interpretations
MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ plus(x, y) -> ifPlus(isZero(x), x, inc(y))
, ifPlus(true(), x, y) -> p(y)
, ifPlus(false(), x, y) -> plus(p(x), y)
, isZero(0()) -> true()
, isZero(s(0())) -> false()
, isZero(s(s(x))) -> isZero(s(x))
, inc(x) -> s(x)
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, p(0()) -> 0()
, p(s(x)) -> x
, p(s(s(x))) -> s(p(s(x)))
, times(x, y) -> timesIter(0(), x, y, 0())
, timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z)
, ifTimes(true(), i, x, y, z) -> z
, ifTimes(false(), i, x, y, z) ->
timesIter(inc(i), x, y, plus(z, y))
, ge(x, 0()) -> true()
, ge(0(), s(y)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, f0(x, y, z) -> d()
, f0(0(), y, x) -> f1(x, y, x)
, f1(x, y, z) -> f2(x, y, z)
, f1(x, y, z) -> c()
, f2(x, 1(), z) -> f0(x, z, z) }
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) 'matrix interpretation of dimension 1' failed due to the
following reason:
The input cannot be shown compatible
4) 'custom shape polynomial interpretation' 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:
{ plus(x, y) -> ifPlus(isZero(x), x, inc(y))
, ifPlus(true(), x, y) -> p(y)
, ifPlus(false(), x, y) -> plus(p(x), y)
, times(x, y) -> timesIter(0(), x, y, 0())
, timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z)
, ifTimes(true(), i, x, y, z) -> z
, ifTimes(false(), i, x, y, z) ->
timesIter(inc(i), x, y, plus(z, y))
, isZero(0()) -> true()
, isZero(s(0())) -> false()
, isZero(s(s(x))) -> isZero(s(x))
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, inc(x) -> s(x)
, p(0()) -> 0()
, p(s(x)) -> x
, p(s(s(x))) -> s(p(s(x)))
, ge(x, 0()) -> true()
, ge(0(), s(y)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, f0(0(), y, x) -> f1(x, y, x)
, f1(x, y, z) -> f2(x, y, z)
, f2(x, 1(), z) -> f0(x, z, z)
, f0(x, y, z) -> d()
, f1(x, y, z) -> c() }
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:
{ plus(x, y) -> ifPlus(isZero(x), x, inc(y))
, ifPlus(true(), x, y) -> p(y)
, ifPlus(false(), x, y) -> plus(p(x), y)
, times(x, y) -> timesIter(0(), x, y, 0())
, timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z)
, ifTimes(true(), i, x, y, z) -> z
, ifTimes(false(), i, x, y, z) ->
timesIter(inc(i), x, y, plus(z, y))
, isZero(0()) -> true()
, isZero(s(0())) -> false()
, isZero(s(s(x))) -> isZero(s(x))
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, inc(x) -> s(x)
, p(0()) -> 0()
, p(s(x)) -> x
, p(s(s(x))) -> s(p(s(x)))
, ge(x, 0()) -> true()
, ge(0(), s(y)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, f0(0(), y, x) -> f1(x, y, x)
, f1(x, y, z) -> f2(x, y, z)
, f2(x, 1(), z) -> f0(x, z, z)
, f0(x, y, z) -> d()
, f1(x, y, z) -> c() }
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:
{ plus(x, y) -> ifPlus(isZero(x), x, inc(y))
, ifPlus(true(), x, y) -> p(y)
, ifPlus(false(), x, y) -> plus(p(x), y)
, times(x, y) -> timesIter(0(), x, y, 0())
, timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z)
, ifTimes(true(), i, x, y, z) -> z
, ifTimes(false(), i, x, y, z) ->
timesIter(inc(i), x, y, plus(z, y))
, isZero(0()) -> true()
, isZero(s(0())) -> false()
, isZero(s(s(x))) -> isZero(s(x))
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, inc(x) -> s(x)
, p(0()) -> 0()
, p(s(x)) -> x
, p(s(s(x))) -> s(p(s(x)))
, ge(x, 0()) -> true()
, ge(0(), s(y)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, f0(0(), y, x) -> f1(x, y, x)
, f1(x, y, z) -> f2(x, y, z)
, f2(x, 1(), z) -> f0(x, z, z)
, f0(x, y, z) -> d()
, f1(x, y, z) -> c() }
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:
{ plus(x, y) -> ifPlus(isZero(x), x, inc(y))
, ifPlus(true(), x, y) -> p(y)
, ifPlus(false(), x, y) -> plus(p(x), y)
, times(x, y) -> timesIter(0(), x, y, 0())
, timesIter(i, x, y, z) -> ifTimes(ge(i, x), i, x, y, z)
, ifTimes(true(), i, x, y, z) -> z
, ifTimes(false(), i, x, y, z) ->
timesIter(inc(i), x, y, plus(z, y))
, isZero(0()) -> true()
, isZero(s(0())) -> false()
, isZero(s(s(x))) -> isZero(s(x))
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, inc(x) -> s(x)
, p(0()) -> 0()
, p(s(x)) -> x
, p(s(s(x))) -> s(p(s(x)))
, ge(x, 0()) -> true()
, ge(0(), s(y)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, f0(0(), y, x) -> f1(x, y, x)
, f1(x, y, z) -> f2(x, y, z)
, f2(x, 1(), z) -> f0(x, z, z)
, f0(x, y, z) -> d()
, f1(x, y, z) -> c() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The input cannot be shown compatible
Arrrr..