LMPO

Execution Time (secs)	0.198
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__and(tt(), T) -> mark(T)
     , a__isNatIList(IL) -> a__isNatList(IL)
     , a__isNat(0()) -> tt()
     , a__isNat(s(N)) -> a__isNat(N)
     , a__isNat(length(L)) -> a__isNatList(L)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
     , a__isNatList(take(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__zeros() -> cons(0(), zeros())
     , a__take(0(), IL) -> a__uTake1(a__isNatIList(IL))
     , a__uTake1(tt()) -> nil()
     , a__take(s(M), cons(N, IL)) ->
       a__uTake2(a__and(a__isNat(M),
                        a__and(a__isNat(N), a__isNatIList(IL))),
                 M,
                 N,
                 IL)
     , a__uTake2(tt(), M, N, IL) -> cons(mark(N), take(M, IL))
     , a__length(cons(N, L)) ->
       a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
     , a__uLength(tt(), L) -> s(a__length(mark(L)))
     , mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(length(X)) -> a__length(mark(X))
     , mark(zeros()) -> a__zeros()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(uTake1(X)) -> a__uTake1(mark(X))
     , mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
     , mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
     , mark(tt()) -> tt()
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(nil()) -> nil()
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNat(X) -> isNat(X)
     , a__length(X) -> length(X)
     , a__zeros() -> zeros()
     , a__take(X1, X2) -> take(X1, X2)
     , a__uTake1(X) -> uTake1(X)
     , a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
     , a__uLength(X1, X2) -> uLength(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.505
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__and(tt(), T) -> mark(T)
     , a__isNatIList(IL) -> a__isNatList(IL)
     , a__isNat(0()) -> tt()
     , a__isNat(s(N)) -> a__isNat(N)
     , a__isNat(length(L)) -> a__isNatList(L)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
     , a__isNatList(take(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__zeros() -> cons(0(), zeros())
     , a__take(0(), IL) -> a__uTake1(a__isNatIList(IL))
     , a__uTake1(tt()) -> nil()
     , a__take(s(M), cons(N, IL)) ->
       a__uTake2(a__and(a__isNat(M),
                        a__and(a__isNat(N), a__isNatIList(IL))),
                 M,
                 N,
                 IL)
     , a__uTake2(tt(), M, N, IL) -> cons(mark(N), take(M, IL))
     , a__length(cons(N, L)) ->
       a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
     , a__uLength(tt(), L) -> s(a__length(mark(L)))
     , mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(length(X)) -> a__length(mark(X))
     , mark(zeros()) -> a__zeros()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(uTake1(X)) -> a__uTake1(mark(X))
     , mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
     , mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
     , mark(tt()) -> tt()
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(nil()) -> nil()
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNat(X) -> isNat(X)
     , a__length(X) -> length(X)
     , a__zeros() -> zeros()
     , a__take(X1, X2) -> take(X1, X2)
     , a__uTake1(X) -> uTake1(X)
     , a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
     , a__uLength(X1, X2) -> uLength(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.311
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__and(tt(), T) -> mark(T)
     , a__isNatIList(IL) -> a__isNatList(IL)
     , a__isNat(0()) -> tt()
     , a__isNat(s(N)) -> a__isNat(N)
     , a__isNat(length(L)) -> a__isNatList(L)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
     , a__isNatList(take(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__zeros() -> cons(0(), zeros())
     , a__take(0(), IL) -> a__uTake1(a__isNatIList(IL))
     , a__uTake1(tt()) -> nil()
     , a__take(s(M), cons(N, IL)) ->
       a__uTake2(a__and(a__isNat(M),
                        a__and(a__isNat(N), a__isNatIList(IL))),
                 M,
                 N,
                 IL)
     , a__uTake2(tt(), M, N, IL) -> cons(mark(N), take(M, IL))
     , a__length(cons(N, L)) ->
       a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
     , a__uLength(tt(), L) -> s(a__length(mark(L)))
     , mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(length(X)) -> a__length(mark(X))
     , mark(zeros()) -> a__zeros()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(uTake1(X)) -> a__uTake1(mark(X))
     , mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
     , mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
     , mark(tt()) -> tt()
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(nil()) -> nil()
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNat(X) -> isNat(X)
     , a__length(X) -> length(X)
     , a__zeros() -> zeros()
     , a__take(X1, X2) -> take(X1, X2)
     , a__uTake1(X) -> uTake1(X)
     , a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
     , a__uLength(X1, X2) -> uLength(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.200
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__and(tt(), T) -> mark(T)
