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Runtime Complexity: TRS pair #487109712
details
property
value
status
complete
benchmark
Ex5_Zan97_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.82555 seconds
cpu usage
4.0204
user time
3.86749
system time
0.152916
max virtual memory
1.827736E7
max residence set size
260148.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 101 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 (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: f(X) -> if(X, c, n__f(n__true)) if(true, X, Y) -> X if(false, X, Y) -> activate(Y) f(X) -> n__f(X) true -> n__true activate(n__f(X)) -> f(activate(X)) activate(n__true) -> true activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(X) -> if(X, c, n__f(n__true)) if(true, X, Y) -> X if(false, X, Y) -> activate(Y) f(X) -> n__f(X) true -> n__true activate(n__f(X)) -> f(activate(X)) activate(n__true) -> true activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (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, 4] transitions: c0() -> 0 n__f0(0) -> 0 n__true0() -> 0 false0() -> 0 f0(0) -> 1 if0(0, 0, 0) -> 2 true0() -> 3 activate0(0) -> 4 c1() -> 5 n__true1() -> 7 n__f1(7) -> 6 if1(0, 5, 6) -> 1 activate1(0) -> 2 n__f1(0) -> 1 n__true1() -> 3 activate1(0) -> 8 f1(8) -> 4 true1() -> 4 c2() -> 9 n__true2() -> 11 n__f2(11) -> 10 if2(8, 9, 10) -> 4 activate1(6) -> 1 n__f2(8) -> 4 n__true2() -> 4 f1(8) -> 2
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