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Runtime Complexity: TRS pair #487111190
details
property
value
status
complete
benchmark
ex2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Strategy_removed_mixed_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.50869 seconds
cpu usage
3.13006
user time
2.99112
system time
0.138935
max virtual memory
1.8275312E7
max residence set size
211652.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) InfiniteLowerBoundProof [FINISHED, 0 ms] (4) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: cons(x, cons(y, z)) -> big inf(x) -> cons(x, inf(s(x))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: cons(x, cons(y, z)) -> big inf(x) -> cons(x, inf(s(x))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) InfiniteLowerBoundProof (FINISHED) The following loop proves infinite runtime complexity: The rewrite sequence inf(x) ->^+ cons(x, inf(s(x))) gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. The pumping substitution is [ ]. The result substitution is [x / s(x)]. ---------------------------------------- (4) BOUNDS(INF, INF)
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