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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307718
details
property
value
status
complete
benchmark
#3.51.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.14823 seconds
cpu usage
20.0123
user time
18.091
system time
1.92123
max virtual memory
1.8746052E7
max residence set size
4341292.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
19.91/7.08 WORST_CASE(Omega(n^1), O(n^1)) 19.91/7.09 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 19.91/7.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.91/7.09 19.91/7.09 19.91/7.09 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.91/7.09 19.91/7.09 (0) CpxTRS 19.91/7.09 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 19.91/7.09 (2) CpxTRS 19.91/7.09 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 19.91/7.09 (4) CpxTRS 19.91/7.09 (5) CpxTrsMatchBoundsProof [FINISHED, 0 ms] 19.91/7.09 (6) BOUNDS(1, n^1) 19.91/7.09 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 19.91/7.09 (8) TRS for Loop Detection 19.91/7.09 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 19.91/7.09 (10) BEST 19.91/7.09 (11) proven lower bound 19.91/7.09 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 19.91/7.09 (13) BOUNDS(n^1, INF) 19.91/7.09 (14) TRS for Loop Detection 19.91/7.09 19.91/7.09 19.91/7.09 ---------------------------------------- 19.91/7.09 19.91/7.09 (0) 19.91/7.09 Obligation: 19.91/7.09 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.91/7.09 19.91/7.09 19.91/7.09 The TRS R consists of the following rules: 19.91/7.09 19.91/7.09 f(f(x)) -> f(c(f(x))) 19.91/7.09 f(f(x)) -> f(d(f(x))) 19.91/7.09 g(c(x)) -> x 19.91/7.09 g(d(x)) -> x 19.91/7.09 g(c(h(0))) -> g(d(1)) 19.91/7.09 g(c(1)) -> g(d(h(0))) 19.91/7.09 g(h(x)) -> g(x) 19.91/7.09 19.91/7.09 S is empty. 19.91/7.09 Rewrite Strategy: FULL 19.91/7.09 ---------------------------------------- 19.91/7.09 19.91/7.09 (1) DependencyGraphProof (UPPER BOUND(ID)) 19.91/7.09 The following rules are not reachable from basic terms in the dependency graph and can be removed: 19.91/7.09 19.91/7.09 f(f(x)) -> f(c(f(x))) 19.91/7.09 f(f(x)) -> f(d(f(x))) 19.91/7.09 19.91/7.09 ---------------------------------------- 19.91/7.09 19.91/7.09 (2) 19.91/7.09 Obligation: 19.91/7.09 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 19.91/7.09 19.91/7.09 19.91/7.09 The TRS R consists of the following rules: 19.91/7.09 19.91/7.09 g(c(x)) -> x 19.91/7.09 g(d(x)) -> x 19.91/7.09 g(c(h(0))) -> g(d(1)) 19.91/7.09 g(c(1)) -> g(d(h(0))) 19.91/7.09 g(h(x)) -> g(x) 19.91/7.09 19.91/7.09 S is empty. 19.91/7.09 Rewrite Strategy: FULL 19.91/7.09 ---------------------------------------- 19.91/7.09 19.91/7.09 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 19.91/7.09 transformed relative TRS to TRS 19.91/7.09 ---------------------------------------- 19.91/7.09 19.91/7.09 (4) 19.91/7.09 Obligation: 19.91/7.09 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 19.91/7.09 19.91/7.09 19.91/7.09 The TRS R consists of the following rules: 19.91/7.09 19.91/7.09 g(c(x)) -> x 19.91/7.09 g(d(x)) -> x 19.91/7.09 g(c(h(0))) -> g(d(1)) 19.91/7.09 g(c(1)) -> g(d(h(0))) 19.91/7.09 g(h(x)) -> g(x) 19.91/7.09 19.91/7.09 S is empty. 19.91/7.09 Rewrite Strategy: FULL 19.91/7.09 ---------------------------------------- 19.91/7.09 19.91/7.09 (5) CpxTrsMatchBoundsProof (FINISHED) 19.91/7.09 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. 19.91/7.09 The certificate found is represented by the following graph. 19.91/7.09 19.91/7.09 "[5, 6, 7, 8, 9, 10, 11] 19.91/7.09 {(5,6,[g_1|0, c_1|1, d_1|1, h_1|1, 0|1, 1|1, g_1|1, 1|2]), (5,7,[g_1|1]), (5,9,[g_1|1]), (5,11,[h_1|2]), (6,6,[c_1|0, d_1|0, h_1|0, 0|0, 1|0]), (7,8,[d_1|1]), (8,6,[1|1]), (9,10,[d_1|1]), (10,11,[h_1|1]), (11,6,[0|1])}" 19.91/7.09 ---------------------------------------- 19.91/7.09 19.91/7.09 (6)
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