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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307962
details
property
value
status
complete
benchmark
04.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.8862 seconds
cpu usage
3.98617
user time
3.80139
system time
0.184783
max virtual memory
1.8277336E7
max residence set size
250580.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
3.79/1.81 WORST_CASE(?, O(1)) 3.79/1.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.79/1.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.79/1.84 3.79/1.84 3.79/1.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.79/1.84 3.79/1.84 (0) CpxTRS 3.79/1.84 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 3.79/1.84 (2) CpxTRS 3.79/1.84 (3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] 3.79/1.84 (4) BOUNDS(1, 1) 3.79/1.84 3.79/1.84 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (0) 3.79/1.84 Obligation: 3.79/1.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.79/1.84 3.79/1.84 3.79/1.84 The TRS R consists of the following rules: 3.79/1.84 3.79/1.84 f1 -> g1 3.79/1.84 f1 -> g2 3.79/1.84 f2 -> g1 3.79/1.84 f2 -> g2 3.79/1.84 g1 -> h1 3.79/1.84 g1 -> h2 3.79/1.84 g2 -> h1 3.79/1.84 g2 -> h2 3.79/1.84 h1 -> i 3.79/1.84 h2 -> i 3.79/1.84 e1(h1, h2, x, y, z) -> e2(x, x, y, z, z) 3.79/1.84 e1(x1, x1, x, y, z) -> e5(x1, x, y, z) 3.79/1.84 e2(f1, x, y, z, f2) -> e3(x, y, x, y, y, z, y, z, x, y, z) 3.79/1.84 e2(x, x, y, z, z) -> e6(x, y, z) 3.79/1.84 e2(i, x, y, z, i) -> e6(x, y, z) 3.79/1.84 e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) 3.79/1.84 e3(x, y, x, y, y, z, y, z, x, y, z) -> e6(x, y, z) 3.79/1.84 e4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> e1(x1, x1, x, y, z) 3.79/1.84 e4(i, x1, i, x1, i, x1, i, x1, x, y, z) -> e5(x1, x, y, z) 3.79/1.84 e4(x, x, x, x, x, x, x, x, x, x, x) -> e6(x, x, x) 3.79/1.84 e5(i, x, y, z) -> e6(x, y, z) 3.79/1.84 3.79/1.84 S is empty. 3.79/1.84 Rewrite Strategy: FULL 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 3.79/1.84 The TRS does not nest defined symbols. 3.79/1.84 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 3.79/1.84 e1(h1, h2, x, y, z) -> e2(x, x, y, z, z) 3.79/1.84 e2(f1, x, y, z, f2) -> e3(x, y, x, y, y, z, y, z, x, y, z) 3.79/1.84 e4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> e1(x1, x1, x, y, z) 3.79/1.84 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (2) 3.79/1.84 Obligation: 3.79/1.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). 3.79/1.84 3.79/1.84 3.79/1.84 The TRS R consists of the following rules: 3.79/1.84 3.79/1.84 f1 -> g1 3.79/1.84 f1 -> g2 3.79/1.84 f2 -> g1 3.79/1.84 f2 -> g2 3.79/1.84 g1 -> h1 3.79/1.84 g1 -> h2 3.79/1.84 g2 -> h1 3.79/1.84 g2 -> h2 3.79/1.84 h1 -> i 3.79/1.84 h2 -> i 3.79/1.84 e1(x1, x1, x, y, z) -> e5(x1, x, y, z) 3.79/1.84 e2(x, x, y, z, z) -> e6(x, y, z) 3.79/1.84 e2(i, x, y, z, i) -> e6(x, y, z) 3.79/1.84 e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) 3.79/1.84 e3(x, y, x, y, y, z, y, z, x, y, z) -> e6(x, y, z) 3.79/1.84 e4(i, x1, i, x1, i, x1, i, x1, x, y, z) -> e5(x1, x, y, z) 3.79/1.84 e4(x, x, x, x, x, x, x, x, x, x, x) -> e6(x, x, x) 3.79/1.84 e5(i, x, y, z) -> e6(x, y, z) 3.79/1.84 3.79/1.84 S is empty. 3.79/1.84 Rewrite Strategy: FULL 3.79/1.84 ---------------------------------------- 3.79/1.84 3.79/1.84 (3) NarrowingOnBasicTermsTerminatesProof (FINISHED) 3.79/1.84 Constant runtime complexity proven by termination of constructor-based narrowing. 3.79/1.84 3.79/1.84 The maximal most general narrowing sequences give rise to the following rewrite sequences: 3.79/1.84 3.79/1.84 h2 ->^* i 3.79/1.84 3.79/1.84 g2 ->^* i 3.79/1.84 3.79/1.84 e4(x0, x0, x0, x0, x0, x0, x0, x0, x0, x0, x0) ->^* e6(x0, x0, x0) 3.79/1.84 3.79/1.84 e4(i, i, i, i, i, i, i, i, x0, x1, x2) ->^* e6(x0, x1, x2)
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