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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313758
details
property
value
status
complete
benchmark
#3.15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n170.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.82874 seconds
cpu usage
11.4676
user time
10.778
system time
0.689564
max virtual memory
1.8941276E7
max residence set size
1959752.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
11.07/3.77 WORST_CASE(Omega(n^1), O(n^1)) 11.07/3.79 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.07/3.79 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.07/3.79 11.07/3.79 11.07/3.79 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 11.07/3.79 11.07/3.79 (0) CpxTRS 11.07/3.79 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 11.07/3.79 (2) CdtProblem 11.07/3.79 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 11.07/3.79 (4) CdtProblem 11.07/3.79 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 11.07/3.79 (6) CdtProblem 11.07/3.79 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 38 ms] 11.07/3.79 (8) CdtProblem 11.07/3.79 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 5 ms] 11.07/3.79 (10) CdtProblem 11.07/3.79 (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 11.07/3.79 (12) BOUNDS(1, 1) 11.07/3.79 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 11.07/3.79 (14) TRS for Loop Detection 11.07/3.79 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 11.07/3.79 (16) BEST 11.07/3.79 (17) proven lower bound 11.07/3.79 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 11.07/3.79 (19) BOUNDS(n^1, INF) 11.07/3.79 (20) TRS for Loop Detection 11.07/3.79 11.07/3.79 11.07/3.79 ---------------------------------------- 11.07/3.79 11.07/3.79 (0) 11.07/3.79 Obligation: 11.07/3.79 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 11.07/3.79 11.07/3.79 11.07/3.79 The TRS R consists of the following rules: 11.07/3.79 11.07/3.79 average(s(x), y) -> average(x, s(y)) 11.07/3.79 average(x, s(s(s(y)))) -> s(average(s(x), y)) 11.07/3.79 average(0, 0) -> 0 11.07/3.79 average(0, s(0)) -> 0 11.07/3.79 average(0, s(s(0))) -> s(0) 11.07/3.79 11.07/3.79 S is empty. 11.07/3.79 Rewrite Strategy: INNERMOST 11.07/3.79 ---------------------------------------- 11.07/3.79 11.07/3.79 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 11.07/3.79 Converted Cpx (relative) TRS to CDT 11.07/3.79 ---------------------------------------- 11.07/3.79 11.07/3.79 (2) 11.07/3.79 Obligation: 11.07/3.79 Complexity Dependency Tuples Problem 11.07/3.79 11.07/3.79 Rules: 11.07/3.79 average(s(z0), z1) -> average(z0, s(z1)) 11.07/3.79 average(z0, s(s(s(z1)))) -> s(average(s(z0), z1)) 11.07/3.79 average(0, 0) -> 0 11.07/3.79 average(0, s(0)) -> 0 11.07/3.79 average(0, s(s(0))) -> s(0) 11.07/3.79 Tuples: 11.07/3.79 AVERAGE(s(z0), z1) -> c(AVERAGE(z0, s(z1))) 11.07/3.79 AVERAGE(z0, s(s(s(z1)))) -> c1(AVERAGE(s(z0), z1)) 11.07/3.79 AVERAGE(0, 0) -> c2 11.07/3.79 AVERAGE(0, s(0)) -> c3 11.07/3.79 AVERAGE(0, s(s(0))) -> c4 11.07/3.79 S tuples: 11.07/3.79 AVERAGE(s(z0), z1) -> c(AVERAGE(z0, s(z1))) 11.07/3.79 AVERAGE(z0, s(s(s(z1)))) -> c1(AVERAGE(s(z0), z1)) 11.07/3.79 AVERAGE(0, 0) -> c2 11.07/3.79 AVERAGE(0, s(0)) -> c3 11.07/3.79 AVERAGE(0, s(s(0))) -> c4 11.07/3.79 K tuples:none 11.07/3.79 Defined Rule Symbols: average_2 11.07/3.79 11.07/3.79 Defined Pair Symbols: AVERAGE_2 11.07/3.79 11.07/3.79 Compound Symbols: c_1, c1_1, c2, c3, c4 11.07/3.79 11.07/3.79 11.07/3.79 ---------------------------------------- 11.07/3.79 11.07/3.79 (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 11.07/3.79 Removed 3 trailing nodes: 11.07/3.79 AVERAGE(0, s(0)) -> c3 11.07/3.79 AVERAGE(0, 0) -> c2 11.07/3.79 AVERAGE(0, s(s(0))) -> c4 11.07/3.79 11.07/3.79 ---------------------------------------- 11.07/3.79 11.07/3.79 (4) 11.07/3.79 Obligation: 11.07/3.79 Complexity Dependency Tuples Problem 11.07/3.79 11.07/3.79 Rules: 11.07/3.79 average(s(z0), z1) -> average(z0, s(z1)) 11.07/3.79 average(z0, s(s(s(z1)))) -> s(average(s(z0), z1))
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