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Complexity_ITS 2019-03-21 04.46 pair #429990846
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
n178.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.06058 seconds
cpu usage
10.3494
user time
9.89832
system time
0.451091
max virtual memory
1.8894976E7
max residence set size
229800.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
10.26/5.02 WORST_CASE(Omega(n^1), O(n^2)) 10.26/5.03 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 10.26/5.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.26/5.03 10.26/5.03 10.26/5.03 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 10.26/5.03 10.26/5.03 (0) CpxIntTrs 10.26/5.03 (1) Koat Proof [FINISHED, 724 ms] 10.26/5.03 (2) BOUNDS(1, n^2) 10.26/5.03 (3) Loat Proof [FINISHED, 3347 ms] 10.26/5.03 (4) BOUNDS(n^1, INF) 10.26/5.03 10.26/5.03 10.26/5.03 ---------------------------------------- 10.26/5.03 10.26/5.03 (0) 10.26/5.03 Obligation: 10.26/5.03 Complexity Int TRS consisting of the following rules: 10.26/5.03 f0(A, B) -> Com_1(f2(A, B)) :|: A >= 1 && B >= 1 10.26/5.03 f0(A, B) -> Com_1(f2(A, B)) :|: A >= 1 && 0 >= B + 1 10.26/5.03 f0(A, B) -> Com_1(f2(A, B)) :|: 0 >= A + 1 && B >= 1 10.26/5.03 f0(A, B) -> Com_1(f2(A, B)) :|: 0 >= A + 1 && 0 >= B + 1 10.26/5.03 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= B && B >= 2 && A >= 1 && A + B >= 2 10.26/5.03 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= B && B >= 2 && 0 >= A + 1 && A + B >= 2 10.26/5.03 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= B && 0 >= B && A >= 1 && A + B >= 2 10.26/5.03 f2(A, B) -> Com_1(f2(A, B - 1)) :|: A >= B && 0 >= B && 0 >= A + 1 && A + B >= 2 10.26/5.03 f2(A, B) -> Com_1(f2(A - 1, B)) :|: 1 >= A + B && A >= B + 1 && A >= 2 && B >= 1 10.26/5.03 f2(A, B) -> Com_1(f2(A - 1, B)) :|: 1 >= A + B && A >= B + 1 && A >= 2 && 0 >= B + 1 10.26/5.03 f2(A, B) -> Com_1(f2(A - 1, B)) :|: 1 >= A + B && A >= B + 1 && 0 >= A && B >= 1 10.26/5.03 f2(A, B) -> Com_1(f2(A - 1, B)) :|: 1 >= A + B && A >= B + 1 && 0 >= A && 0 >= B + 1 10.26/5.03 f2(A, B) -> Com_1(f2(A, B + 1)) :|: B >= A && B >= 0 && A >= 1 && 0 >= B + A + 1 10.26/5.03 f2(A, B) -> Com_1(f2(A, B + 1)) :|: B >= A && B >= 0 && 0 >= A + 1 && 0 >= B + A + 1 10.26/5.03 f2(A, B) -> Com_1(f2(A, B + 1)) :|: B >= A && 0 >= B + 2 && A >= 1 && 0 >= B + A + 1 10.26/5.03 f2(A, B) -> Com_1(f2(A, B + 1)) :|: B >= A && 0 >= B + 2 && 0 >= A + 1 && 0 >= B + A + 1 10.26/5.03 f2(A, B) -> Com_1(f2(A + 1, B)) :|: B + A >= 0 && B >= A + 1 && A >= 0 && B >= 1 10.26/5.03 f2(A, B) -> Com_1(f2(A + 1, B)) :|: B + A >= 0 && B >= A + 1 && A >= 0 && 0 >= B + 1 10.26/5.03 f2(A, B) -> Com_1(f2(A + 1, B)) :|: B + A >= 0 && B >= A + 1 && 0 >= A + 2 && B >= 1 10.26/5.03 f2(A, B) -> Com_1(f2(A + 1, B)) :|: B + A >= 0 && B >= A + 1 && 0 >= A + 2 && 0 >= B + 1 10.26/5.03 10.26/5.03 The start-symbols are:[f0_2] 10.26/5.03 10.26/5.03 10.26/5.03 ---------------------------------------- 10.26/5.03 10.26/5.03 (1) Koat Proof (FINISHED) 10.26/5.03 YES(?, 8*ar_1 + 3*ar_0^2 + 4*ar_0*ar_1 + 6*ar_0 + ar_1^2 + 4) 10.26/5.03 10.26/5.03 10.26/5.03 10.26/5.03 Initial complexity problem: 10.26/5.03 10.26/5.03 1: T: 10.26/5.03 10.26/5.03 (Comp: ?, Cost: 1) f0(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1)) [ ar_0 >= 1 /\ ar_1 >= 1 ] 10.26/5.03 10.26/5.03 (Comp: ?, Cost: 1) f0(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1)) [ ar_0 >= 1 /\ 0 >= ar_1 + 1 ] 10.26/5.03 10.26/5.03 (Comp: ?, Cost: 1) f0(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1)) [ 0 >= ar_0 + 1 /\ ar_1 >= 1 ] 10.26/5.03 10.26/5.03 (Comp: ?, Cost: 1) f0(ar_0, ar_1) -> Com_1(f2(ar_0, ar_1)) [ 0 >= ar_0 + 1 /\ 0 >= ar_1 + 1 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (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 ] 10.26/5.03 10.26/5.03 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ] 10.26/5.03 10.26/5.03 start location: koat_start 10.26/5.03 10.26/5.03 leaf cost: 0 10.26/5.03
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