LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ 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)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..