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	n137.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.82393 seconds
cpu usage	3.87581
user time	3.68255
system time	0.193254
max virtual memory	1.841096E7
max residence set size	299376.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 152 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) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost 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 add00(0, 0) -> 1 +0(0, 0) -> 2 01() -> 4 S1(4) -> 3 add01(0, 0) -> 5 +1(3, 5) -> 1 popout

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all output return to Runtime Complexity: TRS Innermost