interpretations
TIMEOUT
We are left with following problem, upon which TcT provides the
certificate TIMEOUT.
Strict Trs:
{ a__U11(X1, X2) -> U11(X1, X2)
, a__U11(tt(), N) -> mark(N)
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(isNat(X)) -> a__isNat(X)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U31(X)) -> a__U31(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__plus(X1, X2) -> plus(X1, X2)
, a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N)
, a__plus(N, 0()) -> a__U11(a__isNat(N), N)
, a__U31(X) -> U31(X)
, a__U31(tt()) -> 0()
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U41(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__x(X1, X2) -> x(X1, X2)
, a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N)
, a__x(N, 0()) -> a__U31(a__isNat(N))
, a__and(X1, X2) -> and(X1, X2)
, a__and(tt(), X) -> mark(X)
, a__isNat(X) -> isNat(X)
, a__isNat(s(V1)) -> a__isNat(V1)
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) }
Obligation:
innermost runtime complexity
Answer:
TIMEOUT
Computation stopped due to timeout after 20.0 seconds.
Arrrr..
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ a__U11(tt(), N) -> mark(N)
, a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U31(tt()) -> 0()
, a__U41(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__and(tt(), X) -> mark(X)
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__isNat(s(V1)) -> a__isNat(V1)
, a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__plus(N, 0()) -> a__U11(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N)
, a__x(N, 0()) -> a__U31(a__isNat(N))
, a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U31(X)) -> a__U31(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2) -> U11(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U31(X) -> U31(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNat(X) -> isNat(X) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
mpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ a__U11(tt(), N) -> mark(N)
, a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U31(tt()) -> 0()
, a__U41(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__and(tt(), X) -> mark(X)
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__isNat(s(V1)) -> a__isNat(V1)
, a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__plus(N, 0()) -> a__U11(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N)
, a__x(N, 0()) -> a__U31(a__isNat(N))
, a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U31(X)) -> a__U31(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2) -> U11(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U31(X) -> U31(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNat(X) -> isNat(X) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ a__U11(tt(), N) -> mark(N)
, a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U31(tt()) -> 0()
, a__U41(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__and(tt(), X) -> mark(X)
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__isNat(s(V1)) -> a__isNat(V1)
, a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__plus(N, 0()) -> a__U11(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N)
, a__x(N, 0()) -> a__U31(a__isNat(N))
, a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U31(X)) -> a__U31(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2) -> U11(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U31(X) -> U31(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNat(X) -> isNat(X) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..
popstar-ps
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ a__U11(tt(), N) -> mark(N)
, a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M)))
, a__U31(tt()) -> 0()
, a__U41(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
, a__and(tt(), X) -> mark(X)
, a__isNat(0()) -> tt()
, a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__isNat(s(V1)) -> a__isNat(V1)
, a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2))
, a__plus(N, 0()) -> a__U11(a__isNat(N), N)
, a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N)
, a__x(N, 0()) -> a__U31(a__isNat(N))
, a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
, mark(U31(X)) -> a__U31(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(tt()) -> tt()
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, a__U11(X1, X2) -> U11(X1, X2)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__plus(X1, X2) -> plus(X1, X2)
, a__U31(X) -> U31(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__x(X1, X2) -> x(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNat(X) -> isNat(X) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..