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Runti Compl Full Rewri 10127 pair #381903253
details
property
value
status
complete
benchmark
thiemann08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.64226794243 seconds
cpu usage
3.549939179
max memory
1.90472192E8
stage attributes
key
value
output-size
5023
starexec-result
WORST_CASE(NON_POLY, ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection (9) DecreasingLoopProof [FINISHED, 0 ms] (10) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: empty(nil) -> true empty(cons(x, l)) -> false head(cons(x, l)) -> x tail(nil) -> nil tail(cons(x, l)) -> l rev(nil) -> nil rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l)) last(x, l) -> if(empty(l), x, l) if(true, x, l) -> x if(false, x, l) -> last(head(l), tail(l)) rev2(x, nil) -> nil rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) 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(EXP, INF). The TRS R consists of the following rules: empty(nil) -> true empty(cons(x, l)) -> false head(cons(x, l)) -> x tail(nil) -> nil tail(cons(x, l)) -> l rev(nil) -> nil rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l)) last(x, l) -> if(empty(l), x, l) if(true, x, l) -> x if(false, x, l) -> last(head(l), tail(l)) rev2(x, nil) -> nil rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence rev2(x, cons(y, l)) ->^+ rev(cons(x, rev2(y, l))) gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1]. The pumping substitution is [l / cons(y, l)]. The result substitution is [x / y]. ----------------------------------------
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