interpretations
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
, ifPlus(false(), x, y, z) -> plus(x, z)
, ifPlus(true(), x, y, z) -> y
, eq(x, x) -> true()
, eq(s(x), s(y)) -> eq(x, y)
, eq(s(x), 0()) -> false()
, eq(0(), s(x)) -> false()
, eq(0(), 0()) -> true()
, minus(x, x) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, minus(0(), x) -> 0()
, times(x, y) -> timesIter(x, y, 0())
, timesIter(x, y, z) ->
ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
, ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
, ifTimes(true(), x, y, z, u) -> z
, f() -> g()
, f() -> h() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'matrix interpretation of dimension 3' failed due to the
following reason:
The input cannot be shown compatible
2) 'custom shape polynomial interpretation' failed due to the
following reason:
The input cannot be shown compatible
3) 'custom shape polynomial interpretation' failed due to the
following reason:
The input cannot be shown compatible
4) 'matrix interpretation of dimension 1' failed due to the
following reason:
The input cannot be shown compatible
Arrrr..
lmpo
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
, ifPlus(false(), x, y, z) -> plus(x, z)
, ifPlus(true(), x, y, z) -> y
, minus(s(x), s(y)) -> minus(x, y)
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(x, x) -> 0()
, eq(s(x), s(y)) -> eq(x, y)
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(0(), 0()) -> true()
, eq(x, x) -> true()
, times(x, y) -> timesIter(x, y, 0())
, timesIter(x, y, z) ->
ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
, ifTimes(true(), x, y, z, u) -> z
, ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
, f() -> g()
, f() -> h() }
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:
{ inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
, ifPlus(false(), x, y, z) -> plus(x, z)
, ifPlus(true(), x, y, z) -> y
, minus(s(x), s(y)) -> minus(x, y)
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(x, x) -> 0()
, eq(s(x), s(y)) -> eq(x, y)
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(0(), 0()) -> true()
, eq(x, x) -> true()
, times(x, y) -> timesIter(x, y, 0())
, timesIter(x, y, z) ->
ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
, ifTimes(true(), x, y, z, u) -> z
, ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
, f() -> g()
, f() -> h() }
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:
{ inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
, ifPlus(false(), x, y, z) -> plus(x, z)
, ifPlus(true(), x, y, z) -> y
, minus(s(x), s(y)) -> minus(x, y)
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(x, x) -> 0()
, eq(s(x), s(y)) -> eq(x, y)
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(0(), 0()) -> true()
, eq(x, x) -> true()
, times(x, y) -> timesIter(x, y, 0())
, timesIter(x, y, z) ->
ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
, ifTimes(true(), x, y, z, u) -> z
, ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
, f() -> g()
, f() -> h() }
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:
{ inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
, ifPlus(false(), x, y, z) -> plus(x, z)
, ifPlus(true(), x, y, z) -> y
, minus(s(x), s(y)) -> minus(x, y)
, minus(0(), x) -> 0()
, minus(x, 0()) -> x
, minus(x, x) -> 0()
, eq(s(x), s(y)) -> eq(x, y)
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(0(), 0()) -> true()
, eq(x, x) -> true()
, times(x, y) -> timesIter(x, y, 0())
, timesIter(x, y, z) ->
ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
, ifTimes(true(), x, y, z, u) -> z
, ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
, f() -> g()
, f() -> h() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..