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(0(), y) -> 0()
, minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
, if_minus(true(), s(x), y) -> 0()
, if_minus(false(), s(x), y) -> s(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
, if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(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) '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 minimal-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-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^#(0(), y) -> c_4()
, minus^#(s(x), y) -> c_5(if_minus^#(le(s(x), y), s(x), y))
, if_minus^#(true(), s(x), y) -> c_6()
, if_minus^#(false(), s(x), y) -> c_7(minus^#(x, y))
, gcd^#(0(), y) -> c_8(y)
, gcd^#(s(x), 0()) -> c_9(x)
, gcd^#(s(x), s(y)) -> c_10(if_gcd^#(le(y, x), s(x), s(y)))
, if_gcd^#(true(), s(x), s(y)) -> c_11(gcd^#(minus(x, y), s(y)))
, if_gcd^#(false(), s(x), s(y)) -> c_12(gcd^#(minus(y, x), s(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^#(0(), y) -> c_4()
, minus^#(s(x), y) -> c_5(if_minus^#(le(s(x), y), s(x), y))
, if_minus^#(true(), s(x), y) -> c_6()
, if_minus^#(false(), s(x), y) -> c_7(minus^#(x, y))
, gcd^#(0(), y) -> c_8(y)
, gcd^#(s(x), 0()) -> c_9(x)
, gcd^#(s(x), s(y)) -> c_10(if_gcd^#(le(y, x), s(x), s(y)))
, if_gcd^#(true(), s(x), s(y)) -> c_11(gcd^#(minus(x, y), s(y)))
, if_gcd^#(false(), s(x), s(y)) -> c_12(gcd^#(minus(y, x), s(x))) }
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(0(), y) -> 0()
, minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
, if_minus(true(), s(x), y) -> 0()
, if_minus(false(), s(x), y) -> s(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
, if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(x)) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,2,4,6} by applications
of Pre({1,2,4,6}) = {3,5,7,8,9}. 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^#(0(), y) -> c_4()
, 5: minus^#(s(x), y) -> c_5(if_minus^#(le(s(x), y), s(x), y))
, 6: if_minus^#(true(), s(x), y) -> c_6()
, 7: if_minus^#(false(), s(x), y) -> c_7(minus^#(x, y))
, 8: gcd^#(0(), y) -> c_8(y)
, 9: gcd^#(s(x), 0()) -> c_9(x)
, 10: gcd^#(s(x), s(y)) -> c_10(if_gcd^#(le(y, x), s(x), s(y)))
, 11: if_gcd^#(true(), s(x), s(y)) ->
c_11(gcd^#(minus(x, y), s(y)))
, 12: if_gcd^#(false(), s(x), s(y)) ->
c_12(gcd^#(minus(y, x), s(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^#(s(x), y) -> c_5(if_minus^#(le(s(x), y), s(x), y))
, if_minus^#(false(), s(x), y) -> c_7(minus^#(x, y))
, gcd^#(0(), y) -> c_8(y)
, gcd^#(s(x), 0()) -> c_9(x)
, gcd^#(s(x), s(y)) -> c_10(if_gcd^#(le(y, x), s(x), s(y)))
, if_gcd^#(true(), s(x), s(y)) -> c_11(gcd^#(minus(x, y), s(y)))
, if_gcd^#(false(), s(x), s(y)) -> c_12(gcd^#(minus(y, x), s(x))) }
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(0(), y) -> 0()
, minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
, if_minus(true(), s(x), y) -> 0()
, if_minus(false(), s(x), y) -> s(minus(x, y))
, gcd(0(), y) -> y
, gcd(s(x), 0()) -> s(x)
, gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
, if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
, if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(x)) }
Weak DPs:
{ le^#(0(), y) -> c_1()
, le^#(s(x), 0()) -> c_2()
, minus^#(0(), y) -> c_4()
, if_minus^#(true(), s(x), y) -> c_6() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..