     , a__isNatIList(IL) -> a__isNatList(IL)
     , a__isNat(0()) -> tt()
     , a__isNat(s(N)) -> a__isNat(N)
     , a__isNat(length(L)) -> a__isNatList(L)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
     , a__isNatList(take(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__zeros() -> cons(0(), zeros())
     , a__take(0(), IL) -> a__uTake1(a__isNatIList(IL))
     , a__uTake1(tt()) -> nil()
     , a__take(s(M), cons(N, IL)) ->
       a__uTake2(a__and(a__isNat(M),
                        a__and(a__isNat(N), a__isNatIList(IL))),
                 M,
                 N,
                 IL)
     , a__uTake2(tt(), M, N, IL) -> cons(mark(N), take(M, IL))
     , a__length(cons(N, L)) ->
       a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
     , a__uLength(tt(), L) -> s(a__length(mark(L)))
     , mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(length(X)) -> a__length(mark(X))
     , mark(zeros()) -> a__zeros()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(uTake1(X)) -> a__uTake1(mark(X))
     , mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
     , mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
     , mark(tt()) -> tt()
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(nil()) -> nil()
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNat(X) -> isNat(X)
     , a__length(X) -> length(X)
     , a__zeros() -> zeros()
     , a__take(X1, X2) -> take(X1, X2)
     , a__uTake1(X) -> uTake1(X)
     , a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
     , a__uLength(X1, X2) -> uLength(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.173
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__and(tt(), T) -> mark(T)
     , a__isNatIList(IL) -> a__isNatList(IL)
     , a__isNat(0()) -> tt()
     , a__isNat(s(N)) -> a__isNat(N)
     , a__isNat(length(L)) -> a__isNatList(L)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
     , a__isNatList(take(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__zeros() -> cons(0(), zeros())
     , a__take(0(), IL) -> a__uTake1(a__isNatIList(IL))
     , a__uTake1(tt()) -> nil()
     , a__take(s(M), cons(N, IL)) ->
       a__uTake2(a__and(a__isNat(M),
                        a__and(a__isNat(N), a__isNatIList(IL))),
                 M,
                 N,
                 IL)
     , a__uTake2(tt(), M, N, IL) -> cons(mark(N), take(M, IL))
     , a__length(cons(N, L)) ->
       a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
     , a__uLength(tt(), L) -> s(a__length(mark(L)))
     , mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(length(X)) -> a__length(mark(X))
     , mark(zeros()) -> a__zeros()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(uTake1(X)) -> a__uTake1(mark(X))
     , mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
     , mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
     , mark(tt()) -> tt()
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(nil()) -> nil()
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNat(X) -> isNat(X)
     , a__length(X) -> length(X)
     , a__zeros() -> zeros()
     , a__take(X1, X2) -> take(X1, X2)
     , a__uTake1(X) -> uTake1(X)
     , a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
     , a__uLength(X1, X2) -> uLength(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.312
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__and(tt(), T) -> mark(T)
     , a__isNatIList(IL) -> a__isNatList(IL)
     , a__isNat(0()) -> tt()
     , a__isNat(s(N)) -> a__isNat(N)
     , a__isNat(length(L)) -> a__isNatList(L)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
     , a__isNatList(take(N, IL)) ->
       a__and(a__isNat(N), a__isNatIList(IL))
     , a__zeros() -> cons(0(), zeros())
     , a__take(0(), IL) -> a__uTake1(a__isNatIList(IL))
     , a__uTake1(tt()) -> nil()
     , a__take(s(M), cons(N, IL)) ->
       a__uTake2(a__and(a__isNat(M),
                        a__and(a__isNat(N), a__isNatIList(IL))),
                 M,
                 N,
                 IL)
     , a__uTake2(tt(), M, N, IL) -> cons(mark(N), take(M, IL))
     , a__length(cons(N, L)) ->
       a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
     , a__uLength(tt(), L) -> s(a__length(mark(L)))
     , mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(length(X)) -> a__length(mark(X))
     , mark(zeros()) -> a__zeros()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(uTake1(X)) -> a__uTake1(mark(X))
     , mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
     , mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
     , mark(tt()) -> tt()
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(nil()) -> nil()
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatIList(X) -> isNatIList(X)
     , a__isNatList(X) -> isNatList(X)
     , a__isNat(X) -> isNat(X)
     , a__length(X) -> length(X)
     , a__zeros() -> zeros()
     , a__take(X1, X2) -> take(X1, X2)
     , a__uTake1(X) -> uTake1(X)
     , a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
     , a__uLength(X1, X2) -> uLength(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 Ex4 DLMMU04 GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)