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Runti Compl Inner Rewri 22807 pair #381905263
details
property
value
status
complete
benchmark
Ex4_7_77_Bor03_GM.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
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.7870490551 seconds
cpu usage
4.213933952
max memory
2.40611328E8
stage attributes
key
value
output-size
5963
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 87 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: a__zeros -> cons(0, zeros) a__tail(cons(X, XS)) -> mark(XS) mark(zeros) -> a__zeros mark(tail(X)) -> a__tail(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 a__zeros -> zeros a__tail(X) -> tail(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: a__zeros -> cons(0, zeros) a__tail(cons(X, XS)) -> mark(XS) mark(zeros) -> a__zeros mark(tail(X)) -> a__tail(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 a__zeros -> zeros a__tail(X) -> tail(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 4. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2, 3] transitions: cons0(0, 0) -> 0 00() -> 0 zeros0() -> 0 tail0(0) -> 0 a__zeros0() -> 1 a__tail0(0) -> 2 mark0(0) -> 3 01() -> 4 zeros1() -> 5 cons1(4, 5) -> 1 mark1(0) -> 2 a__zeros1() -> 3 mark1(0) -> 6 a__tail1(6) -> 3 mark1(0) -> 7 cons1(7, 0) -> 3 01() -> 3 zeros1() -> 1 tail1(0) -> 2 02() -> 8
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