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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307694
details
property
value
status
complete
benchmark
#3.35.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
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.00303 seconds
cpu usage
18.8424
user time
17.4631
system time
1.37938
max virtual memory
1.9075672E7
max residence set size
3815564.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
18.61/5.96 WORST_CASE(Omega(n^1), O(n^1)) 18.61/5.97 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 18.61/5.97 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.61/5.97 18.61/5.97 18.61/5.97 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.61/5.97 18.61/5.97 (0) CpxTRS 18.61/5.97 (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 18.61/5.97 (2) CpxTRS 18.61/5.97 (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms] 18.61/5.97 (4) BOUNDS(1, n^1) 18.61/5.97 (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 18.61/5.97 (6) TRS for Loop Detection 18.61/5.97 (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 18.61/5.97 (8) BEST 18.61/5.97 (9) proven lower bound 18.61/5.97 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 18.61/5.97 (11) BOUNDS(n^1, INF) 18.61/5.97 (12) TRS for Loop Detection 18.61/5.97 18.61/5.97 18.61/5.97 ---------------------------------------- 18.61/5.97 18.61/5.97 (0) 18.61/5.97 Obligation: 18.61/5.97 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.61/5.97 18.61/5.97 18.61/5.97 The TRS R consists of the following rules: 18.61/5.97 18.61/5.97 g(s(x)) -> f(x) 18.61/5.97 f(0) -> s(0) 18.61/5.97 f(s(x)) -> s(s(g(x))) 18.61/5.97 g(0) -> 0 18.61/5.97 18.61/5.97 S is empty. 18.61/5.97 Rewrite Strategy: FULL 18.61/5.97 ---------------------------------------- 18.61/5.97 18.61/5.97 (1) RelTrsToTrsProof (UPPER BOUND(ID)) 18.61/5.97 transformed relative TRS to TRS 18.61/5.97 ---------------------------------------- 18.61/5.97 18.61/5.97 (2) 18.61/5.97 Obligation: 18.61/5.97 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 18.61/5.97 18.61/5.97 18.61/5.97 The TRS R consists of the following rules: 18.61/5.97 18.61/5.97 g(s(x)) -> f(x) 18.61/5.97 f(0) -> s(0) 18.61/5.97 f(s(x)) -> s(s(g(x))) 18.61/5.97 g(0) -> 0 18.61/5.97 18.61/5.97 S is empty. 18.61/5.97 Rewrite Strategy: FULL 18.61/5.97 ---------------------------------------- 18.61/5.97 18.61/5.97 (3) CpxTrsMatchBoundsProof (FINISHED) 18.61/5.97 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. 18.61/5.97 The certificate found is represented by the following graph. 18.61/5.97 18.61/5.97 "[1, 2, 3, 4, 5] 18.61/5.97 {(1,2,[g_1|0, f_1|0, f_1|1, 0|1]), (1,3,[s_1|1]), (1,4,[s_1|1]), (2,2,[s_1|0, 0|0]), (3,2,[0|1]), (4,5,[s_1|1]), (5,2,[g_1|1, f_1|1, 0|1]), (5,3,[s_1|1]), (5,4,[s_1|1])}" 18.61/5.97 ---------------------------------------- 18.61/5.97 18.61/5.97 (4) 18.61/5.97 BOUNDS(1, n^1) 18.61/5.97 18.61/5.97 ---------------------------------------- 18.61/5.97 18.61/5.97 (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 18.61/5.97 Transformed a relative TRS into a decreasing-loop problem. 18.79/5.97 ---------------------------------------- 18.79/5.97 18.79/5.97 (6) 18.79/5.97 Obligation: 18.79/5.97 Analyzing the following TRS for decreasing loops: 18.79/5.97 18.79/5.97 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.79/5.97 18.79/5.97 18.79/5.97 The TRS R consists of the following rules: 18.79/5.97 18.79/5.97 g(s(x)) -> f(x) 18.79/5.97 f(0) -> s(0) 18.79/5.97 f(s(x)) -> s(s(g(x))) 18.79/5.97 g(0) -> 0 18.79/5.97 18.79/5.97 S is empty. 18.79/5.97 Rewrite Strategy: FULL 18.79/5.97 ---------------------------------------- 18.79/5.97 18.79/5.97 (7) DecreasingLoopProof (LOWER BOUND(ID)) 18.79/5.97 The following loop(s) give(s) rise to the lower bound Omega(n^1): 18.79/5.97 18.79/5.97 The rewrite sequence 18.79/5.97
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