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Runtime Complexity: TRS Innermost pair #487112614
details
property
value
status
complete
benchmark
rev-fletf.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
hoca
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.04182 seconds
cpu usage
3.67217
user time
3.50877
system time
0.163402
max virtual memory
1.827736E7
max residence set size
249520.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 33 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: rev_l#2(x8, x10) -> Cons(x10, x8) step_x_f#1(rev_l, x5, step_x_f(x2, x3, x4), x1) -> step_x_f#1(x2, x3, x4, rev_l#2(x1, x5)) step_x_f#1(rev_l, x5, fleft_op_e_xs_1, x3) -> rev_l#2(x3, x5) foldr#3(Nil) -> fleft_op_e_xs_1 foldr#3(Cons(x16, x6)) -> step_x_f(rev_l, x16, foldr#3(x6)) main(Nil) -> Nil main(Cons(x8, x9)) -> step_x_f#1(rev_l, x8, foldr#3(x9), Nil) 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: rev_l#2(x8, x10) -> Cons(x10, x8) step_x_f#1(rev_l, x5, step_x_f(x2, x3, x4), x1) -> step_x_f#1(x2, x3, x4, rev_l#2(x1, x5)) step_x_f#1(rev_l, x5, fleft_op_e_xs_1, x3) -> rev_l#2(x3, x5) foldr#3(Nil) -> fleft_op_e_xs_1 foldr#3(Cons(x16, x6)) -> step_x_f(rev_l, x16, foldr#3(x6)) main(Nil) -> Nil main(Cons(x8, x9)) -> step_x_f#1(rev_l, x8, foldr#3(x9), Nil) 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. 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: Cons0(0, 0) -> 0 rev_l0() -> 0 step_x_f0(0, 0, 0) -> 0 fleft_op_e_xs_10() -> 0 Nil0() -> 0 rev_l#20(0, 0) -> 1 step_x_f#10(0, 0, 0, 0) -> 2 foldr#30(0) -> 3 main0(0) -> 4 Cons1(0, 0) -> 1 rev_l#21(0, 0) -> 5 step_x_f#11(0, 0, 0, 5) -> 2 rev_l#21(0, 0) -> 2 fleft_op_e_xs_11() -> 3 rev_l1() -> 6 foldr#31(0) -> 7 step_x_f1(6, 0, 7) -> 3 Nil1() -> 4 rev_l1() -> 8 foldr#31(0) -> 9 Nil1() -> 10 step_x_f#11(8, 0, 9, 10) -> 4 Cons2(0, 0) -> 2 Cons2(0, 0) -> 5 rev_l#21(5, 0) -> 5 rev_l#21(5, 0) -> 2 fleft_op_e_xs_11() -> 7 fleft_op_e_xs_11() -> 9
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