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Runtime Complexity: TRS Innermost pair #487112250
details
property
value
status
complete
benchmark
Ex4_7_77_Bor03_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.55719 seconds
cpu usage
3.36789
user time
3.22812
system time
0.139771
max virtual memory
1.827736E7
max residence set size
221840.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1). (0) CpxTRS (1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: zeros -> cons(0, n__zeros) tail(cons(X, XS)) -> activate(XS) zeros -> n__zeros activate(n__zeros) -> zeros activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) 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: activate(n__zeros) ->^* n__zeros activate(n__zeros) ->^* cons(0, n__zeros) tail(cons(x0, n__zeros)) ->^* n__zeros tail(cons(x0, n__zeros)) ->^* cons(0, n__zeros) zeros ->^* n__zeros zeros ->^* cons(0, n__zeros) ---------------------------------------- (2) BOUNDS(1, 1)
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