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Runtime Complexity: TRS pair #487110882
details
property
value
status
complete
benchmark
ttt1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.53622 seconds
cpu usage
3.23966
user time
3.10251
system time
0.137144
max virtual memory
1.8273228E7
max residence set size
214936.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).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) DependencyGraphProof [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: f(s(a), s(b), x) -> f(x, x, x) g(f(s(x), s(y), z)) -> g(f(x, y, z)) cons(x, y) -> x cons(x, y) -> y S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DependencyGraphProof (UPPER BOUND(ID)) The following rules are not reachable from basic terms in the dependency graph and can be removed: g(f(s(x), s(y), z)) -> g(f(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: f(s(a), s(b), x) -> f(x, x, x) cons(x, y) -> x cons(x, y) -> y 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: cons(x0, x1) ->^* cons(x0, x1) f(s(a), s(b), x0) ->^* f(x0, x0, x0) ---------------------------------------- (4) BOUNDS(1, 1)
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