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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313598
details
property
value
status
complete
benchmark
4.05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.948 seconds
cpu usage
352.559
user time
345.594
system time
6.96465
max virtual memory
1.8947704E7
max residence set size
9820172.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
352.37/291.88 WORST_CASE(Omega(n^1), O(n^2)) 352.37/291.89 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 352.37/291.89 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 352.37/291.89 352.37/291.89 352.37/291.89 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 352.37/291.89 352.37/291.89 (0) CpxTRS 352.37/291.89 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 352.37/291.89 (2) CdtProblem 352.37/291.89 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 352.37/291.89 (4) CdtProblem 352.37/291.89 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 352.37/291.89 (6) CdtProblem 352.37/291.89 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 25 ms] 352.37/291.89 (8) CdtProblem 352.37/291.89 (9) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 352.37/291.89 (10) BOUNDS(1, 1) 352.37/291.89 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 352.37/291.89 (12) TRS for Loop Detection 352.37/291.89 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 352.37/291.89 (14) BEST 352.37/291.89 (15) proven lower bound 352.37/291.89 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 352.37/291.89 (17) BOUNDS(n^1, INF) 352.37/291.89 (18) TRS for Loop Detection 352.37/291.89 352.37/291.89 352.37/291.89 ---------------------------------------- 352.37/291.89 352.37/291.89 (0) 352.37/291.89 Obligation: 352.37/291.89 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 352.37/291.89 352.37/291.89 352.37/291.89 The TRS R consists of the following rules: 352.37/291.89 352.37/291.89 *(x, +(y, z)) -> +(*(x, y), *(x, z)) 352.37/291.89 *(+(x, y), z) -> +(*(x, z), *(y, z)) 352.37/291.89 *(x, 1) -> x 352.37/291.89 *(1, y) -> y 352.37/291.89 352.37/291.89 S is empty. 352.37/291.89 Rewrite Strategy: INNERMOST 352.37/291.89 ---------------------------------------- 352.37/291.89 352.37/291.89 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 352.37/291.89 Converted Cpx (relative) TRS to CDT 352.37/291.89 ---------------------------------------- 352.37/291.89 352.37/291.89 (2) 352.37/291.89 Obligation: 352.37/291.89 Complexity Dependency Tuples Problem 352.37/291.89 352.37/291.89 Rules: 352.37/291.89 *(z0, +(z1, z2)) -> +(*(z0, z1), *(z0, z2)) 352.37/291.89 *(+(z0, z1), z2) -> +(*(z0, z2), *(z1, z2)) 352.37/291.89 *(z0, 1) -> z0 352.37/291.89 *(1, z0) -> z0 352.37/291.89 Tuples: 352.37/291.89 *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) 352.37/291.89 *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) 352.37/291.89 *'(z0, 1) -> c2 352.37/291.89 *'(1, z0) -> c3 352.37/291.89 S tuples: 352.37/291.89 *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) 352.37/291.89 *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) 352.37/291.89 *'(z0, 1) -> c2 352.37/291.89 *'(1, z0) -> c3 352.37/291.89 K tuples:none 352.37/291.89 Defined Rule Symbols: *_2 352.37/291.89 352.37/291.89 Defined Pair Symbols: *'_2 352.37/291.89 352.37/291.89 Compound Symbols: c_2, c1_2, c2, c3 352.37/291.89 352.37/291.89 352.37/291.89 ---------------------------------------- 352.37/291.89 352.37/291.89 (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 352.37/291.89 Removed 2 trailing nodes: 352.37/291.89 *'(1, z0) -> c3 352.37/291.89 *'(z0, 1) -> c2 352.37/291.89 352.37/291.89 ---------------------------------------- 352.37/291.89 352.37/291.89 (4) 352.37/291.89 Obligation: 352.37/291.89 Complexity Dependency Tuples Problem 352.37/291.89 352.37/291.89 Rules: 352.37/291.89 *(z0, +(z1, z2)) -> +(*(z0, z1), *(z0, z2)) 352.37/291.89 *(+(z0, z1), z2) -> +(*(z0, z2), *(z1, z2)) 352.37/291.89 *(z0, 1) -> z0 352.37/291.89 *(1, z0) -> z0 352.37/291.89 Tuples: 352.37/291.89 *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) 352.37/291.89 *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) 352.37/291.89 S tuples: 352.37/291.89 *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2))
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