Problem Strategy outermost added 08 LengthOfFiniteLists complete-noand Z

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 LengthOfFiniteLists complete-noand Z

stdout:

MAYBE

Problem:
zeros() -> cons(0(),n__zeros())
U11(tt(),V1) -> U12(isNatIListKind(activate(V1)),activate(V1))
U12(tt(),V1) -> U13(isNatList(activate(V1)))
U13(tt()) -> tt()
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()) -> tt()
U71(tt()) -> tt()
U81(tt(),V1,V2) -> U82(isNatKind(activate(V1)),activate(V1),activate(V2))
U82(tt(),V1,V2) -> U83(isNatIListKind(activate(V2)),activate(V1),activate(V2))
U83(tt(),V1,V2) -> U84(isNatIListKind(activate(V2)),activate(V1),activate(V2))
U84(tt(),V1,V2) -> U85(isNat(activate(V1)),activate(V2))
U85(tt(),V2) -> U86(isNatList(activate(V2)))
U86(tt()) -> tt()
U91(tt(),L,N) -> U92(isNatIListKind(activate(L)),activate(L),activate(N))
U92(tt(),L,N) -> U93(isNat(activate(N)),activate(L),activate(N))
U93(tt(),L,N) -> U94(isNatKind(activate(N)),activate(L))
U94(tt(),L) -> s(length(activate(L)))
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))
isNatKind(n__0()) -> tt()
isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1)))
isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1)))
isNatList(n__nil()) -> tt()
isNatList(n__cons(V1,V2)) -> U81(isNatKind(activate(V1)),activate(V1),activate(V2))
length(nil()) -> 0()
length(cons(N,L)) -> U91(isNatList(activate(L)),activate(L),N)
zeros() -> n__zeros()
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__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	Strategy outermost added 08 LengthOfFiniteLists complete-noand Z

stdout:

MAYBE
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Strategy outermost added 08 LengthOfFiniteLists 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())
     , U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1))
     , U12(tt(), V1) -> U13(isNatList(activate(V1)))
     , U13(tt()) -> tt()
     , 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()) -> tt()
     , U71(tt()) -> tt()
     , U81(tt(), V1, V2) ->
       U82(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U82(tt(), V1, V2) ->
       U83(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U83(tt(), V1, V2) ->
       U84(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U84(tt(), V1, V2) -> U85(isNat(activate(V1)), activate(V2))
     , U85(tt(), V2) -> U86(isNatList(activate(V2)))
     , U86(tt()) -> tt()
     , U91(tt(), L, N) ->
       U92(isNatIListKind(activate(L)), activate(L), activate(N))
     , U92(tt(), L, N) ->
       U93(isNat(activate(N)), activate(L), activate(N))
     , U93(tt(), L, N) -> U94(isNatKind(activate(N)), activate(L))
     , U94(tt(), L) -> s(length(activate(L)))
     , 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))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1)))
     , isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1)))
     , isNatList(n__nil()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U81(isNatKind(activate(V1)), activate(V1), activate(V2))
     , length(nil()) -> 0()
     , length(cons(N, L)) -> U91(isNatList(activate(L)), activate(L), N)
     , zeros() -> n__zeros()
     , 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__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	Strategy outermost added 08 LengthOfFiniteLists complete-noand Z

stdout:

MAYBE
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Strategy outermost added 08 LengthOfFiniteLists 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())
     , U11(tt(), V1) -> U12(isNatIListKind(activate(V1)), activate(V1))
     , U12(tt(), V1) -> U13(isNatList(activate(V1)))
     , U13(tt()) -> tt()
     , 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()) -> tt()
     , U71(tt()) -> tt()
     , U81(tt(), V1, V2) ->
       U82(isNatKind(activate(V1)), activate(V1), activate(V2))
     , U82(tt(), V1, V2) ->
       U83(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U83(tt(), V1, V2) ->
       U84(isNatIListKind(activate(V2)), activate(V1), activate(V2))
     , U84(tt(), V1, V2) -> U85(isNat(activate(V1)), activate(V2))
     , U85(tt(), V2) -> U86(isNatList(activate(V2)))
     , U86(tt()) -> tt()
     , U91(tt(), L, N) ->
       U92(isNatIListKind(activate(L)), activate(L), activate(N))
     , U92(tt(), L, N) ->
       U93(isNat(activate(N)), activate(L), activate(N))
     , U93(tt(), L, N) -> U94(isNatKind(activate(N)), activate(L))
     , U94(tt(), L) -> s(length(activate(L)))
     , 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))
     , isNatKind(n__0()) -> tt()
     , isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1)))
     , isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1)))
     , isNatList(n__nil()) -> tt()
     , isNatList(n__cons(V1, V2)) ->
       U81(isNatKind(activate(V1)), activate(V1), activate(V2))
     , length(nil()) -> 0()
     , length(cons(N, L)) -> U91(isNatList(activate(L)), activate(L), N)
     , zeros() -> n__zeros()
     , 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__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