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Compl Integ Trans Syste 26843 pair #381744220
details
property
value
status
complete
benchmark
NestedSingle.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n040.star.cs.uiowa.edu
space
POPL09
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.32888889313 seconds
cpu usage
5.067426583
max memory
2.6116096E8
stage attributes
key
value
output-size
20655
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 22 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 636 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalNestedSinglestart(A, B, C) -> Com_1(evalNestedSingleentryin(A, B, C)) :|: TRUE evalNestedSingleentryin(A, B, C) -> Com_1(evalNestedSinglebb5in(0, B, C)) :|: TRUE evalNestedSinglebb5in(A, B, C) -> Com_1(evalNestedSinglebb2in(A, B, A)) :|: B >= A + 1 evalNestedSinglebb5in(A, B, C) -> Com_1(evalNestedSinglereturnin(A, B, C)) :|: A >= B evalNestedSinglebb2in(A, B, C) -> Com_1(evalNestedSinglebb4in(A, B, C)) :|: C >= B evalNestedSinglebb2in(A, B, C) -> Com_1(evalNestedSinglebb3in(A, B, C)) :|: B >= C + 1 evalNestedSinglebb3in(A, B, C) -> Com_1(evalNestedSinglebb1in(A, B, C)) :|: 0 >= D + 1 evalNestedSinglebb3in(A, B, C) -> Com_1(evalNestedSinglebb1in(A, B, C)) :|: D >= 1 evalNestedSinglebb3in(A, B, C) -> Com_1(evalNestedSinglebb4in(A, B, C)) :|: TRUE evalNestedSinglebb1in(A, B, C) -> Com_1(evalNestedSinglebb2in(A, B, C + 1)) :|: TRUE evalNestedSinglebb4in(A, B, C) -> Com_1(evalNestedSinglebb5in(C + 1, B, C)) :|: TRUE evalNestedSinglereturnin(A, B, C) -> Com_1(evalNestedSinglestop(A, B, C)) :|: TRUE The start-symbols are:[evalNestedSinglestart_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 24*ar_1 + 30) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalNestedSinglestart(ar_0, ar_1, ar_2) -> Com_1(evalNestedSingleentryin(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalNestedSingleentryin(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb5in(0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb5in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb5in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglereturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb1in(ar_0, ar_1, ar_2)) [ 0 >= d + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb1in(ar_0, ar_1, ar_2)) [ d >= 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb3in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb4in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb1in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evalNestedSinglebb4in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb5in(ar_2 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evalNestedSinglereturnin(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglestop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglestart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalNestedSinglestart(ar_0, ar_1, ar_2) -> Com_1(evalNestedSingleentryin(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalNestedSingleentryin(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb5in(0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalNestedSinglebb5in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalNestedSinglebb5in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglereturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] (Comp: ?, Cost: 1) evalNestedSinglebb2in(ar_0, ar_1, ar_2) -> Com_1(evalNestedSinglebb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
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