Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime Complexity: TRS Innermost pair #487112878
details
property
value
status
complete
benchmark
test4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.72628 seconds
cpu usage
3.976
user time
3.80029
system time
0.17571
max virtual memory
1.827736E7
max residence set size
280140.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 117 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: f(a, a) -> f(a, b) f(a, b) -> f(s(a), c) f(s(X), c) -> f(X, c) f(c, c) -> f(a, a) 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: f(a, a) -> f(a, b) f(a, b) -> f(s(a), c) f(s(X), c) -> f(X, c) f(c, c) -> f(a, a) 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] transitions: a0() -> 0 b0() -> 0 s0(0) -> 0 c0() -> 0 f0(0, 0) -> 1 a1() -> 2 b1() -> 3 f1(2, 3) -> 1 a1() -> 5 s1(5) -> 4 c1() -> 6 f1(4, 6) -> 1 f1(0, 6) -> 1 a1() -> 7 f1(2, 7) -> 1 a2() -> 8 b2() -> 9 f2(8, 9) -> 1 a2() -> 11 s2(11) -> 10 c2() -> 12 f2(10, 12) -> 1 f2(5, 12) -> 1 a3() -> 14 s3(14) -> 13 c3() -> 15 f3(13, 15) -> 1 f3(11, 15) -> 1 c4() -> 16 f4(14, 16) -> 1 ---------------------------------------- (4)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime Complexity: TRS Innermost