LMPO

Execution Time (secs)	0.348
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__zeros() -> cons(0(), zeros())
     , a__U11(tt(), L) -> s(a__length(mark(L)))
     , a__U21(tt()) -> nil()
     , a__U31(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__isNatList(V1)
     , a__isNat(s(V1)) -> a__isNat(V1)
     , a__isNatIList(V) -> a__isNatList(V)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2))
     , a__isNatList(take(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) ->
       a__U11(a__and(a__isNatList(L), isNat(N)), L)
     , a__take(0(), IL) -> a__U21(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U31(a__and(a__isNatIList(IL), and(isNat(M), isNat(N))),
              IL,
              M,
              N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(length(X)) -> a__length(mark(X))
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2, X3, X4)) -> a__U31(mark(X1), X2, X3, X4)
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , a__zeros() -> zeros()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__length(X) -> length(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2, X3, X4) -> U31(X1, X2, X3, X4)
     , a__take(X1, X2) -> take(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNatIList(X) -> isNatIList(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.571
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__zeros() -> cons(0(), zeros())
     , a__U11(tt(), L) -> s(a__length(mark(L)))
     , a__U21(tt()) -> nil()
     , a__U31(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__isNatList(V1)
     , a__isNat(s(V1)) -> a__isNat(V1)
     , a__isNatIList(V) -> a__isNatList(V)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2))
     , a__isNatList(take(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) ->
       a__U11(a__and(a__isNatList(L), isNat(N)), L)
     , a__take(0(), IL) -> a__U21(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U31(a__and(a__isNatIList(IL), and(isNat(M), isNat(N))),
              IL,
              M,
              N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(length(X)) -> a__length(mark(X))
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2, X3, X4)) -> a__U31(mark(X1), X2, X3, X4)
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , a__zeros() -> zeros()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__length(X) -> length(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2, X3, X4) -> U31(X1, X2, X3, X4)
     , a__take(X1, X2) -> take(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNatIList(X) -> isNatIList(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.396
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__zeros() -> cons(0(), zeros())
     , a__U11(tt(), L) -> s(a__length(mark(L)))
     , a__U21(tt()) -> nil()
     , a__U31(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__isNatList(V1)
     , a__isNat(s(V1)) -> a__isNat(V1)
     , a__isNatIList(V) -> a__isNatList(V)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2))
     , a__isNatList(take(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) ->
       a__U11(a__and(a__isNatList(L), isNat(N)), L)
     , a__take(0(), IL) -> a__U21(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U31(a__and(a__isNatIList(IL), and(isNat(M), isNat(N))),
              IL,
              M,
              N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(length(X)) -> a__length(mark(X))
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2, X3, X4)) -> a__U31(mark(X1), X2, X3, X4)
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , a__zeros() -> zeros()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__length(X) -> length(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2, X3, X4) -> U31(X1, X2, X3, X4)
     , a__take(X1, X2) -> take(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNatIList(X) -> isNatIList(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.209
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__zeros() -> cons(0(), zeros())
     , a__U11(tt(), L) -> s(a__length(mark(L)))
     , a__U21(tt()) -> nil()
     , a__U31(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__isNatList(V1)
     , a__isNat(s(V1)) -> a__isNat(V1)
     , a__isNatIList(V) -> a__isNatList(V)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2))
     , a__isNatList(take(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) ->
       a__U11(a__and(a__isNatList(L), isNat(N)), L)
     , a__take(0(), IL) -> a__U21(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U31(a__and(a__isNatIList(IL), and(isNat(M), isNat(N))),
              IL,
              M,
              N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(length(X)) -> a__length(mark(X))
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2, X3, X4)) -> a__U31(mark(X1), X2, X3, X4)
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , a__zeros() -> zeros()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__length(X) -> length(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2, X3, X4) -> U31(X1, X2, X3, X4)
     , a__take(X1, X2) -> take(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNatIList(X) -> isNatIList(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.349
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__zeros() -> cons(0(), zeros())
     , a__U11(tt(), L) -> s(a__length(mark(L)))
     , a__U21(tt()) -> nil()
     , a__U31(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__isNatList(V1)
     , a__isNat(s(V1)) -> a__isNat(V1)
     , a__isNatIList(V) -> a__isNatList(V)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2))
     , a__isNatList(take(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) ->
       a__U11(a__and(a__isNatList(L), isNat(N)), L)
     , a__take(0(), IL) -> a__U21(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U31(a__and(a__isNatIList(IL), and(isNat(M), isNat(N))),
              IL,
              M,
              N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(length(X)) -> a__length(mark(X))
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2, X3, X4)) -> a__U31(mark(X1), X2, X3, X4)
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , a__zeros() -> zeros()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__length(X) -> length(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2, X3, X4) -> U31(X1, X2, X3, X4)
     , a__take(X1, X2) -> take(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNatIList(X) -> isNatIList(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.275
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__zeros() -> cons(0(), zeros())
     , a__U11(tt(), L) -> s(a__length(mark(L)))
     , a__U21(tt()) -> nil()
     , a__U31(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__isNatList(V1)
     , a__isNat(s(V1)) -> a__isNat(V1)
     , a__isNatIList(V) -> a__isNatList(V)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2))
     , a__isNatList(take(V1, V2)) ->
       a__and(a__isNat(V1), isNatIList(V2))
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) ->
       a__U11(a__and(a__isNatList(L), isNat(N)), L)
     , a__take(0(), IL) -> a__U21(a__isNatIList(IL))
     , a__take(s(M), cons(N, IL)) ->
       a__U31(a__and(a__isNatIList(IL), and(isNat(M), isNat(N))),
              IL,
              M,
              N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(length(X)) -> a__length(mark(X))
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X1, X2, X3, X4)) -> a__U31(mark(X1), X2, X3, X4)
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , a__zeros() -> zeros()
     , a__U11(X1, X2) -> U11(X1, X2)
     , a__length(X) -> length(X)
     , a__U21(X) -> U21(X)
     , a__U31(X1, X2, X3, X4) -> U31(X1, X2, X3, X4)
     , a__take(X1, X2) -> take(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNatIList(X) -> isNatIList(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 OvConsOS nokinds GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)