Problem Transformed CSR 04 LengthOfFiniteLists nokinds noand GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LengthOfFiniteLists nokinds noand GM

stdout:

MAYBE

Problem:
a__zeros() -> cons(0(),zeros())
a__U11(tt()) -> tt()
a__U21(tt()) -> tt()
a__U31(tt()) -> tt()
a__U41(tt(),V2) -> a__U42(a__isNatIList(V2))
a__U42(tt()) -> tt()
a__U51(tt(),V2) -> a__U52(a__isNatList(V2))
a__U52(tt()) -> tt()
a__U61(tt(),L,N) -> a__U62(a__isNat(N),L)
a__U62(tt(),L) -> s(a__length(mark(L)))
a__isNat(0()) -> tt()
a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
a__isNat(s(V1)) -> a__U21(a__isNat(V1))
a__isNatIList(V) -> a__U31(a__isNatList(V))
a__isNatIList(zeros()) -> tt()
a__isNatIList(cons(V1,V2)) -> a__U41(a__isNat(V1),V2)
a__isNatList(nil()) -> tt()
a__isNatList(cons(V1,V2)) -> a__U51(a__isNat(V1),V2)
a__length(nil()) -> 0()
a__length(cons(N,L)) -> a__U61(a__isNatList(L),L,N)
mark(zeros()) -> a__zeros()
mark(U11(X)) -> a__U11(mark(X))
mark(U21(X)) -> a__U21(mark(X))
mark(U31(X)) -> a__U31(mark(X))
mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
mark(U42(X)) -> a__U42(mark(X))
mark(isNatIList(X)) -> a__isNatIList(X)
mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
mark(U52(X)) -> a__U52(mark(X))
mark(isNatList(X)) -> a__isNatList(X)
mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3)
mark(U62(X1,X2)) -> a__U62(mark(X1),X2)
mark(isNat(X)) -> a__isNat(X)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(0()) -> 0()
mark(tt()) -> tt()
mark(s(X)) -> s(mark(X))
mark(nil()) -> nil()
a__zeros() -> zeros()
a__U11(X) -> U11(X)
a__U21(X) -> U21(X)
a__U31(X) -> U31(X)
a__U41(X1,X2) -> U41(X1,X2)
a__U42(X) -> U42(X)
a__isNatIList(X) -> isNatIList(X)
a__U51(X1,X2) -> U51(X1,X2)
a__U52(X) -> U52(X)
a__isNatList(X) -> isNatList(X)
a__U61(X1,X2,X3) -> U61(X1,X2,X3)
a__U62(X1,X2) -> U62(X1,X2)
a__isNat(X) -> isNat(X)
a__length(X) -> length(X)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LengthOfFiniteLists nokinds noand GM

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LengthOfFiniteLists nokinds noand GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__zeros() -> cons(0(), zeros())
     , a__U11(tt()) -> tt()
     , a__U21(tt()) -> tt()
     , a__U31(tt()) -> tt()
     , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2))
     , a__U42(tt()) -> tt()
     , a__U51(tt(), V2) -> a__U52(a__isNatList(V2))
     , a__U52(tt()) -> tt()
     , a__U61(tt(), L, N) -> a__U62(a__isNat(N), L)
     , a__U62(tt(), L) -> s(a__length(mark(L)))
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNatIList(V) -> a__U31(a__isNatList(V))
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2)
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2)
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) -> a__U61(a__isNatList(L), L, N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X)) -> a__U11(mark(X))
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X)) -> a__U31(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U42(X)) -> a__U42(mark(X))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X)) -> a__U52(mark(X))
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(length(X)) -> a__length(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , a__zeros() -> zeros()
     , a__U11(X) -> U11(X)
     , a__U21(X) -> U21(X)
     , a__U31(X) -> U31(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U42(X) -> U42(X)
     , a__isNatIList(X) -> isNatIList(X)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X) -> U52(X)
     , a__isNatList(X) -> isNatList(X)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2) -> U62(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__length(X) -> length(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LengthOfFiniteLists nokinds noand GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LengthOfFiniteLists nokinds noand GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a__zeros() -> cons(0(), zeros())
     , a__U11(tt()) -> tt()
     , a__U21(tt()) -> tt()
     , a__U31(tt()) -> tt()
     , a__U41(tt(), V2) -> a__U42(a__isNatIList(V2))
     , a__U42(tt()) -> tt()
     , a__U51(tt(), V2) -> a__U52(a__isNatList(V2))
     , a__U52(tt()) -> tt()
     , a__U61(tt(), L, N) -> a__U62(a__isNat(N), L)
     , a__U62(tt(), L) -> s(a__length(mark(L)))
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
     , a__isNat(s(V1)) -> a__U21(a__isNat(V1))
     , a__isNatIList(V) -> a__U31(a__isNatList(V))
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2)
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2)
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) -> a__U61(a__isNatList(L), L, N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X)) -> a__U11(mark(X))
     , mark(U21(X)) -> a__U21(mark(X))
     , mark(U31(X)) -> a__U31(mark(X))
     , mark(U41(X1, X2)) -> a__U41(mark(X1), X2)
     , mark(U42(X)) -> a__U42(mark(X))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
     , mark(U52(X)) -> a__U52(mark(X))
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
     , mark(isNat(X)) -> a__isNat(X)
     , mark(length(X)) -> a__length(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(tt()) -> tt()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , a__zeros() -> zeros()
     , a__U11(X) -> U11(X)
     , a__U21(X) -> U21(X)
     , a__U31(X) -> U31(X)
     , a__U41(X1, X2) -> U41(X1, X2)
     , a__U42(X) -> U42(X)
     , a__isNatIList(X) -> isNatIList(X)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X) -> U52(X)
     , a__isNatList(X) -> isNatList(X)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2) -> U62(X1, X2)
     , a__isNat(X) -> isNat(X)
     , a__length(X) -> length(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds