Problem Transformed CSR 04 OvConsOS complete GM

Tool CaT

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

stdout:

MAYBE

Problem:
a__zeros() -> cons(0(),zeros())
a__U11(tt(),V1) -> a__U12(a__isNatList(V1))
a__U12(tt()) -> tt()
a__U21(tt(),V1) -> a__U22(a__isNat(V1))
a__U22(tt()) -> tt()
a__U31(tt(),V) -> a__U32(a__isNatList(V))
a__U32(tt()) -> tt()
a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2)
a__U42(tt(),V2) -> a__U43(a__isNatIList(V2))
a__U43(tt()) -> tt()
a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2)
a__U52(tt(),V2) -> a__U53(a__isNatList(V2))
a__U53(tt()) -> tt()
a__U61(tt(),V1,V2) -> a__U62(a__isNat(V1),V2)
a__U62(tt(),V2) -> a__U63(a__isNatIList(V2))
a__U63(tt()) -> tt()
a__U71(tt(),L) -> s(a__length(mark(L)))
a__U81(tt()) -> nil()
a__U91(tt(),IL,M,N) -> cons(mark(N),take(M,IL))
a__and(tt(),X) -> mark(X)
a__isNat(0()) -> tt()
a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1)
a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V)
a__isNatIList(zeros()) -> tt()
a__isNatIList(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2)
a__isNatIListKind(nil()) -> tt()
a__isNatIListKind(zeros()) -> tt()
a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2))
a__isNatIListKind(take(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2))
a__isNatKind(0()) -> tt()
a__isNatKind(length(V1)) -> a__isNatIListKind(V1)
a__isNatKind(s(V1)) -> a__isNatKind(V1)
a__isNatList(nil()) -> tt()
a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2)
a__isNatList(take(V1,V2)) -> a__U61(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2)
a__length(nil()) -> 0()
a__length(cons(N,L)) ->
a__U71(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L)
a__take(0(),IL) -> a__U81(a__and(a__isNatIList(IL),isNatIListKind(IL)))
a__take(s(M),cons(N,IL)) ->
a__U91(a__and(a__and(a__isNatIList(IL),isNatIListKind(IL)),and(and(isNat(M),isNatKind(M)),
and(isNat(N),isNatKind(N)))),
IL,M,N)
mark(zeros()) -> a__zeros()
mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
mark(U12(X)) -> a__U12(mark(X))
mark(isNatList(X)) -> a__isNatList(X)
mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
mark(U22(X)) -> a__U22(mark(X))
mark(isNat(X)) -> a__isNat(X)
mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
mark(U32(X)) -> a__U32(mark(X))
mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
mark(U43(X)) -> a__U43(mark(X))
mark(isNatIList(X)) -> a__isNatIList(X)
mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
mark(U53(X)) -> a__U53(mark(X))
mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3)
mark(U62(X1,X2)) -> a__U62(mark(X1),X2)
mark(U63(X)) -> a__U63(mark(X))
mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(U81(X)) -> a__U81(mark(X))
mark(U91(X1,X2,X3,X4)) -> a__U91(mark(X1),X2,X3,X4)
mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(isNatIListKind(X)) -> a__isNatIListKind(X)
mark(isNatKind(X)) -> a__isNatKind(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(X1,X2) -> U11(X1,X2)
a__U12(X) -> U12(X)
a__isNatList(X) -> isNatList(X)
a__U21(X1,X2) -> U21(X1,X2)
a__U22(X) -> U22(X)
a__isNat(X) -> isNat(X)
a__U31(X1,X2) -> U31(X1,X2)
a__U32(X) -> U32(X)
a__U41(X1,X2,X3) -> U41(X1,X2,X3)
a__U42(X1,X2) -> U42(X1,X2)
a__U43(X) -> U43(X)
a__isNatIList(X) -> isNatIList(X)
a__U51(X1,X2,X3) -> U51(X1,X2,X3)
a__U52(X1,X2) -> U52(X1,X2)
a__U53(X) -> U53(X)
a__U61(X1,X2,X3) -> U61(X1,X2,X3)
a__U62(X1,X2) -> U62(X1,X2)
a__U63(X) -> U63(X)
a__U71(X1,X2) -> U71(X1,X2)
a__length(X) -> length(X)
a__U81(X) -> U81(X)
a__U91(X1,X2,X3,X4) -> U91(X1,X2,X3,X4)
a__take(X1,X2) -> take(X1,X2)
a__and(X1,X2) -> and(X1,X2)
a__isNatIListKind(X) -> isNatIListKind(X)
a__isNatKind(X) -> isNatKind(X)

Proof:
Open

Tool IRC1

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

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS complete 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(), V1) -> a__U12(a__isNatList(V1))
     , a__U12(tt()) -> tt()
     , a__U21(tt(), V1) -> a__U22(a__isNat(V1))
     , a__U22(tt()) -> tt()
     , a__U31(tt(), V) -> a__U32(a__isNatList(V))
     , a__U32(tt()) -> tt()
     , a__U41(tt(), V1, V2) -> a__U42(a__isNat(V1), V2)
     , a__U42(tt(), V2) -> a__U43(a__isNatIList(V2))
     , a__U43(tt()) -> tt()
     , a__U51(tt(), V1, V2) -> a__U52(a__isNat(V1), V2)
     , a__U52(tt(), V2) -> a__U53(a__isNatList(V2))
     , a__U53(tt()) -> tt()
     , a__U61(tt(), V1, V2) -> a__U62(a__isNat(V1), V2)
     , a__U62(tt(), V2) -> a__U63(a__isNatIList(V2))
     , a__U63(tt()) -> tt()
     , a__U71(tt(), L) -> s(a__length(mark(L)))
     , a__U81(tt()) -> nil()
     , a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1)
     , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
     , a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) ->
       a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
     , a__isNatIListKind(nil()) -> tt()
     , a__isNatIListKind(zeros()) -> tt()
     , a__isNatIListKind(cons(V1, V2)) ->
       a__and(a__isNatKind(V1), isNatIListKind(V2))
     , a__isNatIListKind(take(V1, V2)) ->
       a__and(a__isNatKind(V1), isNatIListKind(V2))
     , a__isNatKind(0()) -> tt()
     , a__isNatKind(length(V1)) -> a__isNatIListKind(V1)
     , a__isNatKind(s(V1)) -> a__isNatKind(V1)
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) ->
       a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
     , a__isNatList(take(V1, V2)) ->
       a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) ->
       a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)),
                     and(isNat(N), isNatKind(N))),
              L)
     , a__take(0(), IL) ->
       a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
     , a__take(s(M), cons(N, IL)) ->
       a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)),
                     and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))),
              IL,
              M,
              N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(U12(X)) -> a__U12(mark(X))
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
     , mark(U22(X)) -> a__U22(mark(X))
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
     , mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
     , mark(U43(X)) -> a__U43(mark(X))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
     , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
     , mark(U53(X)) -> a__U53(mark(X))
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
     , mark(U63(X)) -> a__U63(mark(X))
     , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
     , mark(length(X)) -> a__length(mark(X))
     , mark(U81(X)) -> a__U81(mark(X))
     , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNatIListKind(X)) -> a__isNatIListKind(X)
     , mark(isNatKind(X)) -> a__isNatKind(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(X1, X2) -> U11(X1, X2)
     , a__U12(X) -> U12(X)
     , a__isNatList(X) -> isNatList(X)
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U22(X) -> U22(X)
     , a__isNat(X) -> isNat(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
     , a__U42(X1, X2) -> U42(X1, X2)
     , a__U43(X) -> U43(X)
     , a__isNatIList(X) -> isNatIList(X)
     , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U53(X) -> U53(X)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2) -> U62(X1, X2)
     , a__U63(X) -> U63(X)
     , a__U71(X1, X2) -> U71(X1, X2)
     , a__length(X) -> length(X)
     , a__U81(X) -> U81(X)
     , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
     , a__take(X1, X2) -> take(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatIListKind(X) -> isNatIListKind(X)
     , a__isNatKind(X) -> isNatKind(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 GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS complete 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(), V1) -> a__U12(a__isNatList(V1))
     , a__U12(tt()) -> tt()
     , a__U21(tt(), V1) -> a__U22(a__isNat(V1))
     , a__U22(tt()) -> tt()
     , a__U31(tt(), V) -> a__U32(a__isNatList(V))
     , a__U32(tt()) -> tt()
     , a__U41(tt(), V1, V2) -> a__U42(a__isNat(V1), V2)
