details

property	value
status	complete
benchmark	Ex25_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n030.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.99056220055 seconds
cpu usage	8.90562525
max memory	1.286959104E9

stage attributes

key	value
output-size	7527
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms] (4) BOUNDS(1, n^1) (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTRS (7) SlicingProof [LOWER BOUND(ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 675 ms] (14) proven lower bound (15) LowerBoundPropagationProof [FINISHED, 0 ms] (16) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a__f(f(X)) -> a__c(f(g(f(X)))) a__c(X) -> d(X) a__h(X) -> a__c(d(X)) mark(f(X)) -> a__f(mark(X)) mark(c(X)) -> a__c(X) mark(h(X)) -> a__h(mark(X)) mark(g(X)) -> g(X) mark(d(X)) -> d(X) a__f(X) -> f(X) a__c(X) -> c(X) a__h(X) -> h(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) 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: a__f(f(X)) -> a__c(f(g(f(X)))) a__c(X) -> d(X) a__h(X) -> a__c(d(X)) mark(f(X)) -> a__f(mark(X)) mark(c(X)) -> a__c(X) mark(h(X)) -> a__h(mark(X)) mark(g(X)) -> g(X) mark(d(X)) -> d(X) a__f(X) -> f(X) a__c(X) -> c(X) a__h(X) -> h(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. The certificate found is represented by the following graph. "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] {(1,2,[a__f_1|0, a__c_1|0, a__h_1|0, mark_1|0, f_1|1, d_1|1, c_1|1, h_1|1, a__c_1|1, g_1|1, d_1|2, c_1|2]), (1,3,[a__c_1|1, d_1|2, c_1|2]), (1,6,[a__c_1|1, d_1|2, c_1|2]), (1,7,[a__f_1|1, f_1|2]), (1,8,[a__h_1|1, h_1|2]), (1,9,[a__c_1|2, d_1|3, c_1|3]), (1,10,[a__c_1|2, d_1|3, c_1|3]), (2,2,[f_1|0, g_1|0, d_1|0, c_1|0, h_1|0]), (3,4,[f_1|1]), (4,5,[g_1|1]), (5,2,[f_1|1]), (6,2,[d_1|1]), (7,2,[mark_1|1, a__c_1|1, g_1|1, d_1|1, d_1|2, c_1|2]), (7,7,[a__f_1|1, f_1|2]), (7,8,[a__h_1|1, h_1|2]), (7,9,[a__c_1|2, d_1|3, c_1|3]), (7,10,[a__c_1|2, d_1|3, c_1|3]), (8,2,[mark_1|1, a__c_1|1, g_1|1, d_1|1, d_1|2, c_1|2]), (8,7,[a__f_1|1, f_1|2]), (8,8,[a__h_1|1, h_1|2]), (8,9,[a__c_1|2, d_1|3, c_1|3]), (8,10,[a__c_1|2, d_1|3, c_1|3]), (9,8,[d_1|2]), (10,11,[f_1|2]), (11,12,[g_1|2]), (12,7,[f_1|2])}" ---------------------------------------- (4) BOUNDS(1, n^1) ---------------------------------------- (5) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runti Compl Inner Rewri 22807