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Runti Compl Full Rewri 10127 pair #381902284
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
n057.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.76934695244 seconds
cpu usage
3.96843596
max memory
2.67874304E8
stage attributes
key
value
output-size
3627
starexec-result
WORST_CASE(?, O(1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).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 -> g1 f1 -> g2 f2 -> g1 f2 -> g2 g1 -> h1 g1 -> h2 g2 -> h1 g2 -> h2 h1 -> i h2 -> i e1(h1, h2, x, y, z) -> e2(x, x, y, z, z) e1(x1, x1, x, y, z) -> e5(x1, x, y, z) e2(f1, x, y, z, f2) -> e3(x, y, x, y, y, z, y, z, x, y, z) e2(x, x, y, z, z) -> e6(x, y, z) e2(i, x, y, z, i) -> e6(x, y, z) e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) e3(x, y, x, y, y, z, y, z, x, y, z) -> e6(x, y, z) e4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> e1(x1, x1, x, y, z) e4(i, x1, i, x1, i, x1, i, x1, x, y, z) -> e5(x1, x, y, z) e4(x, x, x, x, x, x, x, x, x, x, x) -> 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, h2, x, y, z) -> e2(x, x, y, z, z) e2(f1, x, y, z, f2) -> e3(x, y, x, y, y, z, y, z, x, y, z) e4(g1, x1, g2, x1, g1, x1, g2, x1, x, y, z) -> e1(x1, x1, x, y, z) ---------------------------------------- (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 -> g1 f1 -> g2 f2 -> g1 f2 -> g2 g1 -> h1 g1 -> h2 g2 -> h1 g2 -> h2 h1 -> i h2 -> i e1(x1, x1, x, y, z) -> e5(x1, x, y, z) e2(x, x, y, z, z) -> e6(x, y, z) e2(i, x, y, z, i) -> e6(x, y, z) e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) -> e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z) e3(x, y, x, y, y, z, y, z, x, y, z) -> e6(x, y, z) e4(i, x1, i, x1, i, x1, i, x1, x, y, z) -> e5(x1, x, y, z) e4(x, x, x, x, x, x, x, x, x, x, x) -> 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: h2 ->^* i
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