Problem Transformed CSR 04 Ex4 DLMMU04 GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

stdout:

MAYBE

Problem:
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)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex4 DLMMU04 GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  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)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex4 DLMMU04 GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex4 DLMMU04 GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  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)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds