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Runti Compl Inner Rewri 22807 pair #381904217
details
property
value
status
complete
benchmark
append.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.3418200016 seconds
cpu usage
11.684332911
max memory
2.617683968E9
stage attributes
key
value
output-size
8531
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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)), 69 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: is_empty(nil) -> true is_empty(cons(x, l)) -> false hd(cons(x, l)) -> x tl(cons(x, l)) -> l append(l1, l2) -> ifappend(l1, l2, l1) ifappend(l1, l2, nil) -> l2 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: is_empty(nil) -> true is_empty(cons(z0, z1)) -> false hd(cons(z0, z1)) -> z0 tl(cons(z0, z1)) -> z1 append(z0, z1) -> ifappend(z0, z1, z0) ifappend(z0, z1, nil) -> z1 ifappend(z0, z1, cons(z2, z3)) -> cons(z2, append(z3, z1)) Tuples: IS_EMPTY(nil) -> c IS_EMPTY(cons(z0, z1)) -> c1 HD(cons(z0, z1)) -> c2 TL(cons(z0, z1)) -> c3 APPEND(z0, z1) -> c4(IFAPPEND(z0, z1, z0)) IFAPPEND(z0, z1, nil) -> c5 IFAPPEND(z0, z1, cons(z2, z3)) -> c6(APPEND(z3, z1)) S tuples: IS_EMPTY(nil) -> c IS_EMPTY(cons(z0, z1)) -> c1 HD(cons(z0, z1)) -> c2 TL(cons(z0, z1)) -> c3 APPEND(z0, z1) -> c4(IFAPPEND(z0, z1, z0)) IFAPPEND(z0, z1, nil) -> c5 IFAPPEND(z0, z1, cons(z2, z3)) -> c6(APPEND(z3, z1)) K tuples:none Defined Rule Symbols: is_empty_1, hd_1, tl_1, append_2, ifappend_3 Defined Pair Symbols: IS_EMPTY_1, HD_1, TL_1, APPEND_2, IFAPPEND_3 Compound Symbols: c, c1, c2, c3, c4_1, c5, c6_1 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: IFAPPEND(z0, z1, nil) -> c5
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