MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, x) -> 0()
, minus(x, 0()) -> x
, minus(0(), x) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y))
, if_mod(true(), b, x, y, z) -> divByZeroError()
, if_mod(false(), true(), x, y, z) -> mod(z, y)
, if_mod(false(), false(), x, y, z) -> x }
Obligation:
runtime complexity
Answer:
MAYBE
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:
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) 'WithProblem' failed due to the following reason:
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) 'Fastest' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem' failed due to the following reason:
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) 'WithProblem' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
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) 'WithProblem' failed due to the following reason:
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) 'WithProblem' failed due to the following reason:
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) 'WithProblem' 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) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
to the following reason:
The processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
following reason:
The processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
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 perSymbol-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with minimal-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
due to the following reason:
We add the following weak dependency pairs:
Strict DPs:
{ le^#(0(), y) -> c_1()
, le^#(s(x), 0()) -> c_2()
, le^#(s(x), s(y)) -> c_3(le^#(x, y))
, minus^#(x, x) -> c_4()
, minus^#(x, 0()) -> c_5(x)
, minus^#(0(), x) -> c_6()
, minus^#(s(x), s(y)) -> c_7(minus^#(x, y))
, isZero^#(0()) -> c_8()
, isZero^#(s(x)) -> c_9()
, mod^#(x, y) ->
c_10(if_mod^#(isZero(y), le(y, x), x, y, minus(x, y)))
, if_mod^#(true(), b, x, y, z) -> c_11()
, if_mod^#(false(), true(), x, y, z) -> c_12(mod^#(z, y))
, if_mod^#(false(), false(), x, y, z) -> c_13(x) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ le^#(0(), y) -> c_1()
, le^#(s(x), 0()) -> c_2()
, le^#(s(x), s(y)) -> c_3(le^#(x, y))
, minus^#(x, x) -> c_4()
, minus^#(x, 0()) -> c_5(x)
, minus^#(0(), x) -> c_6()
, minus^#(s(x), s(y)) -> c_7(minus^#(x, y))
, isZero^#(0()) -> c_8()
, isZero^#(s(x)) -> c_9()
, mod^#(x, y) ->
c_10(if_mod^#(isZero(y), le(y, x), x, y, minus(x, y)))
, if_mod^#(true(), b, x, y, z) -> c_11()
, if_mod^#(false(), true(), x, y, z) -> c_12(mod^#(z, y))
, if_mod^#(false(), false(), x, y, z) -> c_13(x) }
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, x) -> 0()
, minus(x, 0()) -> x
, minus(0(), x) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y))
, if_mod(true(), b, x, y, z) -> divByZeroError()
, if_mod(false(), true(), x, y, z) -> mod(z, y)
, if_mod(false(), false(), x, y, z) -> x }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,2,4,6,8,9,11} by
applications of Pre({1,2,4,6,8,9,11}) = {3,5,7,10,13}. Here rules
are labeled as follows:
DPs:
{ 1: le^#(0(), y) -> c_1()
, 2: le^#(s(x), 0()) -> c_2()
, 3: le^#(s(x), s(y)) -> c_3(le^#(x, y))
, 4: minus^#(x, x) -> c_4()
, 5: minus^#(x, 0()) -> c_5(x)
, 6: minus^#(0(), x) -> c_6()
, 7: minus^#(s(x), s(y)) -> c_7(minus^#(x, y))
, 8: isZero^#(0()) -> c_8()
, 9: isZero^#(s(x)) -> c_9()
, 10: mod^#(x, y) ->
c_10(if_mod^#(isZero(y), le(y, x), x, y, minus(x, y)))
, 11: if_mod^#(true(), b, x, y, z) -> c_11()
, 12: if_mod^#(false(), true(), x, y, z) -> c_12(mod^#(z, y))
, 13: if_mod^#(false(), false(), x, y, z) -> c_13(x) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ le^#(s(x), s(y)) -> c_3(le^#(x, y))
, minus^#(x, 0()) -> c_5(x)
, minus^#(s(x), s(y)) -> c_7(minus^#(x, y))
, mod^#(x, y) ->
c_10(if_mod^#(isZero(y), le(y, x), x, y, minus(x, y)))
, if_mod^#(false(), true(), x, y, z) -> c_12(mod^#(z, y))
, if_mod^#(false(), false(), x, y, z) -> c_13(x) }
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, x) -> 0()
, minus(x, 0()) -> x
, minus(0(), x) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y))
, if_mod(true(), b, x, y, z) -> divByZeroError()
, if_mod(false(), true(), x, y, z) -> mod(z, y)
, if_mod(false(), false(), x, y, z) -> x }
Weak DPs:
{ le^#(0(), y) -> c_1()
, le^#(s(x), 0()) -> c_2()
, minus^#(x, x) -> c_4()
, minus^#(0(), x) -> c_6()
, isZero^#(0()) -> c_8()
, isZero^#(s(x)) -> c_9()
, if_mod^#(true(), b, x, y, z) -> c_11() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..