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	n139.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.43172 seconds
cpu usage	18.4231
user time	16.8005
system time	1.62255
max virtual memory	1.8745592E7
max residence set size	4262232.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsProof [FINISHED, 0 ms] (6) BOUNDS(1, n^1) (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (8) TRS for Loop Detection (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: f(f(x)) -> f(c(f(x))) f(f(x)) -> f(d(f(x))) g(c(x)) -> x g(d(x)) -> x g(c(h(0))) -> g(d(1)) g(c(1)) -> g(d(h(0))) g(h(x)) -> g(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DependencyGraphProof (UPPER BOUND(ID)) The following rules are not reachable from basic terms in the dependency graph and can be removed: f(f(x)) -> f(c(f(x))) f(f(x)) -> f(d(f(x))) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: g(c(x)) -> x g(d(x)) -> x g(c(h(0))) -> g(d(1)) g(c(1)) -> g(d(h(0))) g(h(x)) -> g(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: g(c(x)) -> x g(d(x)) -> x g(c(h(0))) -> g(d(1)) g(c(1)) -> g(d(h(0))) g(h(x)) -> g(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (5) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. The certificate found is represented by the following graph. "[1, 2, 7, 8, 9, 10, 11] {(1,2,[g_1|0, c_1|1, d_1|1, h_1|1, 0|1, 1|1, g_1|1, 1|2]), (1,7,[g_1|1]), (1,9,[g_1|1]), (1,11,[h_1|2]), (2,2,[c_1|0, d_1|0, h_1|0, 0|0, 1|0]), (7,8,[d_1|1]), (8,2,[1|1]), (9,10,[d_1|1]), (10,11,[h_1|1]), (11,2,[0|1])}" ---------------------------------------- (6) popout

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actions

all output return to Runtime Complexity: TRS