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Runti Compl Inner Rewri 22807 pair #381904572
details
property
value
status
complete
benchmark
add.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n040.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.73494505882 seconds
cpu usage
4.013962411
max memory
2.978816E8
stage attributes
key
value
output-size
5280
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 145 ms] (2) CpxRelTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms] (6) BOUNDS(1, n^1) (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (8) TRS for Loop Detection (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: add0(S(x), x2) -> +(S(0), add0(x2, x)) add0(0, x2) -> x2 The (relative) TRS S consists of the following rules: +(x, S(0)) -> S(x) +(S(0), y) -> S(y) Rewrite Strategy: INNERMOST ---------------------------------------- (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: add0(S(x), x2) -> +(S(0), add0(x2, x)) add0(0, x2) -> x2 The (relative) TRS S consists of the following rules: +(x, S(0)) -> S(x) +(S(0), y) -> S(y) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: add0(S(x), x2) -> +(S(0), add0(x2, x)) add0(0, x2) -> x2 +(x, S(0)) -> S(x) +(S(0), y) -> S(y) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (5) CpxTrsMatchBoundsTAProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 2. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2] transitions: S0(0) -> 0 00() -> 0
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