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Runti Compl Inner Rewri 22807 pair #381904471
details
property
value
status
complete
benchmark
double.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.571564913 seconds
cpu usage
1103.88328436
max memory
1.2937326592E10
stage attributes
key
value
output-size
11696
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 564 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 295 ms] (14) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: double(x) -> permute(x, x, a) permute(x, y, a) -> permute(isZero(x), x, b) permute(false, x, b) -> permute(ack(x, x), p(x), c) permute(true, x, b) -> 0 permute(y, x, c) -> s(s(permute(x, y, a))) p(0) -> 0 p(s(x)) -> x ack(0, x) -> plus(x, s(0)) ack(s(x), 0) -> ack(x, s(0)) ack(s(x), s(y)) -> ack(x, ack(s(x), y)) plus(0, y) -> y plus(s(x), y) -> plus(x, s(y)) plus(x, s(s(y))) -> s(plus(s(x), y)) plus(x, s(0)) -> s(x) plus(x, 0) -> x isZero(0) -> true isZero(s(x)) -> false S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: double(x) -> permute(x, x, a) permute(x, y, a) -> permute(isZero(x), x, b) permute(false, x, b) -> permute(ack(x, x), p(x), c) permute(true, x, b) -> 0' permute(y, x, c) -> s(s(permute(x, y, a))) p(0') -> 0' p(s(x)) -> x ack(0', x) -> plus(x, s(0')) ack(s(x), 0') -> ack(x, s(0')) ack(s(x), s(y)) -> ack(x, ack(s(x), y)) plus(0', y) -> y plus(s(x), y) -> plus(x, s(y)) plus(x, s(s(y))) -> s(plus(s(x), y)) plus(x, s(0')) -> s(x) plus(x, 0') -> x isZero(0') -> true isZero(s(x)) -> false S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation:
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