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Complexity_ITS 2019-03-21 04.46 pair #429991076
details
property
value
status
complete
benchmark
Example2.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n111.star.cs.uiowa.edu
space
PLDI09
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.48831 seconds
cpu usage
5.43012
user time
5.10659
system time
0.323531
max virtual memory
1.869466E7
max residence set size
222664.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
5.36/2.45 WORST_CASE(Omega(n^1), O(n^1)) 5.36/2.46 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.36/2.46 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.36/2.46 5.36/2.46 5.36/2.46 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 5.36/2.46 5.36/2.46 (0) CpxIntTrs 5.36/2.46 (1) Koat Proof [FINISHED, 208 ms] 5.36/2.46 (2) BOUNDS(1, n^1) 5.36/2.46 (3) Loat Proof [FINISHED, 811 ms] 5.36/2.46 (4) BOUNDS(n^1, INF) 5.36/2.46 5.36/2.46 5.36/2.46 ---------------------------------------- 5.36/2.46 5.36/2.46 (0) 5.36/2.46 Obligation: 5.36/2.46 Complexity Int TRS consisting of the following rules: 5.36/2.46 evalfstart(A, B, C) -> Com_1(evalfentryin(A, B, C)) :|: TRUE 5.36/2.46 evalfentryin(A, B, C) -> Com_1(evalfbb3in(B, A, 0)) :|: A >= 1 && B >= 1 5.36/2.46 evalfbb3in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: 0 >= B 5.36/2.46 evalfbb3in(A, B, C) -> Com_1(evalfbb4in(A, B, C)) :|: B >= 1 5.36/2.46 evalfbb4in(A, B, C) -> Com_1(evalfbbin(A, B, C)) :|: 0 >= D + 1 5.36/2.46 evalfbb4in(A, B, C) -> Com_1(evalfbbin(A, B, C)) :|: D >= 1 5.36/2.46 evalfbb4in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: TRUE 5.36/2.46 evalfbbin(A, B, C) -> Com_1(evalfbb1in(A, B, C)) :|: A >= C + 1 5.36/2.46 evalfbbin(A, B, C) -> Com_1(evalfbb3in(A, B, 0)) :|: C >= A 5.36/2.46 evalfbb1in(A, B, C) -> Com_1(evalfbb3in(A, B - 1, C + 1)) :|: TRUE 5.36/2.46 evalfreturnin(A, B, C) -> Com_1(evalfstop(A, B, C)) :|: TRUE 5.36/2.46 5.36/2.46 The start-symbols are:[evalfstart_3] 5.36/2.46 5.36/2.46 5.36/2.46 ---------------------------------------- 5.36/2.46 5.36/2.46 (1) Koat Proof (FINISHED) 5.36/2.46 YES(?, 42*ar_0 + 14) 5.36/2.46 5.36/2.46 5.36/2.46 5.36/2.46 Initial complexity problem: 5.36/2.46 5.36/2.46 1: T: 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_1, ar_0, 0)) [ ar_0 >= 1 /\ ar_1 >= 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ 0 >= d + 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ d >= 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, 0)) [ ar_2 >= ar_0 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1 - 1, ar_2 + 1)) 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) 5.36/2.46 5.36/2.46 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 5.36/2.46 5.36/2.46 start location: koat_start 5.36/2.46 5.36/2.46 leaf cost: 0 5.36/2.46 5.36/2.46 5.36/2.46 5.36/2.46 Repeatedly propagating knowledge in problem 1 produces the following problem: 5.36/2.46 5.36/2.46 2: T: 5.36/2.46 5.36/2.46 (Comp: 1, Cost: 1) evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) 5.36/2.46 5.36/2.46 (Comp: 1, Cost: 1) evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_1, ar_0, 0)) [ ar_0 >= 1 /\ ar_1 >= 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ 0 >= d + 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ d >= 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, 0)) [ ar_2 >= ar_0 ] 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1 - 1, ar_2 + 1)) 5.36/2.46 5.36/2.46 (Comp: ?, Cost: 1) evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
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