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Runti Compl Inner Rewri 22807 pair #381905281
details
property
value
status
complete
benchmark
Ex2_Luc03b_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.63827300072 seconds
cpu usage
15.47665142
max memory
4.005777408E9
stage attributes
key
value
output-size
13305
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 91 ms] (8) CdtProblem (9) CdtKnowledgeProof [FINISHED, 0 ms] (10) BOUNDS(1, 1) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) 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: fst(0, Z) -> nil fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z))) from(X) -> cons(X, n__from(s(X))) add(0, X) -> X add(s(X), Y) -> s(n__add(activate(X), Y)) len(nil) -> 0 len(cons(X, Z)) -> s(n__len(activate(Z))) fst(X1, X2) -> n__fst(X1, X2) from(X) -> n__from(X) add(X1, X2) -> n__add(X1, X2) len(X) -> n__len(X) activate(n__fst(X1, X2)) -> fst(X1, X2) activate(n__from(X)) -> from(X) activate(n__add(X1, X2)) -> add(X1, X2) activate(n__len(X)) -> len(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: fst(0, z0) -> nil fst(s(z0), cons(z1, z2)) -> cons(z1, n__fst(activate(z0), activate(z2))) fst(z0, z1) -> n__fst(z0, z1) from(z0) -> cons(z0, n__from(s(z0))) from(z0) -> n__from(z0) add(0, z0) -> z0 add(s(z0), z1) -> s(n__add(activate(z0), z1)) add(z0, z1) -> n__add(z0, z1) len(nil) -> 0 len(cons(z0, z1)) -> s(n__len(activate(z1))) len(z0) -> n__len(z0) activate(n__fst(z0, z1)) -> fst(z0, z1) activate(n__from(z0)) -> from(z0) activate(n__add(z0, z1)) -> add(z0, z1) activate(n__len(z0)) -> len(z0) activate(z0) -> z0 Tuples: FST(0, z0) -> c FST(s(z0), cons(z1, z2)) -> c1(ACTIVATE(z0), ACTIVATE(z2)) FST(z0, z1) -> c2 FROM(z0) -> c3 FROM(z0) -> c4 ADD(0, z0) -> c5 ADD(s(z0), z1) -> c6(ACTIVATE(z0)) ADD(z0, z1) -> c7 LEN(nil) -> c8 LEN(cons(z0, z1)) -> c9(ACTIVATE(z1))
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