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Runti Compl Inner Rewri 22807 pair #381904233
details
property
value
status
complete
benchmark
sat.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
TCT_12
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.025541067 seconds
cpu usage
375.438743464
max memory
6.513106944E9
stage attributes
key
value
output-size
33260
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
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), O(n^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 2 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (10) CdtProblem (11) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 3 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 86 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 55 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 38 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 28 ms] (22) CdtProblem (23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (24) BOUNDS(1, 1) (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (26) TRS for Loop Detection (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (28) BEST (29) proven lower bound (30) LowerBoundPropagationProof [FINISHED, 0 ms] (31) BOUNDS(n^1, INF) (32) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: if(true, t, e) -> t if(false, t, e) -> e member(x, nil) -> false member(x, cons(y, ys)) -> if(eq(x, y), true, member(x, ys)) eq(nil, nil) -> true eq(O(x), 0(y)) -> eq(x, y) eq(0(x), 1(y)) -> false eq(1(x), 0(y)) -> false eq(1(x), 1(y)) -> eq(x, y) negate(0(x)) -> 1(x) negate(1(x)) -> 0(x) choice(cons(x, xs)) -> x choice(cons(x, xs)) -> choice(xs) guess(nil) -> nil guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf)) verify(nil) -> true verify(cons(l, ls)) -> if(member(negate(l), ls), false, verify(ls)) sat(cnf) -> satck(cnf, guess(cnf)) satck(cnf, assign) -> if(verify(assign), assign, unsat) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: if(true, z0, z1) -> z0 if(false, z0, z1) -> z1 member(z0, nil) -> false member(z0, cons(z1, z2)) -> if(eq(z0, z1), true, member(z0, z2)) eq(nil, nil) -> true eq(O(z0), 0(z1)) -> eq(z0, z1) eq(0(z0), 1(z1)) -> false eq(1(z0), 0(z1)) -> false eq(1(z0), 1(z1)) -> eq(z0, z1) negate(0(z0)) -> 1(z0)
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