Problem Transformed CSR 04 OvConsOS complete-noand Z

Tool CaT

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

stdout:

MAYBE

Problem:
zeros() -> cons(0(),n__zeros())
U101(tt(),V1,V2) -> U102(isNatKind(activate(V1)),activate(V1),activate(V2))
U102(tt(),V1,V2) -> U103(isNatIListKind(activate(V2)),activate(V1),activate(V2))
U103(tt(),V1,V2) -> U104(isNatIListKind(activate(V2)),activate(V1),activate(V2))
U104(tt(),V1,V2) -> U105(isNat(activate(V1)),activate(V2))
U105(tt(),V2) -> U106(isNatIList(activate(V2)))
U106(tt()) -> tt()
U11(tt(),V1) -> U12(isNatIListKind(activate(V1)),activate(V1))
U111(tt(),L,N) -> U112(isNatIListKind(activate(L)),activate(L),activate(N))
U112(tt(),L,N) -> U113(isNat(activate(N)),activate(L),activate(N))
U113(tt(),L,N) -> U114(isNatKind(activate(N)),activate(L))
U114(tt(),L) -> s(length(activate(L)))
U12(tt(),V1) -> U13(isNatList(activate(V1)))
U121(tt(),IL) -> U122(isNatIListKind(activate(IL)))
U122(tt()) -> nil()
U13(tt()) -> tt()
U131(tt(),IL,M,N) -> U132(isNatIListKind(activate(IL)),activate(IL),activate(M),activate(N))
U132(tt(),IL,M,N) -> U133(isNat(activate(M)),activate(IL),activate(M),activate(N))
U133(tt(),IL,M,N) -> U134(isNatKind(activate(M)),activate(IL),activate(M),activate(N))
U134(tt(),IL,M,N) -> U135(isNat(activate(N)),activate(IL),activate(M),activate(N))
U135(tt(),IL,M,N) -> U136(isNatKind(activate(N)),activate(IL),activate(M),activate(N))
U136(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
U22(tt(),V1) -> U23(isNat(activate(V1)))
U23(tt()) -> tt()
U31(tt(),V) -> U32(isNatIListKind(activate(V)),activate(V))
U32(tt(),V) -> U33(isNatList(activate(V)))
U33(tt()) -> tt()
U41(tt(),V1,V2) -> U42(isNatKind(activate(V1)),activate(V1),activate(V2))
U42(tt(),V1,V2) -> U43(isNatIListKind(activate(V2)),activate(V1),activate(V2))
U43(tt(),V1,V2) -> U44(isNatIListKind(activate(V2)),activate(V1),activate(V2))
U44(tt(),V1,V2) -> U45(isNat(activate(V1)),activate(V2))
U45(tt(),V2) -> U46(isNatIList(activate(V2)))
U46(tt()) -> tt()
U51(tt(),V2) -> U52(isNatIListKind(activate(V2)))
U52(tt()) -> tt()
U61(tt(),V2) -> U62(isNatIListKind(activate(V2)))
U62(tt()) -> tt()
U71(tt()) -> tt()
U81(tt()) -> tt()
U91(tt(),V1,V2) -> U92(isNatKind(activate(V1)),activate(V1),activate(V2))
U92(tt(),V1,V2) -> U93(isNatIListKind(activate(V2)),activate(V1),activate(V2))
U93(tt(),V1,V2) -> U94(isNatIListKind(activate(V2)),activate(V1),activate(V2))
U94(tt(),V1,V2) -> U95(isNat(activate(V1)),activate(V2))
U95(tt(),V2) -> U96(isNatList(activate(V2)))
U96(tt()) -> tt()
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(isNatKind(activate(V1)),activate(V1),activate(V2))
isNatIListKind(n__nil()) -> tt()
isNatIListKind(n__zeros()) -> tt()
isNatIListKind(n__cons(V1,V2)) -> U51(isNatKind(activate(V1)),activate(V2))
isNatIListKind(n__take(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2))
isNatKind(n__0()) -> tt()
isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1)))
isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1)))
isNatList(n__nil()) -> tt()
isNatList(n__cons(V1,V2)) -> U91(isNatKind(activate(V1)),activate(V1),activate(V2))
isNatList(n__take(V1,V2)) -> U101(isNatKind(activate(V1)),activate(V1),activate(V2))
length(nil()) -> 0()
length(cons(N,L)) -> U111(isNatList(activate(L)),activate(L),N)
take(0(),IL) -> U121(isNatIList(IL),IL)
take(s(M),cons(N,IL)) -> U131(isNatIList(activate(IL)),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)
nil() -> n__nil()
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__nil()) -> nil()
activate(X) -> X

