MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ active(zeros()) -> mark(cons(0(), zeros()))
, active(cons(X1, X2)) -> cons(active(X1), X2)
, active(U11(X1, X2)) -> U11(active(X1), X2)
, active(U11(tt(), V1)) -> mark(U12(isNatList(V1)))
, active(U12(X)) -> U12(active(X))
, active(U12(tt())) -> mark(tt())
, active(isNatList(cons(V1, V2))) ->
mark(U51(and(isNatKind(V1), isNatIListKind(V2)), V1, V2))
, active(isNatList(nil())) -> mark(tt())
, active(U21(X1, X2)) -> U21(active(X1), X2)
, active(U21(tt(), V1)) -> mark(U22(isNat(V1)))
, active(U22(X)) -> U22(active(X))
, active(U22(tt())) -> mark(tt())
, active(isNat(0())) -> mark(tt())
, active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
, active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1), V1))
, active(U31(X1, X2)) -> U31(active(X1), X2)
, active(U31(tt(), V)) -> mark(U32(isNatList(V)))
, active(U32(X)) -> U32(active(X))
, active(U32(tt())) -> mark(tt())
, active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
, active(U41(tt(), V1, V2)) -> mark(U42(isNat(V1), V2))
, active(U42(X1, X2)) -> U42(active(X1), X2)
, active(U42(tt(), V2)) -> mark(U43(isNatIList(V2)))
, active(U43(X)) -> U43(active(X))
, active(U43(tt())) -> mark(tt())
, active(isNatIList(V)) -> mark(U31(isNatIListKind(V), V))
, active(isNatIList(zeros())) -> mark(tt())
, active(isNatIList(cons(V1, V2))) ->
mark(U41(and(isNatKind(V1), isNatIListKind(V2)), V1, V2))
, active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3)
, active(U51(tt(), V1, V2)) -> mark(U52(isNat(V1), V2))
, active(U52(X1, X2)) -> U52(active(X1), X2)
, active(U52(tt(), V2)) -> mark(U53(isNatList(V2)))
, active(U53(X)) -> U53(active(X))
, active(U53(tt())) -> mark(tt())
, active(U61(X1, X2)) -> U61(active(X1), X2)
, active(U61(tt(), L)) -> mark(s(length(L)))
, active(s(X)) -> s(active(X))
, active(length(X)) -> length(active(X))
, active(length(cons(N, L))) ->
mark(U61(and(and(isNatList(L), isNatIListKind(L)),
and(isNat(N), isNatKind(N))),
L))
, active(length(nil())) -> mark(0())
, active(and(X1, X2)) -> and(active(X1), X2)
, active(and(tt(), X)) -> mark(X)
, active(isNatIListKind(zeros())) -> mark(tt())
, active(isNatIListKind(cons(V1, V2))) ->
mark(and(isNatKind(V1), isNatIListKind(V2)))
, active(isNatIListKind(nil())) -> mark(tt())
, active(isNatKind(0())) -> mark(tt())
, active(isNatKind(s(V1))) -> mark(isNatKind(V1))
, active(isNatKind(length(V1))) -> mark(isNatIListKind(V1))
, cons(mark(X1), X2) -> mark(cons(X1, X2))
, cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
, U11(mark(X1), X2) -> mark(U11(X1, X2))
, U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
, U12(mark(X)) -> mark(U12(X))
, U12(ok(X)) -> ok(U12(X))
, isNatList(ok(X)) -> ok(isNatList(X))
, U21(mark(X1), X2) -> mark(U21(X1, X2))
, U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
, U22(mark(X)) -> mark(U22(X))
, U22(ok(X)) -> ok(U22(X))
, isNat(ok(X)) -> ok(isNat(X))
, U31(mark(X1), X2) -> mark(U31(X1, X2))
, U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
, U32(mark(X)) -> mark(U32(X))
, U32(ok(X)) -> ok(U32(X))
, U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
, U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
, U42(mark(X1), X2) -> mark(U42(X1, X2))
, U42(ok(X1), ok(X2)) -> ok(U42(X1, X2))
, U43(mark(X)) -> mark(U43(X))
, U43(ok(X)) -> ok(U43(X))
, isNatIList(ok(X)) -> ok(isNatIList(X))
, U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3))
, U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3))
, U52(mark(X1), X2) -> mark(U52(X1, X2))
, U52(ok(X1), ok(X2)) -> ok(U52(X1, X2))
, U53(mark(X)) -> mark(U53(X))
, U53(ok(X)) -> ok(U53(X))
, U61(mark(X1), X2) -> mark(U61(X1, X2))
, U61(ok(X1), ok(X2)) -> ok(U61(X1, X2))
, s(mark(X)) -> mark(s(X))
, s(ok(X)) -> ok(s(X))
, length(mark(X)) -> mark(length(X))
, length(ok(X)) -> ok(length(X))
, and(mark(X1), X2) -> mark(and(X1, X2))
, and(ok(X1), ok(X2)) -> ok(and(X1, X2))
, isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
, isNatKind(ok(X)) -> ok(isNatKind(X))
, proper(zeros()) -> ok(zeros())
, proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
, proper(0()) -> ok(0())
, proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
, proper(tt()) -> ok(tt())
, proper(U12(X)) -> U12(proper(X))
, proper(isNatList(X)) -> isNatList(proper(X))
, proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
, proper(U22(X)) -> U22(proper(X))
, proper(isNat(X)) -> isNat(proper(X))
, proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
, proper(U32(X)) -> U32(proper(X))
, proper(U41(X1, X2, X3)) ->
U41(proper(X1), proper(X2), proper(X3))
, proper(U42(X1, X2)) -> U42(proper(X1), proper(X2))
, proper(U43(X)) -> U43(proper(X))
, proper(isNatIList(X)) -> isNatIList(proper(X))
, proper(U51(X1, X2, X3)) ->
U51(proper(X1), proper(X2), proper(X3))
, proper(U52(X1, X2)) -> U52(proper(X1), proper(X2))
, proper(U53(X)) -> U53(proper(X))
, proper(U61(X1, X2)) -> U61(proper(X1), proper(X2))
, proper(s(X)) -> s(proper(X))
, proper(length(X)) -> length(proper(X))
, proper(and(X1, X2)) -> and(proper(X1), proper(X2))
, proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
, proper(isNatKind(X)) -> isNatKind(proper(X))
, proper(nil()) -> ok(nil())
, top(mark(X)) -> top(proper(X))
, top(ok(X)) -> top(active(X)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
following reason:
Computation stopped due to timeout after 60.0 seconds.
2) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
failed due to the following reason:
Computation stopped due to timeout after 30.0 seconds.
2) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
to the following reason:
The input cannot be shown compatible
2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
following reason:
The input cannot be shown compatible
3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Bounds with minimal-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
Arrrr..