     , a__U42(tt(), V2) -> a__U43(a__isNatIList(V2))
     , a__U43(tt()) -> tt()
     , a__U51(tt(), V1, V2) -> a__U52(a__isNat(V1), V2)
     , a__U52(tt(), V2) -> a__U53(a__isNatList(V2))
     , a__U53(tt()) -> tt()
     , a__U61(tt(), V1, V2) -> a__U62(a__isNat(V1), V2)
     , a__U62(tt(), V2) -> a__U63(a__isNatIList(V2))
     , a__U63(tt()) -> tt()
     , a__U71(tt(), L) -> s(a__length(mark(L)))
     , a__U81(tt()) -> nil()
     , a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
     , a__and(tt(), X) -> mark(X)
     , a__isNat(0()) -> tt()
     , a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1)
     , a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
     , a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V)
     , a__isNatIList(zeros()) -> tt()
     , a__isNatIList(cons(V1, V2)) ->
       a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
     , a__isNatIListKind(nil()) -> tt()
     , a__isNatIListKind(zeros()) -> tt()
     , a__isNatIListKind(cons(V1, V2)) ->
       a__and(a__isNatKind(V1), isNatIListKind(V2))
     , a__isNatIListKind(take(V1, V2)) ->
       a__and(a__isNatKind(V1), isNatIListKind(V2))
     , a__isNatKind(0()) -> tt()
     , a__isNatKind(length(V1)) -> a__isNatIListKind(V1)
     , a__isNatKind(s(V1)) -> a__isNatKind(V1)
     , a__isNatList(nil()) -> tt()
     , a__isNatList(cons(V1, V2)) ->
       a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
     , a__isNatList(take(V1, V2)) ->
       a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
     , a__length(nil()) -> 0()
     , a__length(cons(N, L)) ->
       a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)),
                     and(isNat(N), isNatKind(N))),
              L)
     , a__take(0(), IL) ->
       a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
     , a__take(s(M), cons(N, IL)) ->
       a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)),
                     and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))),
              IL,
              M,
              N)
     , mark(zeros()) -> a__zeros()
     , mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
     , mark(U12(X)) -> a__U12(mark(X))
     , mark(isNatList(X)) -> a__isNatList(X)
     , mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
     , mark(U22(X)) -> a__U22(mark(X))
     , mark(isNat(X)) -> a__isNat(X)
     , mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
     , mark(U32(X)) -> a__U32(mark(X))
     , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
     , mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
     , mark(U43(X)) -> a__U43(mark(X))
     , mark(isNatIList(X)) -> a__isNatIList(X)
     , mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
     , mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
     , mark(U53(X)) -> a__U53(mark(X))
     , mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
     , mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
     , mark(U63(X)) -> a__U63(mark(X))
     , mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
     , mark(length(X)) -> a__length(mark(X))
     , mark(U81(X)) -> a__U81(mark(X))
     , mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(and(X1, X2)) -> a__and(mark(X1), X2)
     , mark(isNatIListKind(X)) -> a__isNatIListKind(X)
     , mark(isNatKind(X)) -> a__isNatKind(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(X1, X2) -> U11(X1, X2)
     , a__U12(X) -> U12(X)
     , a__isNatList(X) -> isNatList(X)
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U22(X) -> U22(X)
     , a__isNat(X) -> isNat(X)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X) -> U32(X)
     , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
     , a__U42(X1, X2) -> U42(X1, X2)
     , a__U43(X) -> U43(X)
     , a__isNatIList(X) -> isNatIList(X)
     , a__U51(X1, X2, X3) -> U51(X1, X2, X3)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U53(X) -> U53(X)
     , a__U61(X1, X2, X3) -> U61(X1, X2, X3)
     , a__U62(X1, X2) -> U62(X1, X2)
     , a__U63(X) -> U63(X)
     , a__U71(X1, X2) -> U71(X1, X2)
     , a__length(X) -> length(X)
     , a__U81(X) -> U81(X)
     , a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
     , a__take(X1, X2) -> take(X1, X2)
     , a__and(X1, X2) -> and(X1, X2)
     , a__isNatIListKind(X) -> isNatIListKind(X)
     , a__isNatKind(X) -> isNatKind(X)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds