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Runti Compl Inner Rewri 22807 pair #381904709
details
property
value
status
complete
benchmark
Ex6_9_Luc02c_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.38291597366 seconds
cpu usage
14.070107605
max memory
3.45649152E9
stage attributes
key
value
output-size
11856
starexec-result
WORST_CASE(Omega(n^1), O(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), O(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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 52 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 5 ms] (14) CdtProblem (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (16) BOUNDS(1, 1) (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (18) TRS for Loop Detection (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) TRS for Loop Detection ---------------------------------------- (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: 2nd(cons1(X, cons(Y, Z))) -> Y 2nd(cons(X, X1)) -> 2nd(cons1(X, activate(X1))) from(X) -> cons(X, n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: 2nd(cons1(z0, cons(z1, z2))) -> z1 2nd(cons(z0, z1)) -> 2nd(cons1(z0, activate(z1))) from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(z0) -> z0 Tuples: 2ND(cons1(z0, cons(z1, z2))) -> c 2ND(cons(z0, z1)) -> c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1)) FROM(z0) -> c2 FROM(z0) -> c3 S(z0) -> c4 ACTIVATE(n__from(z0)) -> c5(FROM(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c6(S(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c7 S tuples: 2ND(cons1(z0, cons(z1, z2))) -> c 2ND(cons(z0, z1)) -> c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1)) FROM(z0) -> c2 FROM(z0) -> c3 S(z0) -> c4 ACTIVATE(n__from(z0)) -> c5(FROM(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c6(S(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c7 K tuples:none Defined Rule Symbols: 2nd_1, from_1, s_1, activate_1
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