Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307698
details
property
value
status
complete
benchmark
#3.47.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.69589 seconds
cpu usage
17.9467
user time
16.9067
system time
1.04008
max virtual memory
3.6842736E7
max residence set size
3340880.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
17.55/5.35 WORST_CASE(Omega(n^1), O(n^1)) 17.57/5.36 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.57/5.36 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.57/5.36 17.57/5.36 17.57/5.36 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 17.57/5.36 17.57/5.36 (0) CpxTRS 17.57/5.36 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 17.57/5.36 (2) CpxTRS 17.57/5.36 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 11 ms] 17.57/5.36 (4) CdtProblem 17.57/5.36 (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 82 ms] 17.57/5.36 (6) CdtProblem 17.57/5.36 (7) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] 17.57/5.36 (8) CdtProblem 17.57/5.36 (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 17.57/5.36 (10) CdtProblem 17.57/5.36 (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 17.57/5.36 (12) CdtProblem 17.57/5.36 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] 17.57/5.36 (14) CdtProblem 17.57/5.36 (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 17.57/5.36 (16) BOUNDS(1, 1) 17.57/5.36 (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 17.57/5.36 (18) TRS for Loop Detection 17.57/5.36 (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 17.57/5.36 (20) BEST 17.57/5.36 (21) proven lower bound 17.57/5.36 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 17.57/5.36 (23) BOUNDS(n^1, INF) 17.57/5.36 (24) TRS for Loop Detection 17.57/5.36 17.57/5.36 17.57/5.36 ---------------------------------------- 17.57/5.36 17.57/5.36 (0) 17.57/5.36 Obligation: 17.57/5.36 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 17.57/5.36 17.57/5.36 17.57/5.36 The TRS R consists of the following rules: 17.57/5.36 17.57/5.36 f(x, c(y)) -> f(x, s(f(y, y))) 17.57/5.36 f(s(x), y) -> f(x, s(c(y))) 17.57/5.36 17.57/5.36 S is empty. 17.57/5.36 Rewrite Strategy: FULL 17.57/5.36 ---------------------------------------- 17.57/5.36 17.57/5.36 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 17.57/5.36 Converted rc-obligation to irc-obligation. 17.57/5.36 17.57/5.36 The duplicating contexts are: 17.57/5.36 f(x, c([])) 17.57/5.36 17.57/5.36 17.57/5.36 The defined contexts are: 17.57/5.36 f(x0, s([])) 17.57/5.36 f(x0, s(c([]))) 17.57/5.36 17.57/5.36 17.57/5.36 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 17.57/5.36 ---------------------------------------- 17.57/5.36 17.57/5.36 (2) 17.57/5.36 Obligation: 17.57/5.36 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 17.57/5.36 17.57/5.36 17.57/5.36 The TRS R consists of the following rules: 17.57/5.36 17.57/5.36 f(x, c(y)) -> f(x, s(f(y, y))) 17.57/5.36 f(s(x), y) -> f(x, s(c(y))) 17.57/5.36 17.57/5.36 S is empty. 17.57/5.36 Rewrite Strategy: INNERMOST 17.57/5.36 ---------------------------------------- 17.57/5.36 17.57/5.36 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 17.57/5.36 Converted Cpx (relative) TRS to CDT 17.57/5.36 ---------------------------------------- 17.57/5.36 17.57/5.36 (4) 17.57/5.36 Obligation: 17.57/5.36 Complexity Dependency Tuples Problem 17.57/5.36 17.57/5.36 Rules: 17.57/5.36 f(z0, c(z1)) -> f(z0, s(f(z1, z1))) 17.57/5.36 f(s(z0), z1) -> f(z0, s(c(z1))) 17.57/5.36 Tuples: 17.57/5.36 F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1)) 17.57/5.36 F(s(z0), z1) -> c2(F(z0, s(c(z1)))) 17.57/5.36 S tuples: 17.57/5.36 F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1)) 17.57/5.36 F(s(z0), z1) -> c2(F(z0, s(c(z1)))) 17.57/5.36 K tuples:none 17.57/5.36 Defined Rule Symbols: f_2 17.57/5.36 17.57/5.36 Defined Pair Symbols: F_2
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11