Problem Transformed CSR 04 OvConsOS complete Z

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS complete Z

stdout:

MAYBE

Problem:
zeros() -> cons(0(),n__zeros())
U11(tt(),V1) -> U12(isNatList(activate(V1)))
U12(tt()) -> tt()
U21(tt(),V1) -> U22(isNat(activate(V1)))
U22(tt()) -> tt()
U31(tt(),V) -> U32(isNatList(activate(V)))
U32(tt()) -> tt()
U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2))
U42(tt(),V2) -> U43(isNatIList(activate(V2)))
U43(tt()) -> tt()
U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2))
U52(tt(),V2) -> U53(isNatList(activate(V2)))
U53(tt()) -> tt()
U61(tt(),V1,V2) -> U62(isNat(activate(V1)),activate(V2))
U62(tt(),V2) -> U63(isNatIList(activate(V2)))
U63(tt()) -> tt()
U71(tt(),L) -> s(length(activate(L)))
U81(tt()) -> nil()
U91(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
and(tt(),X) -> activate(X)
isNat(n__0()) -> tt()
isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1))
isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V))
isNatIList(n__zeros()) -> tt()
isNatIList(n__cons(V1,V2)) ->
U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
isNatIListKind(n__nil()) -> tt()
isNatIListKind(n__zeros()) -> tt()
isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
isNatIListKind(n__take(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
isNatKind(n__0()) -> tt()
isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
isNatKind(n__s(V1)) -> isNatKind(activate(V1))
isNatList(n__nil()) -> tt()
isNatList(n__cons(V1,V2)) ->
U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
isNatList(n__take(V1,V2)) ->
U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
length(nil()) -> 0()
length(cons(N,L)) ->
U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and
                                                                    (
                                                                    isNat(N),n__isNatKind(N))),
     activate(L))
take(0(),IL) -> U81(and(isNatIList(IL),n__isNatIListKind(IL)))
take(s(M),cons(N,IL)) ->
U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),
         n__and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N)))),
     activate(IL),M,N)
zeros() -> n__zeros()
take(X1,X2) -> n__take(X1,X2)
0() -> n__0()
length(X) -> n__length(X)
s(X) -> n__s(X)
cons(X1,X2) -> n__cons(X1,X2)
isNatIListKind(X) -> n__isNatIListKind(X)
nil() -> n__nil()
and(X1,X2) -> n__and(X1,X2)
isNatKind(X) -> n__isNatKind(X)
activate(n__zeros()) -> zeros()
activate(n__take(X1,X2)) -> take(X1,X2)
activate(n__0()) -> 0()
activate(n__length(X)) -> length(X)
activate(n__s(X)) -> s(X)
activate(n__cons(X1,X2)) -> cons(X1,X2)
activate(n__isNatIListKind(X)) -> isNatIListKind(X)
activate(n__nil()) -> nil()
activate(n__and(X1,X2)) -> and(X1,X2)
activate(n__isNatKind(X)) -> isNatKind(X)
activate(X) -> X

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS complete Z

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS complete Z

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  zeros() -> cons(0(), n__zeros())
     , U11(tt(), V1) -> U12(isNatList(activate(V1)))
     , U12(tt()) -> tt()
     , U21(tt(), V1) -> U22(isNat(activate(V1)))
     , U22(tt()) -> tt()
     , U31(tt(), V) -> U32(isNatList(activate(V)))
     , U32(tt()) -> tt()
     , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2))
     , U42(tt(), V2) -> U43(isNatIList(activate(V2)))
     , U43(tt()) -> tt()
     , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2))
     , U52(tt(), V2) -> U53(isNatList(activate(V2)))
     , U53(tt()) -> tt()
     , U61(tt(), V1, V2) -> U62(isNat(activate(V1)), activate(V2))
     , U62(tt(), V2) -> U63(isNatIList(activate(V2)))
     , U63(tt()) -> tt()
     , U71(tt(), L) -> s(length(activate(L)))
     , U81(tt()) -> nil()
     , U91(tt(), IL, M, N) ->
       cons(activate(N), n__take(activate(M), activate(IL)))
     , and(tt(), X) -> activate(X)
     , isNat(n__0()) -> tt()
     , isNat(n__length(V1)) ->
       U11(isNatIListKind(activate(V1)), activate(V1))
     , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
     , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V))
     , isNatIList(n__zeros()) -> tt()
     , isNatIList(n__cons(V1, V2)) ->
       U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))),
           activate(V1),
           activate(V2))
     , isNatIListKind(n__nil()) -> tt()
     , isNatIListKind(n__zeros()) -> tt()
     , isNatIListKind(n__cons(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2)))
     , isNatIListKind(n__take(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2)))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
     , isNatKind(n__s(V1)) -> isNatKind(activate(V1))
     , isNatList(n__nil()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))),
           activate(V1),
           activate(V2))
     , isNatList(n__take(V1, V2)) ->
       U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))),
           activate(V1),
           activate(V2))
     , length(nil()) -> 0()
     , length(cons(N, L)) ->
       U71(and(and(isNatList(activate(L)),
                   n__isNatIListKind(activate(L))),
               n__and(isNat(N), n__isNatKind(N))),
           activate(L))
     , take(0(), IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL)))
     , take(s(M), cons(N, IL)) ->
       U91(and(and(isNatIList(activate(IL)),
                   n__isNatIListKind(activate(IL))),
               n__and(and(isNat(M), n__isNatKind(M)),
                      n__and(isNat(N), n__isNatKind(N)))),
           activate(IL),
           M,
           N)
     , zeros() -> n__zeros()
     , take(X1, X2) -> n__take(X1, X2)
     , 0() -> n__0()
     , length(X) -> n__length(X)
     , s(X) -> n__s(X)
     , cons(X1, X2) -> n__cons(X1, X2)
     , isNatIListKind(X) -> n__isNatIListKind(X)
     , nil() -> n__nil()
     , and(X1, X2) -> n__and(X1, X2)
     , isNatKind(X) -> n__isNatKind(X)
     , activate(n__zeros()) -> zeros()
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , activate(n__0()) -> 0()
     , activate(n__length(X)) -> length(X)
     , activate(n__s(X)) -> s(X)
     , activate(n__cons(X1, X2)) -> cons(X1, X2)
     , activate(n__isNatIListKind(X)) -> isNatIListKind(X)
     , activate(n__nil()) -> nil()
     , activate(n__and(X1, X2)) -> and(X1, X2)
     , activate(n__isNatKind(X)) -> isNatKind(X)
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS complete Z

