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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308383
details
property
value
status
complete
benchmark
2.49.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n101.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.65418 seconds
cpu usage
3.34538
user time
3.20779
system time
0.137594
max virtual memory
1.8275288E7
max residence set size
220128.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
3.18/1.58 WORST_CASE(?, O(1)) 3.18/1.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.18/1.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.18/1.58 3.18/1.58 3.18/1.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.18/1.58 3.18/1.58 (0) CpxTRS 3.18/1.58 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 3.18/1.58 (2) CpxTRS 3.18/1.58 (3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] 3.18/1.58 (4) BOUNDS(1, 1) 3.18/1.58 3.18/1.58 3.18/1.58 ---------------------------------------- 3.18/1.58 3.18/1.58 (0) 3.18/1.58 Obligation: 3.18/1.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.18/1.58 3.18/1.58 3.18/1.58 The TRS R consists of the following rules: 3.18/1.58 3.18/1.58 a(c(d(x))) -> c(x) 3.18/1.58 u(b(d(d(x)))) -> b(x) 3.18/1.58 v(a(a(x))) -> u(v(x)) 3.18/1.58 v(a(c(x))) -> u(b(d(x))) 3.18/1.58 v(c(x)) -> b(x) 3.18/1.58 w(a(a(x))) -> u(w(x)) 3.18/1.58 w(a(c(x))) -> u(b(d(x))) 3.18/1.58 w(c(x)) -> b(x) 3.18/1.58 3.18/1.58 S is empty. 3.18/1.58 Rewrite Strategy: FULL 3.18/1.58 ---------------------------------------- 3.18/1.58 3.18/1.58 (1) DependencyGraphProof (UPPER BOUND(ID)) 3.18/1.58 The following rules are not reachable from basic terms in the dependency graph and can be removed: 3.18/1.58 3.18/1.58 v(a(a(x))) -> u(v(x)) 3.18/1.58 v(a(c(x))) -> u(b(d(x))) 3.18/1.59 w(a(a(x))) -> u(w(x)) 3.18/1.59 w(a(c(x))) -> u(b(d(x))) 3.18/1.59 3.18/1.59 ---------------------------------------- 3.18/1.59 3.18/1.59 (2) 3.18/1.59 Obligation: 3.18/1.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.18/1.59 3.18/1.59 3.18/1.59 The TRS R consists of the following rules: 3.18/1.59 3.18/1.59 a(c(d(x))) -> c(x) 3.18/1.59 u(b(d(d(x)))) -> b(x) 3.18/1.59 v(c(x)) -> b(x) 3.18/1.59 w(c(x)) -> b(x) 3.18/1.59 3.18/1.59 S is empty. 3.18/1.59 Rewrite Strategy: FULL 3.18/1.59 ---------------------------------------- 3.18/1.59 3.18/1.59 (3) NarrowingOnBasicTermsTerminatesProof (FINISHED) 3.18/1.59 Constant runtime complexity proven by termination of constructor-based narrowing. 3.18/1.59 3.18/1.59 The maximal most general narrowing sequences give rise to the following rewrite sequences: 3.18/1.59 3.18/1.59 u(b(d(d(x0)))) ->^* b(x0) 3.18/1.59 3.18/1.59 w(c(x0)) ->^* b(x0) 3.18/1.59 3.18/1.59 v(c(x0)) ->^* b(x0) 3.18/1.59 3.18/1.59 a(c(d(x0))) ->^* c(x0) 3.18/1.59 3.18/1.59 3.18/1.59 3.18/1.59 3.18/1.59 ---------------------------------------- 3.18/1.59 3.18/1.59 (4) 3.18/1.59 BOUNDS(1, 1) 3.18/1.65 EOF
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