Proof:
Open

Tool IRC1

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

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS complete-noand 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())
     , U101(tt(), V1, V2) ->
       U102(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U102(tt(), V1, V2) ->
       U103(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U103(tt(), V1, V2) ->
       U104(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2))
     , U105(tt(), V2) -> U106(isNatIList(activate(V2)))
     , U106(tt()) -> tt()
     , U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1))
     , U111(tt(), L, N) ->
       U112(isNatIListKind(activate(L)), activate(L), activate(N))
     , U112(tt(), L, N) ->
       U113(isNat(activate(N)), activate(L), activate(N))
     , U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L))
     , U114(tt(), L) -> s(length(activate(L)))
     , U12(tt(), V1) -> U13(isNatList(activate(V1)))
     , U121(tt(), IL) -> U122(isNatIListKind(activate(IL)))
     , U122(tt()) -> nil()
     , U13(tt()) -> tt()
     , U131(tt(), IL, M, N) ->
       U132(isNatIListKind(activate(IL)),
            activate(IL),
            activate(M),
            activate(N))
     , U132(tt(), IL, M, N) ->
       U133(isNat(activate(M)), activate(IL), activate(M), activate(N))
     , U133(tt(), IL, M, N) ->
       U134(isNatKind(activate(M)),
            activate(IL),
            activate(M),
            activate(N))
     , U134(tt(), IL, M, N) ->
       U135(isNat(activate(N)), activate(IL), activate(M), activate(N))
     , U135(tt(), IL, M, N) ->
       U136(isNatKind(activate(N)),
            activate(IL),
            activate(M),
            activate(N))
     , U136(tt(), IL, M, N) ->
       cons(activate(N), n__take(activate(M), activate(IL)))
     , U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1))
     , U22(tt(), V1) -> U23(isNat(activate(V1)))
     , U23(tt()) -> tt()
     , U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V))
     , U32(tt(), V) -> U33(isNatList(activate(V)))
     , U33(tt()) -> tt()
     , U41(tt(), V1, V2) ->
       U42(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U42(tt(), V1, V2) ->
       U43(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U43(tt(), V1, V2) ->
       U44(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2))
     , U45(tt(), V2) -> U46(isNatIList(activate(V2)))
     , U46(tt()) -> tt()
     , U51(tt(), V2) -> U52(isNatIListKind(activate(V2)))
     , U52(tt()) -> tt()
     , U61(tt(), V2) -> U62(isNatIListKind(activate(V2)))
     , U62(tt()) -> tt()
     , U71(tt()) -> tt()
     , U81(tt()) -> tt()
     , U91(tt(), V1, V2) ->
       U92(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U92(tt(), V1, V2) ->
       U93(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U93(tt(), V1, V2) ->
       U94(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2))
     , U95(tt(), V2) -> U96(isNatList(activate(V2)))
     , U96(tt()) -> tt()
     , 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(isNatKind(activate(V1)), activate(V1), activate(V2))
     , isNatIListKind(n__nil()) -> tt()
     , isNatIListKind(n__zeros()) -> tt()
     , isNatIListKind(n__cons(V1, V2)) ->
       U51(isNatKind(activate(V1)), activate(V2))
     , isNatIListKind(n__take(V1, V2)) ->
       U61(isNatKind(activate(V1)), activate(V2))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1)))
     , isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1)))
     , isNatList(n__nil()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U91(isNatKind(activate(V1)), activate(V1), activate(V2))
     , isNatList(n__take(V1, V2)) ->
       U101(isNatKind(activate(V1)), activate(V1), activate(V2))
     , length(nil()) -> 0()
     , length(cons(N, L)) ->
       U111(isNatList(activate(L)), activate(L), N)
     , take(0(), IL) -> U121(isNatIList(IL), IL)
     , take(s(M), cons(N, IL)) ->
       U131(isNatIList(activate(IL)), 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)
     , nil() -> n__nil()
     , 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__nil()) -> nil()
     , 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-noand Z

stdout:

MAYBE

Tool RC2

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

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  zeros() -> cons(0(), n__zeros())
     , U101(tt(), V1, V2) ->
       U102(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U102(tt(), V1, V2) ->
       U103(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U103(tt(), V1, V2) ->
       U104(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2))
     , U105(tt(), V2) -> U106(isNatIList(activate(V2)))
     , U106(tt()) -> tt()
     , U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1))
     , U111(tt(), L, N) ->
       U112(isNatIListKind(activate(L)), activate(L), activate(N))
     , U112(tt(), L, N) ->
       U113(isNat(activate(N)), activate(L), activate(N))
     , U113(tt(), L, N) -> U114(isNatKind(activate(N)), activate(L))
     , U114(tt(), L) -> s(length(activate(L)))
     , U12(tt(), V1) -> U13(isNatList(activate(V1)))
     , U121(tt(), IL) -> U122(isNatIListKind(activate(IL)))
     , U122(tt()) -> nil()
     , U13(tt()) -> tt()
     , U131(tt(), IL, M, N) ->
       U132(isNatIListKind(activate(IL)),
            activate(IL),
            activate(M),
            activate(N))
     , U132(tt(), IL, M, N) ->
       U133(isNat(activate(M)), activate(IL), activate(M), activate(N))
     , U133(tt(), IL, M, N) ->
       U134(isNatKind(activate(M)),
            activate(IL),
            activate(M),
            activate(N))
     , U134(tt(), IL, M, N) ->
       U135(isNat(activate(N)), activate(IL), activate(M), activate(N))
     , U135(tt(), IL, M, N) ->
       U136(isNatKind(activate(N)),
            activate(IL),
            activate(M),
            activate(N))
     , U136(tt(), IL, M, N) ->
       cons(activate(N), n__take(activate(M), activate(IL)))
     , U21(tt(), V1) -> U22(isNatKind(activate(V1)), activate(V1))
     , U22(tt(), V1) -> U23(isNat(activate(V1)))
     , U23(tt()) -> tt()
     , U31(tt(), V) -> U32(isNatIListKind(activate(V)), activate(V))
     , U32(tt(), V) -> U33(isNatList(activate(V)))
     , U33(tt()) -> tt()
     , U41(tt(), V1, V2) ->
       U42(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U42(tt(), V1, V2) ->
       U43(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U43(tt(), V1, V2) ->
       U44(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2))
     , U45(tt(), V2) -> U46(isNatIList(activate(V2)))
     , U46(tt()) -> tt()
     , U51(tt(), V2) -> U52(isNatIListKind(activate(V2)))
     , U52(tt()) -> tt()
     , U61(tt(), V2) -> U62(isNatIListKind(activate(V2)))
     , U62(tt()) -> tt()
     , U71(tt()) -> tt()
     , U81(tt()) -> tt()
     , U91(tt(), V1, V2) ->
       U92(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U92(tt(), V1, V2) ->
       U93(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U93(tt(), V1, V2) ->
       U94(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2))
     , U95(tt(), V2) -> U96(isNatList(activate(V2)))
     , U96(tt()) -> tt()
     , 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(isNatKind(activate(V1)), activate(V1), activate(V2))
     , isNatIListKind(n__nil()) -> tt()
     , isNatIListKind(n__zeros()) -> tt()
     , isNatIListKind(n__cons(V1, V2)) ->
       U51(isNatKind(activate(V1)), activate(V2))
     , isNatIListKind(n__take(V1, V2)) ->
       U61(isNatKind(activate(V1)), activate(V2))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1)))
     , isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1)))
     , isNatList(n__nil()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U91(isNatKind(activate(V1)), activate(V1), activate(V2))
     , isNatList(n__take(V1, V2)) ->
       U101(isNatKind(activate(V1)), activate(V1), activate(V2))
     , length(nil()) -> 0()
     , length(cons(N, L)) ->
       U111(isNatList(activate(L)), activate(L), N)
     , take(0(), IL) -> U121(isNatIList(IL), IL)
     , take(s(M), cons(N, IL)) ->
       U131(isNatIList(activate(IL)), 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)
     , nil() -> n__nil()
     , 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__nil()) -> nil()
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds