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Complexity_ITS 2019-03-21 04.46 pair #429990724
details
property
value
status
complete
benchmark
bf19.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n166.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.87649 seconds
cpu usage
4.43614
user time
4.15131
system time
0.284832
max virtual memory
1.8409268E7
max residence set size
222008.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
3.55/1.85 WORST_CASE(?, O(1)) 4.38/1.86 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.38/1.86 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.38/1.86 4.38/1.86 4.38/1.86 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 4.38/1.86 4.38/1.86 (0) CpxIntTrs 4.38/1.86 (1) Koat Proof [FINISHED, 201 ms] 4.38/1.86 (2) BOUNDS(1, 1) 4.38/1.86 4.38/1.86 4.38/1.86 ---------------------------------------- 4.38/1.86 4.38/1.86 (0) 4.38/1.86 Obligation: 4.38/1.86 Complexity Int TRS consisting of the following rules: 4.38/1.86 f0(A, B, C, D, E, F, G) -> Com_1(f67(5, 19, 0, 0, E, F, G)) :|: TRUE 4.38/1.86 f67(A, B, C, D, E, F, G) -> Com_1(f67(A, B, C, C + 1, E, F, G)) :|: A >= D + 1 && C >= D && C <= D 4.38/1.86 f67(A, B, C, D, E, F, G) -> Com_1(f67(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && C >= D + 1 4.38/1.86 f67(A, B, C, D, E, F, G) -> Com_1(f67(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && D >= 1 + C 4.38/1.86 f75(A, B, C, D, E, F, G) -> Com_1(f78(A, B, C, D, 0, F, G)) :|: A >= D + 1 4.38/1.86 f78(A, B, C, D, E, F, G) -> Com_1(f78(A, B, C, D, E + 1, H, I)) :|: B >= E + 1 4.38/1.86 f89(A, B, C, D, E, F, G) -> Com_1(f95(A, B, C, D, E, H, I)) :|: B >= D + 1 4.38/1.86 f89(A, B, C, D, E, F, G) -> Com_1(f89(A, B, C, D + 1, E, H, I)) :|: B >= D + 1 4.38/1.86 f99(A, B, C, D, E, F, G) -> Com_1(f99(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 4.38/1.86 f99(A, B, C, D, E, F, G) -> Com_1(f95(A, B, C, D, E, F, G)) :|: D >= A 4.38/1.86 f89(A, B, C, D, E, F, G) -> Com_1(f99(A, B, C, 0, E, F, G)) :|: D >= B 4.38/1.86 f78(A, B, C, D, E, F, G) -> Com_1(f75(A, B, C, D + 1, E, F, G)) :|: E >= B 4.38/1.86 f75(A, B, C, D, E, F, G) -> Com_1(f89(A, B, C, 0, E, F, G)) :|: D >= A 4.38/1.86 f67(A, B, C, D, E, F, G) -> Com_1(f75(A, B, C, 0, E, F, G)) :|: D >= A 4.38/1.86 4.38/1.86 The start-symbols are:[f0_7] 4.38/1.86 4.38/1.86 4.38/1.86 ---------------------------------------- 4.38/1.86 4.38/1.86 (1) Koat Proof (FINISHED) 4.38/1.86 YES(?, 3046) 4.38/1.86 4.38/1.86 4.38/1.86 4.38/1.86 Initial complexity problem: 4.38/1.86 4.38/1.86 1: T: 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f67(5, 19, 0, 0, ar_4, ar_5, ar_6)) 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f67(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f67(ar_0, ar_1, ar_2, ar_2 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f67(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f67(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f67(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f67(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f78(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f78(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f78(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, h, i)) [ ar_1 >= ar_4 + 1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f89(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f95(ar_0, ar_1, ar_2, ar_3, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f89(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f99(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f99(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f99(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f95(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f89(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f99(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f78(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f75(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_4 >= ar_1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f89(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f67(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f75(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.38/1.86 4.38/1.86 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 4.38/1.86 4.38/1.86 start location: koat_start 4.38/1.86 4.38/1.86 leaf cost: 0 4.38/1.86 4.38/1.86 4.38/1.86 4.38/1.86 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4]. 4.38/1.86 4.38/1.86 We thus obtain the following problem: 4.38/1.86 4.38/1.86 2: T: 4.38/1.86 4.38/1.86 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f67(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f75(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f75(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f78(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f75(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f89(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f99(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.38/1.86 4.38/1.86 (Comp: ?, Cost: 1) f99(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f95(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.38/1.86
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