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS complete Z

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  zeros() -> cons(0(), n__zeros())
     , U11(tt(), V1) -> U12(isNatList(activate(V1)))
     , U12(tt()) -> tt()
     , U21(tt(), V1) -> U22(isNat(activate(V1)))
     , U22(tt()) -> tt()
     , U31(tt(), V) -> U32(isNatList(activate(V)))
     , U32(tt()) -> tt()
     , U41(tt(), V1, V2) -> U42(isNat(activate(V1)), activate(V2))
     , U42(tt(), V2) -> U43(isNatIList(activate(V2)))
     , U43(tt()) -> tt()
     , U51(tt(), V1, V2) -> U52(isNat(activate(V1)), activate(V2))
     , U52(tt(), V2) -> U53(isNatList(activate(V2)))
     , U53(tt()) -> tt()
     , U61(tt(), V1, V2) -> U62(isNat(activate(V1)), activate(V2))
     , U62(tt(), V2) -> U63(isNatIList(activate(V2)))
     , U63(tt()) -> tt()
     , U71(tt(), L) -> s(length(activate(L)))
     , U81(tt()) -> nil()
     , U91(tt(), IL, M, N) ->
       cons(activate(N), n__take(activate(M), activate(IL)))
     , and(tt(), X) -> activate(X)
     , isNat(n__0()) -> tt()
     , isNat(n__length(V1)) ->
       U11(isNatIListKind(activate(V1)), activate(V1))
     , isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
     , isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V))
     , isNatIList(n__zeros()) -> tt()
     , isNatIList(n__cons(V1, V2)) ->
       U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))),
           activate(V1),
           activate(V2))
     , isNatIListKind(n__nil()) -> tt()
     , isNatIListKind(n__zeros()) -> tt()
     , isNatIListKind(n__cons(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2)))
     , isNatIListKind(n__take(V1, V2)) ->
       and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2)))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
     , isNatKind(n__s(V1)) -> isNatKind(activate(V1))
     , isNatList(n__nil()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))),
           activate(V1),
           activate(V2))
     , isNatList(n__take(V1, V2)) ->
       U61(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))),
           activate(V1),
           activate(V2))
     , length(nil()) -> 0()
     , length(cons(N, L)) ->
       U71(and(and(isNatList(activate(L)),
                   n__isNatIListKind(activate(L))),
               n__and(isNat(N), n__isNatKind(N))),
           activate(L))
     , take(0(), IL) -> U81(and(isNatIList(IL), n__isNatIListKind(IL)))
     , take(s(M), cons(N, IL)) ->
       U91(and(and(isNatIList(activate(IL)),
                   n__isNatIListKind(activate(IL))),
               n__and(and(isNat(M), n__isNatKind(M)),
                      n__and(isNat(N), n__isNatKind(N)))),
           activate(IL),
           M,
           N)
     , zeros() -> n__zeros()
     , take(X1, X2) -> n__take(X1, X2)
     , 0() -> n__0()
     , length(X) -> n__length(X)
     , s(X) -> n__s(X)
     , cons(X1, X2) -> n__cons(X1, X2)
     , isNatIListKind(X) -> n__isNatIListKind(X)
     , nil() -> n__nil()
     , and(X1, X2) -> n__and(X1, X2)
     , isNatKind(X) -> n__isNatKind(X)
     , activate(n__zeros()) -> zeros()
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , activate(n__0()) -> 0()
     , activate(n__length(X)) -> length(X)
     , activate(n__s(X)) -> s(X)
     , activate(n__cons(X1, X2)) -> cons(X1, X2)
     , activate(n__isNatIListKind(X)) -> isNatIListKind(X)
     , activate(n__nil()) -> nil()
     , activate(n__and(X1, X2)) -> and(X1, X2)
     , activate(n__isNatKind(X)) -> isNatKind(X)
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds