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Runti Compl Full Rewri 10127 pair #381903079
details
property
value
status
complete
benchmark
otto12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.65972208977 seconds
cpu usage
3.697340945
max memory
1.94834432E8
stage attributes
key
value
output-size
5269
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).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: plus(0, x) -> x plus(s(x), y) -> s(plus(x, y)) times(0, y) -> 0 times(s(x), y) -> plus(y, times(x, y)) exp(x, 0) -> s(0) exp(x, s(y)) -> times(x, exp(x, y)) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) tower(x, y) -> towerIter(0, x, y, s(0)) towerIter(c, x, y, z) -> help(ge(c, x), c, x, y, z) help(true, c, x, y, z) -> z help(false, c, x, y, z) -> towerIter(s(c), x, y, exp(y, z)) 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: plus(0, x) -> x plus(s(x), y) -> s(plus(x, y)) times(0, y) -> 0 times(s(x), y) -> plus(y, times(x, y)) exp(x, 0) -> s(0) exp(x, s(y)) -> times(x, exp(x, y)) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) tower(x, y) -> towerIter(0, x, y, s(0)) towerIter(c, x, y, z) -> help(ge(c, x), c, x, y, z) help(true, c, x, y, z) -> z help(false, c, x, y, z) -> towerIter(s(c), x, y, exp(y, z)) 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 exp(x, s(y)) ->^+ times(x, exp(x, y)) gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. The pumping substitution is [y / s(y)]. The result substitution is [ ].
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