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Runti Compl Full Rewri 10127 pair #381902332
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
n054.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.75111198425 seconds
cpu usage
3.882029666
max memory
2.58011136E8
stage attributes
key
value
output-size
4029
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).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(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: h2(a) ->^* i
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