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Runti Compl Full Rewri 10127 pair #381902601
details
property
value
status
complete
benchmark
secret5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.65821695328 seconds
cpu usage
3.550718462
max memory
1.95518464E8
stage attributes
key
value
output-size
5029
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).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, 28 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: t(N) -> cs(r(q(N)), nt(ns(N))) q(0) -> 0 q(s(X)) -> s(p(q(X), d(X))) d(0) -> 0 d(s(X)) -> s(s(d(X))) p(0, X) -> X p(X, 0) -> X p(s(X), s(Y)) -> s(s(p(X, Y))) f(0, X) -> nil f(s(X), cs(Y, Z)) -> cs(Y, nf(X, a(Z))) t(X) -> nt(X) s(X) -> ns(X) f(X1, X2) -> nf(X1, X2) a(nt(X)) -> t(a(X)) a(ns(X)) -> s(a(X)) a(nf(X1, X2)) -> f(a(X1), a(X2)) a(X) -> 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(EXP, INF). The TRS R consists of the following rules: t(N) -> cs(r(q(N)), nt(ns(N))) q(0) -> 0 q(s(X)) -> s(p(q(X), d(X))) d(0) -> 0 d(s(X)) -> s(s(d(X))) p(0, X) -> X p(X, 0) -> X p(s(X), s(Y)) -> s(s(p(X, Y))) f(0, X) -> nil f(s(X), cs(Y, Z)) -> cs(Y, nf(X, a(Z))) t(X) -> nt(X) s(X) -> ns(X) f(X1, X2) -> nf(X1, X2) a(nt(X)) -> t(a(X)) a(ns(X)) -> s(a(X)) a(nf(X1, X2)) -> f(a(X1), a(X2)) a(X) -> X 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 a(nt(X)) ->^+ t(a(X)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
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