details

property	value
status	complete
benchmark	#4.7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.41648 seconds
cpu usage	3.62795
user time	3.47129
system time	0.15666
max virtual memory	1.827736E7
max residence set size	223292.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] (4) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: f(s(x)) -> f(g(x, x)) g(0, 1) -> s(0) 0 -> 1 S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of f: g The following defined symbols can occur below the 0th argument of g: g The following defined symbols can occur below the 1th argument of g: g Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: g(0, 1) -> s(0) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: f(s(x)) -> f(g(x, x)) 0 -> 1 S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) NarrowingOnBasicTermsTerminatesProof (FINISHED) Constant runtime complexity proven by termination of constructor-based narrowing. The maximal most general narrowing sequences give rise to the following rewrite sequences: 0 ->^* 1 f(s(x0)) ->^* f(g(x0, x0)) ---------------------------------------- (4) BOUNDS(1, 1) popout

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job log

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actions

all output return to Runtime Complexity: TRS