details

property	value
status	complete
benchmark	random1d.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n123.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.22996 seconds
cpu usage	4.70929
user time	4.43672
system time	0.272567
max virtual memory	1.8524832E7
max residence set size	218688.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

4.56/2.20 WORST_CASE(Omega(n^1), O(n^1)) 4.56/2.21 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.56/2.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.56/2.21 4.56/2.21 4.56/2.21 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 4.56/2.21 4.56/2.21 (0) CpxIntTrs 4.56/2.21 (1) Koat Proof [FINISHED, 201 ms] 4.56/2.21 (2) BOUNDS(1, n^1) 4.56/2.21 (3) Loat Proof [FINISHED, 531 ms] 4.56/2.21 (4) BOUNDS(n^1, INF) 4.56/2.21 4.56/2.21 4.56/2.21 ---------------------------------------- 4.56/2.21 4.56/2.21 (0) 4.56/2.21 Obligation: 4.56/2.21 Complexity Int TRS consisting of the following rules: 4.56/2.21 start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: 0 >= A && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F 4.56/2.21 start(A, B, C, D, E, F) -> Com_1(lbl101(A, 2, C, D, 1, F)) :|: A >= 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F 4.56/2.21 start(A, B, C, D, E, F) -> Com_1(lbl101(A, 2, C, D, -(1), F)) :|: A >= 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F 4.56/2.21 lbl101(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: E + A >= 0 && A >= 1 && A >= E && B >= A + 1 && B <= A + 1 && D >= A && D <= A 4.56/2.21 lbl101(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + B, C, D, 1 + E, F)) :|: A >= B && E + B >= 1 && A + 1 >= B && B >= 2 && B >= E + 1 && D >= A && D <= A 4.56/2.21 lbl101(A, B, C, D, E, F) -> Com_1(lbl101(A, 1 + B, C, D, E - 1, F)) :|: A >= B && E + B >= 1 && A + 1 >= B && B >= 2 && B >= E + 1 && D >= A && D <= A 4.56/2.21 start0(A, B, C, D, E, F) -> Com_1(start(A, C, C, A, F, F)) :|: TRUE 4.56/2.21 4.56/2.21 The start-symbols are:[start0_6] 4.56/2.21 4.56/2.21 4.56/2.21 ---------------------------------------- 4.56/2.21 4.56/2.21 (1) Koat Proof (FINISHED) 4.56/2.21 YES(?, 4*ar_0 + 17) 4.56/2.21 4.56/2.21 4.56/2.21 4.56/2.21 Initial complexity problem: 4.56/2.21 4.56/2.21 1: T: 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\ ar_0 >= 1 /\ ar_0 >= ar_4 /\ ar_1 = ar_0 + 1 /\ ar_3 = ar_0 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5)) 4.56/2.21 4.56/2.21 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.56/2.21 4.56/2.21 start location: koat_start 4.56/2.21 4.56/2.21 leaf cost: 0 4.56/2.21 4.56/2.21 4.56/2.21 4.56/2.21 Repeatedly propagating knowledge in problem 1 produces the following problem: 4.56/2.21 4.56/2.21 2: T: 4.56/2.21 4.56/2.21 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.56/2.21 4.56/2.21 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, 1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.56/2.21 4.56/2.21 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, 2, ar_2, ar_3, -1, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 + ar_0 >= 0 /\ ar_0 >= 1 /\ ar_0 >= ar_4 /\ ar_1 = ar_0 + 1 /\ ar_3 = ar_0 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ] 4.56/2.21 4.56/2.21 (Comp: ?, Cost: 1) lbl101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl101(ar_0, ar_1 + 1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_0 >= ar_1 /\ ar_4 + ar_1 >= 1 /\ ar_0 + 1 >= ar_1 /\ ar_1 >= 2 /\ ar_1 >= ar_4 + 1 /\ ar_3 = ar_0 ] 4.56/2.21 4.56/2.21 (Comp: 1, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5)) 4.56/2.21 4.56/2.21 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.56/2.21 4.56/2.21 start location: koat_start 4.56/2.21 4.56/2.21 leaf cost: 0 4.56/2.21 4.56/2.21 4.56/2.21 4.56/2.21 A polynomial rank function with 4.56/2.21 4.56/2.21 Pol(start) = 1 4.56/2.21 4.56/2.21 Pol(stop) = 0 4.56/2.21 4.56/2.21 Pol(lbl101) = 1 4.56/2.21 4.56/2.21 Pol(start0) = 1 4.56/2.21 4.56/2.21 Pol(koat_start) = 1 popout

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

job log

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actions

all output return to Complexity_ITS 2019-03-21 04.46