,XS) >= U72(tt,activate(XS)) ;
  U82(tt,N,XS) >= fst(splitAt(activate(N),activate(XS))) ;
  U81(tt,N,XS) >= U82(tt,activate(N),activate(XS)) ;
  fst(pair(X,Y)) >= U21(tt,X) ;
  natsFrom(N) >= cons(N,n__natsFrom(s(N))) ;
  natsFrom(X) >= n__natsFrom(X) ;
  sel(N,XS) >= U41(tt,N,XS) ;
  tail(cons(N,XS)) >= U71(tt,activate(XS)) ;
  take(N,XS) >= U81(tt,N,XS) ;
  Marked_splitAt(s(N),cons(X,XS)) >= Marked_U61(tt,N,X,activate(XS)) ;
  Marked_U61(tt,N,X,XS) >= Marked_U62(tt,activate(N),activate(X),activate(XS)) ;
  Marked_U63(tt,N,X,XS) > Marked_splitAt(activate(N),activate(XS)) ;
  Marked_U62(tt,N,X,XS) >= Marked_U63(tt,activate(N),activate(X),activate(XS)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  U12(tt,N,XS) >= snd(splitAt(activate(N),activate(XS))) ;
  activate(n__natsFrom(X)) >= natsFrom(X) ;
  activate(X) >= X ;
  U11(tt,N,XS) >= U12(tt,activate(N),activate(XS)) ;
  snd(pair(X,Y)) >= U51(tt,Y) ;
  splitAt(s(N),cons(X,XS)) >= U61(tt,N,X,activate(XS)) ;
  splitAt(0,XS) >= pair(nil,XS) ;
  U22(tt,X) >= activate(X) ;
  U21(tt,X) >= U22(tt,activate(X)) ;
  U32(tt,N) >= activate(N) ;
  U31(tt,N) >= U32(tt,activate(N)) ;
  U42(tt,N,XS) >= head(afterNth(activate(N),activate(XS))) ;
  U41(tt,N,XS) >= U42(tt,activate(N),activate(XS)) ;
  head(cons(N,XS)) >= U31(tt,N) ;
  afterNth(N,XS) >= U11(tt,N,XS) ;
  U52(tt,Y) >= activate(Y) ;
  U51(tt,Y) >= U52(tt,activate(Y)) ;
  U62(tt,N,X,XS) >= U63(tt,activate(N),activate(X),activate(XS)) ;
  U61(tt,N,X,XS) >= U62(tt,activate(N),activate(X),activate(XS)) ;
  U63(tt,N,X,XS) >= U64(splitAt(activate(N),activate(XS)),activate(X)) ;
  U64(pair(YS,ZS),X) >= pair(cons(activate(X),YS),ZS) ;
  U72(tt,XS) >= activate(XS) ;
  U71(tt,XS) >= U72(tt,activate(XS)) ;
  U82(tt,N,XS) >= fst(splitAt(activate(N),activate(XS))) ;
  U81(tt,N,XS) >= U82(tt,activate(N),activate(XS)) ;
  fst(pair(X,Y)) >= U21(tt,X) ;
  natsFrom(N) >= cons(N,n__natsFrom(s(N))) ;
  natsFrom(X) >= n__natsFrom(X) ;
  sel(N,XS) >= U41(tt,N,XS) ;
  tail(cons(N,XS)) >= U71(tt,activate(XS)) ;
  take(N,XS) >= U81(tt,N,XS) ;
  Marked_splitAt(s(N),cons(X,XS)) >= Marked_U61(tt,N,X,activate(XS)) ;
  Marked_U61(tt,N,X,XS) >= Marked_U62(tt,activate(N),activate(X),activate(XS)) ;
  Marked_U63(tt,N,X,XS) > Marked_splitAt(activate(N),activate(XS)) ;
  Marked_U62(tt,N,X,XS) >= Marked_U63(tt,activate(N),activate(X),activate(XS)) ;
 }
 + 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 58.246738 seconds (real time)
Cime Exit Status: 0