Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Derivational Complexity: TRS Innermost pair #487108104
details
property
value
status
complete
benchmark
toList.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.746 seconds
cpu usage
1131.94
user time
1120.75
system time
11.1907
max virtual memory
3.774186E7
max residence set size
1.4849872E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 485 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: isEmpty(empty) -> true isEmpty(node(l, x, r)) -> false left(empty) -> empty left(node(l, x, r)) -> l right(empty) -> empty right(node(l, x, r)) -> r elem(node(l, x, r)) -> x append(nil, x) -> cons(x, nil) append(cons(y, ys), x) -> cons(y, append(ys, x)) listify(n, xs) -> if(isEmpty(n), isEmpty(left(n)), right(n), node(left(left(n)), elem(left(n)), node(right(left(n)), elem(n), right(n))), xs, append(xs, n)) if(true, b, n, m, xs, ys) -> xs if(false, false, n, m, xs, ys) -> listify(m, xs) if(false, true, n, m, xs, ys) -> listify(n, ys) toList(n) -> listify(n, nil) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(empty) -> empty encArg(true) -> true encArg(node(x_1, x_2, x_3)) -> node(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(false) -> false encArg(nil) -> nil encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(y) -> y encArg(cons_isEmpty(x_1)) -> isEmpty(encArg(x_1)) encArg(cons_left(x_1)) -> left(encArg(x_1)) encArg(cons_right(x_1)) -> right(encArg(x_1)) encArg(cons_elem(x_1)) -> elem(encArg(x_1)) encArg(cons_append(x_1, x_2)) -> append(encArg(x_1), encArg(x_2)) encArg(cons_listify(x_1, x_2)) -> listify(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3, x_4, x_5, x_6)) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6)) encArg(cons_toList(x_1)) -> toList(encArg(x_1)) encode_isEmpty(x_1) -> isEmpty(encArg(x_1)) encode_empty -> empty encode_true -> true encode_node(x_1, x_2, x_3) -> node(encArg(x_1), encArg(x_2), encArg(x_3)) encode_false -> false encode_left(x_1) -> left(encArg(x_1)) encode_right(x_1) -> right(encArg(x_1)) encode_elem(x_1) -> elem(encArg(x_1)) encode_append(x_1, x_2) -> append(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_y -> y encode_listify(x_1, x_2) -> listify(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3, x_4, x_5, x_6) -> if(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4), encArg(x_5), encArg(x_6)) encode_toList(x_1) -> toList(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: isEmpty(empty) -> true isEmpty(node(l, x, r)) -> false left(empty) -> empty left(node(l, x, r)) -> l right(empty) -> empty right(node(l, x, r)) -> r
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Derivational Complexity: TRS Innermost