details

property	value
status	complete
benchmark	spiral.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n109.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.94805979729 seconds
cpu usage	10.288219982
max memory	4.58469376E8

stage attributes

key	value
output-size	61894
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 628 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 3328 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f0(A, B) -> Com_1(f2(A, B)) :|: A >= 1 && B >= 1 f0(A, B) -> Com_1(f2(A, B)) :|: A >= 1 && 0 >= B + 1 f0(A, B) -> Com_1(f2(A, B)) :|: 0 >= A + 1 && B >= 1 f0(A, B) -> Com_1(f2(A, B)) :|: 0 >= A + 1 && 0 >= B + 1 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= B && B >= 2 && A >= 1 && A + B >= 2 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= B && B >= 2 && 0 >= A + 1 && A + B >= 2 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= B && 0 >= B && A >= 1 && A + B >= 2 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= B && 0 >= B && 0 >= A + 1 && A + B >= 2 f2(A, B) -> Com_1(f2(A - 1, B)) :|: 1 >= A + B && A >= B + 1 && A >= 2 && B >= 1 f2(A, B) -> Com_1(f2(A - 1, B)) :|: 1 >= A + B && A >= B + 1 && A >= 2 && 0 >= B + 1 f2(A, B) -> Com_1(f2(A - 1, B)) :|: 1 >= A + B && A >= B + 1 && 0 >= A && B >= 1 f2(A, B) -> Com_1(f2(A - 1, B)) :|: 1 >= A + B && A >= B + 1 && 0 >= A && 0 >= B + 1 f2(A, B) -> Com_1(f2(A, B + 1)) :|: B >= A && B >= 0 && A >= 1 && 0 >= B + A + 1 f2(A, B) -> Com_1(f2(A, B + 1)) :|: B >= A && B >= 0 && 0 >= A + 1 && 0 >= B + A + 1 f2(A, B) -> Com_1(f2(A, B + 1)) :|: B >= A && 0 >= B + 2 && A >= 1 && 0 >= B + A + 1 f2(A, B) -> Com_1(f2(A, B + 1)) :|: B >= A && 0 >= B + 2 && 0 >= A + 1 && 0 >= B + A + 1 f2(A, B) -> Com_1(f2(A + 1, B)) :|: B + A >= 0 && B >= A + 1 && A >= 0 && B >= 1 f2(A, B) -> Com_1(f2(A + 1, B)) :|: B + A >= 0 && B >= A + 1 && A >= 0 && 0 >= B + 1 f2(A, B) -> Com_1(f2(A + 1, B)) :|: B + A >= 0 && B >= A + 1 && 0 >= A + 2 && B >= 1 f2(A, B) -> Com_1(f2(A + 1, B)) :|: B + A >= 0 && B >= A + 1 && 0 >= A + 2 && 0 >= B + 1 The start-symbols are:[f0_2] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 8*ar_1 + 3*ar_0^2 + 4*ar_0*ar_1 + 6*ar_0 + ar_1^2 + 4) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1)) [ ar_0 >= 1 /\ ar_1 >= 1 ] (Comp: ?, Cost: 1) f0(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1)) [ ar_0 >= 1 /\ 0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f0(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1)) [ 0 >= ar_0 + 1 /\ ar_1 >= 1 ] (Comp: ?, Cost: 1) f0(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1)) [ 0 >= ar_0 + 1 /\ 0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1 - 1)) [ ar_0 >= ar_1 /\ ar_1 >= 2 /\ ar_0 >= 1 /\ ar_0 + ar_1 >= 2 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1 - 1)) [ ar_0 >= ar_1 /\ ar_1 >= 2 /\ 0 >= ar_0 + 1 /\ ar_0 + ar_1 >= 2 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1 - 1)) [ ar_0 >= ar_1 /\ 0 >= ar_1 /\ ar_0 >= 1 /\ ar_0 + ar_1 >= 2 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1 - 1)) [ ar_0 >= ar_1 /\ 0 >= ar_1 /\ 0 >= ar_0 + 1 /\ ar_0 + ar_1 >= 2 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0 - 1, ar_1)) [ 1 >= ar_0 + ar_1 /\ ar_0 >= ar_1 + 1 /\ ar_0 >= 2 /\ ar_1 >= 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0 - 1, ar_1)) [ 1 >= ar_0 + ar_1 /\ ar_0 >= ar_1 + 1 /\ ar_0 >= 2 /\ 0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0 - 1, ar_1)) [ 1 >= ar_0 + ar_1 /\ ar_0 >= ar_1 + 1 /\ 0 >= ar_0 /\ ar_1 >= 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0 - 1, ar_1)) [ 1 >= ar_0 + ar_1 /\ ar_0 >= ar_1 + 1 /\ 0 >= ar_0 /\ 0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1 + 1)) [ ar_1 >= ar_0 /\ ar_1 >= 0 /\ ar_0 >= 1 /\ 0 >= ar_1 + ar_0 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1 + 1)) [ ar_1 >= ar_0 /\ ar_1 >= 0 /\ 0 >= ar_0 + 1 /\ 0 >= ar_1 + ar_0 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1 + 1)) [ ar_1 >= ar_0 /\ 0 >= ar_1 + 2 /\ ar_0 >= 1 /\ 0 >= ar_1 + ar_0 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1 + 1)) [ ar_1 >= ar_0 /\ 0 >= ar_1 + 2 /\ 0 >= ar_0 + 1 /\ 0 >= ar_1 + ar_0 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0 + 1, ar_1)) [ ar_1 + ar_0 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_0 >= 0 /\ ar_1 >= 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0 + 1, ar_1)) [ ar_1 + ar_0 >= 0 /\ ar_1 >= ar_0 + 1 /\ ar_0 >= 0 /\ 0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0 + 1, ar_1)) [ ar_1 + ar_0 >= 0 /\ ar_1 >= ar_0 + 1 /\ 0 >= ar_0 + 2 /\ ar_1 >= 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1) -> Com_1(f2(ar_0 + 1, ar_1)) [ ar_1 + ar_0 >= 0 /\ ar_1 >= ar_0 + 1 /\ 0 >= ar_0 + 2 /\ 0 >= ar_1 + 1 ] popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Compl Integ Trans Syste 26843