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Runtime Complexity: TRS Innermost pair #487112624
details
property
value
status
complete
benchmark
deeprev_typed.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.1576 seconds
cpu usage
5.29025
user time
5.04802
system time
0.24223
max virtual memory
1.827736E7
max residence set size
518008.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsTAProof [FINISHED, 228 ms] (4) BOUNDS(1, n^1) (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: revconsapp(C(x1, x2), r) -> revconsapp(x2, C(x1, r)) deeprevapp(C(x1, x2), rest) -> deeprevapp(x2, C(x1, rest)) deeprevapp(V(n), rest) -> revconsapp(rest, V(n)) deeprevapp(N, rest) -> rest revconsapp(V(n), r) -> r revconsapp(N, r) -> r deeprev(C(x1, x2)) -> deeprevapp(C(x1, x2), N) deeprev(V(n)) -> V(n) deeprev(N) -> N second(V(n)) -> N second(C(x1, x2)) -> x2 isVal(C(x1, x2)) -> False isVal(V(n)) -> True isVal(N) -> False isNotEmptyT(C(x1, x2)) -> True isNotEmptyT(V(n)) -> False isNotEmptyT(N) -> False isEmptyT(C(x1, x2)) -> False isEmptyT(V(n)) -> False isEmptyT(N) -> True first(V(n)) -> N first(C(x1, x2)) -> x1 goal(x) -> deeprev(x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: revconsapp(C(x1, x2), r) -> revconsapp(x2, C(x1, r)) deeprevapp(C(x1, x2), rest) -> deeprevapp(x2, C(x1, rest)) deeprevapp(V(n), rest) -> revconsapp(rest, V(n)) deeprevapp(N, rest) -> rest revconsapp(V(n), r) -> r revconsapp(N, r) -> r deeprev(C(x1, x2)) -> deeprevapp(C(x1, x2), N) deeprev(V(n)) -> V(n) deeprev(N) -> N second(V(n)) -> N second(C(x1, x2)) -> x2 isVal(C(x1, x2)) -> False isVal(V(n)) -> True isVal(N) -> False isNotEmptyT(C(x1, x2)) -> True isNotEmptyT(V(n)) -> False isNotEmptyT(N) -> False isEmptyT(C(x1, x2)) -> False isEmptyT(V(n)) -> False isEmptyT(N) -> True first(V(n)) -> N first(C(x1, x2)) -> x1 goal(x) -> deeprev(x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsTAProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 3.
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