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Runtime Complexity: TRS pair #487109694
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
n148.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.69524 seconds
cpu usage
3.8751
user time
3.71106
system time
0.16404
max virtual memory
1.827736E7
max residence set size
245224.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
WORST_CASE(?, O(1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).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), 8 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: e5(i, x0, x1, x2) ->^* e6(x0, x1, x2) e4(x0, x0, x0, x0, x0, x0, x0, x0, x0, x0, x0) ->^* e6(x0, x0, x0) e4(i, i, i, i, i, i, i, i, x0, x1, x2) ->^* e6(x0, x1, x2) e3(x0, x1, x0, x1, x1, x2, x1, x2, x0, x1, x2) ->^* e6(x0, x1, x2)
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