MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, reach(x, y, empty(), h) -> false()
, reach(x, y, edge(u, v, i), h) ->
if_reach_1(eq(x, u), x, y, edge(u, v, i), h)
, if_reach_1(true(), x, y, edge(u, v, i), h) ->
if_reach_2(eq(y, v), x, y, edge(u, v, i), h)
, if_reach_1(false(), x, y, edge(u, v, i), h) ->
reach(x, y, i, edge(u, v, h))
, if_reach_2(true(), x, y, edge(u, v, i), h) -> true()
, if_reach_2(false(), x, y, edge(u, v, i), h) ->
or(reach(x, y, i, h), reach(v, y, union(i, h), empty())) }
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) '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) '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:
{ eq^#(0(), 0()) -> c_1()
, eq^#(0(), s(x)) -> c_2()
, eq^#(s(x), 0()) -> c_3()
, eq^#(s(x), s(y)) -> c_4(eq^#(x, y))
, or^#(true(), y) -> c_5()
, or^#(false(), y) -> c_6(y)
, union^#(empty(), h) -> c_7(h)
, union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h))
, reach^#(x, y, empty(), h) -> c_9()
, reach^#(x, y, edge(u, v, i), h) ->
c_10(if_reach_1^#(eq(x, u), x, y, edge(u, v, i), h))
, if_reach_1^#(true(), x, y, edge(u, v, i), h) ->
c_11(if_reach_2^#(eq(y, v), x, y, edge(u, v, i), h))
, if_reach_1^#(false(), x, y, edge(u, v, i), h) ->
c_12(reach^#(x, y, i, edge(u, v, h)))
, if_reach_2^#(true(), x, y, edge(u, v, i), h) -> c_13()
, if_reach_2^#(false(), x, y, edge(u, v, i), h) ->
c_14(or^#(reach(x, y, i, h), reach(v, y, union(i, h), empty()))) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ eq^#(0(), 0()) -> c_1()
, eq^#(0(), s(x)) -> c_2()
, eq^#(s(x), 0()) -> c_3()
, eq^#(s(x), s(y)) -> c_4(eq^#(x, y))
, or^#(true(), y) -> c_5()
, or^#(false(), y) -> c_6(y)
, union^#(empty(), h) -> c_7(h)
, union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h))
, reach^#(x, y, empty(), h) -> c_9()
, reach^#(x, y, edge(u, v, i), h) ->
c_10(if_reach_1^#(eq(x, u), x, y, edge(u, v, i), h))
, if_reach_1^#(true(), x, y, edge(u, v, i), h) ->
c_11(if_reach_2^#(eq(y, v), x, y, edge(u, v, i), h))
, if_reach_1^#(false(), x, y, edge(u, v, i), h) ->
c_12(reach^#(x, y, i, edge(u, v, h)))
, if_reach_2^#(true(), x, y, edge(u, v, i), h) -> c_13()
, if_reach_2^#(false(), x, y, edge(u, v, i), h) ->
c_14(or^#(reach(x, y, i, h), reach(v, y, union(i, h), empty()))) }
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, reach(x, y, empty(), h) -> false()
, reach(x, y, edge(u, v, i), h) ->
if_reach_1(eq(x, u), x, y, edge(u, v, i), h)
, if_reach_1(true(), x, y, edge(u, v, i), h) ->
if_reach_2(eq(y, v), x, y, edge(u, v, i), h)
, if_reach_1(false(), x, y, edge(u, v, i), h) ->
reach(x, y, i, edge(u, v, h))
, if_reach_2(true(), x, y, edge(u, v, i), h) -> true()
, if_reach_2(false(), x, y, edge(u, v, i), h) ->
or(reach(x, y, i, h), reach(v, y, union(i, h), empty())) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,2,3,5,9,13} by
applications of Pre({1,2,3,5,9,13}) = {4,6,7,8,11,12,14}. Here
rules are labeled as follows:
DPs:
{ 1: eq^#(0(), 0()) -> c_1()
, 2: eq^#(0(), s(x)) -> c_2()
, 3: eq^#(s(x), 0()) -> c_3()
, 4: eq^#(s(x), s(y)) -> c_4(eq^#(x, y))
, 5: or^#(true(), y) -> c_5()
, 6: or^#(false(), y) -> c_6(y)
, 7: union^#(empty(), h) -> c_7(h)
, 8: union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h))
, 9: reach^#(x, y, empty(), h) -> c_9()
, 10: reach^#(x, y, edge(u, v, i), h) ->
c_10(if_reach_1^#(eq(x, u), x, y, edge(u, v, i), h))
, 11: if_reach_1^#(true(), x, y, edge(u, v, i), h) ->
c_11(if_reach_2^#(eq(y, v), x, y, edge(u, v, i), h))
, 12: if_reach_1^#(false(), x, y, edge(u, v, i), h) ->
c_12(reach^#(x, y, i, edge(u, v, h)))
, 13: if_reach_2^#(true(), x, y, edge(u, v, i), h) -> c_13()
, 14: if_reach_2^#(false(), x, y, edge(u, v, i), h) ->
c_14(or^#(reach(x, y, i, h), reach(v, y, union(i, h), empty()))) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ eq^#(s(x), s(y)) -> c_4(eq^#(x, y))
, or^#(false(), y) -> c_6(y)
, union^#(empty(), h) -> c_7(h)
, union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h))
, reach^#(x, y, edge(u, v, i), h) ->
c_10(if_reach_1^#(eq(x, u), x, y, edge(u, v, i), h))
, if_reach_1^#(true(), x, y, edge(u, v, i), h) ->
c_11(if_reach_2^#(eq(y, v), x, y, edge(u, v, i), h))
, if_reach_1^#(false(), x, y, edge(u, v, i), h) ->
c_12(reach^#(x, y, i, edge(u, v, h)))
, if_reach_2^#(false(), x, y, edge(u, v, i), h) ->
c_14(or^#(reach(x, y, i, h), reach(v, y, union(i, h), empty()))) }
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, reach(x, y, empty(), h) -> false()
, reach(x, y, edge(u, v, i), h) ->
if_reach_1(eq(x, u), x, y, edge(u, v, i), h)
, if_reach_1(true(), x, y, edge(u, v, i), h) ->
if_reach_2(eq(y, v), x, y, edge(u, v, i), h)
, if_reach_1(false(), x, y, edge(u, v, i), h) ->
reach(x, y, i, edge(u, v, h))
, if_reach_2(true(), x, y, edge(u, v, i), h) -> true()
, if_reach_2(false(), x, y, edge(u, v, i), h) ->
or(reach(x, y, i, h), reach(v, y, union(i, h), empty())) }
Weak DPs:
{ eq^#(0(), 0()) -> c_1()
, eq^#(0(), s(x)) -> c_2()
, eq^#(s(x), 0()) -> c_3()
, or^#(true(), y) -> c_5()
, reach^#(x, y, empty(), h) -> c_9()
, if_reach_2^#(true(), x, y, edge(u, v, i), h) -> c_13() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..