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, 0()) -> x
, minus(0(), s(y)) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, mod(x, s(y)) -> help(x, s(y), 0())
, mod(s(x), 0()) -> 0()
, help(x, s(y), c) -> if(le(c, x), x, s(y), c)
, if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y)))
, if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) }
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:
Computation stopped due to timeout after 30.0 seconds.
2) '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) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) '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
2) '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
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, 0()) -> c_4(x)
, minus^#(0(), s(y)) -> c_5()
, minus^#(s(x), s(y)) -> c_6(minus^#(x, y))
, plus^#(x, 0()) -> c_7(x)
, plus^#(x, s(y)) -> c_8(plus^#(x, y))
, mod^#(x, s(y)) -> c_9(help^#(x, s(y), 0()))
, mod^#(s(x), 0()) -> c_10()
, help^#(x, s(y), c) -> c_11(if^#(le(c, x), x, s(y), c))
, if^#(true(), x, s(y), c) -> c_12(help^#(x, s(y), plus(c, s(y))))
, if^#(false(), x, s(y), c) -> c_13(minus^#(x, minus(c, s(y)))) }
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, 0()) -> c_4(x)
, minus^#(0(), s(y)) -> c_5()
, minus^#(s(x), s(y)) -> c_6(minus^#(x, y))
, plus^#(x, 0()) -> c_7(x)
, plus^#(x, s(y)) -> c_8(plus^#(x, y))
, mod^#(x, s(y)) -> c_9(help^#(x, s(y), 0()))
, mod^#(s(x), 0()) -> c_10()
, help^#(x, s(y), c) -> c_11(if^#(le(c, x), x, s(y), c))
, if^#(true(), x, s(y), c) -> c_12(help^#(x, s(y), plus(c, s(y))))
, if^#(false(), x, s(y), c) -> c_13(minus^#(x, minus(c, s(y)))) }
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), s(y)) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, mod(x, s(y)) -> help(x, s(y), 0())
, mod(s(x), 0()) -> 0()
, help(x, s(y), c) -> if(le(c, x), x, s(y), c)
, if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y)))
, if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,2,5,10} by applications
of Pre({1,2,5,10}) = {3,4,6,7,13}. 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, 0()) -> c_4(x)
, 5: minus^#(0(), s(y)) -> c_5()
, 6: minus^#(s(x), s(y)) -> c_6(minus^#(x, y))
, 7: plus^#(x, 0()) -> c_7(x)
, 8: plus^#(x, s(y)) -> c_8(plus^#(x, y))
, 9: mod^#(x, s(y)) -> c_9(help^#(x, s(y), 0()))
, 10: mod^#(s(x), 0()) -> c_10()
, 11: help^#(x, s(y), c) -> c_11(if^#(le(c, x), x, s(y), c))
, 12: if^#(true(), x, s(y), c) ->
c_12(help^#(x, s(y), plus(c, s(y))))
, 13: if^#(false(), x, s(y), c) ->
c_13(minus^#(x, minus(c, s(y)))) }
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_4(x)
, minus^#(s(x), s(y)) -> c_6(minus^#(x, y))
, plus^#(x, 0()) -> c_7(x)
, plus^#(x, s(y)) -> c_8(plus^#(x, y))
, mod^#(x, s(y)) -> c_9(help^#(x, s(y), 0()))
, help^#(x, s(y), c) -> c_11(if^#(le(c, x), x, s(y), c))
, if^#(true(), x, s(y), c) -> c_12(help^#(x, s(y), plus(c, s(y))))
, if^#(false(), x, s(y), c) -> c_13(minus^#(x, minus(c, s(y)))) }
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), s(y)) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, mod(x, s(y)) -> help(x, s(y), 0())
, mod(s(x), 0()) -> 0()
, help(x, s(y), c) -> if(le(c, x), x, s(y), c)
, if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y)))
, if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) }
Weak DPs:
{ le^#(0(), y) -> c_1()
, le^#(s(x), 0()) -> c_2()
, minus^#(0(), s(y)) -> c_5()
, mod^#(s(x), 0()) -> c_10() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..