details

property	value
status	complete
benchmark	08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.76774 seconds
cpu usage	3.9917
user time	3.83241
system time	0.159289
max virtual memory	1.827736E7
max residence set size	278248.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).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: f1(a, x) -> g1(x, x) f1(x, a) -> g2(x, x) f2(a, x) -> g1(x, x) f2(x, a) -> g2(x, x) g1(a, x) -> h1(x) g1(x, a) -> h2(x) g2(a, x) -> h1(x) g2(x, a) -> h2(x) h1(a) -> i h2(a) -> i e1(h1(w), h2(w), x, y, z, w) -> e2(x, x, y, z, z, w) e1(x1, x1, x, y, z, a) -> e5(x1, x, y, z) e2(f1(w, w), x, y, z, f2(w, w), w) -> e3(x, y, x, y, y, z, y, z, x, y, z, w) e2(x, x, y, z, z, a) -> e6(x, y, z) e2(i, x, y, z, i, a) -> e6(x, y, z) e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w) e3(x, y, x, y, y, z, y, z, x, y, z, a) -> e6(x, y, z) e4(g1(w, w), x1, g2(w, w), x1, g1(w, w), x1, g2(w, w), x1, x, y, z, w) -> e1(x1, x1, x, y, z, w) e4(i, x1, i, x1, i, x1, i, x1, x, y, z, a) -> e5(x1, x, y, z) e4(x, x, x, x, x, x, x, x, x, x, x, a) -> e6(x, x, x) e5(i, x, y, z) -> e6(x, y, z) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The TRS does not nest defined symbols. Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: e1(h1(w), h2(w), x, y, z, w) -> e2(x, x, y, z, z, w) e2(f1(w, w), x, y, z, f2(w, w), w) -> e3(x, y, x, y, y, z, y, z, x, y, z, w) e4(g1(w, w), x1, g2(w, w), x1, g1(w, w), x1, g2(w, w), x1, x, y, z, w) -> e1(x1, x1, x, y, z, w) ---------------------------------------- (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: f1(a, x) -> g1(x, x) f1(x, a) -> g2(x, x) f2(a, x) -> g1(x, x) f2(x, a) -> g2(x, x) g1(a, x) -> h1(x) g1(x, a) -> h2(x) g2(a, x) -> h1(x) g2(x, a) -> h2(x) h1(a) -> i h2(a) -> i e1(x1, x1, x, y, z, a) -> e5(x1, x, y, z) e2(x, x, y, z, z, a) -> e6(x, y, z) e2(i, x, y, z, i, a) -> e6(x, y, z) e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w) e3(x, y, x, y, y, z, y, z, x, y, z, a) -> e6(x, y, z) e4(i, x1, i, x1, i, x1, i, x1, x, y, z, a) -> e5(x1, x, y, z) e4(x, x, x, x, x, x, x, x, x, x, x, a) -> e6(x, x, x) e5(i, x, y, z) -> e6(x, y, z) 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: e5(i, x0, x1, x2) ->^* e6(x0, x1, x2) e4(x0, x0, x0, x0, x0, x0, x0, x0, x0, x0, x0, a) ->^* e6(x0, x0, x0) e4(i, i, i, i, i, i, i, i, x0, x1, x2, a) ->^* e6(x0, x1, x2) e3(x0, x1, x0, x1, x1, x2, x1, x2, x0, x1, x2, a) ->^* e6(x0, x1, x2) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Runtime Complexity: TRS