Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runti Compl Inner Rewri 22807 pair #381904375
details
property
value
status
complete
benchmark
jones2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.1958899498 seconds
cpu usage
20.650308203
max memory
2.723885056E9
stage attributes
key
value
output-size
7058
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 33 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: f(empty, l) -> l f(cons(x, k), l) -> g(k, l, cons(x, k)) g(a, b, c) -> f(a, cons(b, c)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: f(empty, z0) -> z0 f(cons(z0, z1), z2) -> g(z1, z2, cons(z0, z1)) g(z0, z1, z2) -> f(z0, cons(z1, z2)) Tuples: F(empty, z0) -> c F(cons(z0, z1), z2) -> c1(G(z1, z2, cons(z0, z1))) G(z0, z1, z2) -> c2(F(z0, cons(z1, z2))) S tuples: F(empty, z0) -> c F(cons(z0, z1), z2) -> c1(G(z1, z2, cons(z0, z1))) G(z0, z1, z2) -> c2(F(z0, cons(z1, z2))) K tuples:none Defined Rule Symbols: f_2, g_3 Defined Pair Symbols: F_2, G_3 Compound Symbols: c, c1_1, c2_1 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: F(empty, z0) -> c ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: f(empty, z0) -> z0 f(cons(z0, z1), z2) -> g(z1, z2, cons(z0, z1)) g(z0, z1, z2) -> f(z0, cons(z1, z2)) Tuples: F(cons(z0, z1), z2) -> c1(G(z1, z2, cons(z0, z1))) G(z0, z1, z2) -> c2(F(z0, cons(z1, z2))) S tuples: F(cons(z0, z1), z2) -> c1(G(z1, z2, cons(z0, z1)))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runti Compl Inner Rewri 22807