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Complexity_ITS 2019-03-21 04.46 pair #429990436
details
property
value
status
complete
benchmark
bf13.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.96987 seconds
cpu usage
4.46422
user time
4.15611
system time
0.30811
max virtual memory
1.8693652E7
max residence set size
225176.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
4.29/1.94 WORST_CASE(?, O(1)) 4.29/1.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.29/1.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.29/1.95 4.29/1.95 4.29/1.95 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 4.29/1.95 4.29/1.95 (0) CpxIntTrs 4.29/1.95 (1) Koat Proof [FINISHED, 197 ms] 4.29/1.95 (2) BOUNDS(1, 1) 4.29/1.95 4.29/1.95 4.29/1.95 ---------------------------------------- 4.29/1.95 4.29/1.95 (0) 4.29/1.95 Obligation: 4.29/1.95 Complexity Int TRS consisting of the following rules: 4.29/1.95 f0(A, B, C, D, E, F, G) -> Com_1(f49(5, 13, 0, 0, E, F, G)) :|: TRUE 4.29/1.95 f49(A, B, C, D, E, F, G) -> Com_1(f49(A, B, C, C + 1, E, F, G)) :|: A >= D + 1 && C >= D && C <= D 4.29/1.95 f49(A, B, C, D, E, F, G) -> Com_1(f49(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && C >= D + 1 4.29/1.95 f49(A, B, C, D, E, F, G) -> Com_1(f49(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && D >= 1 + C 4.29/1.95 f57(A, B, C, D, E, F, G) -> Com_1(f60(A, B, C, D, 0, F, G)) :|: A >= D + 1 4.29/1.95 f60(A, B, C, D, E, F, G) -> Com_1(f60(A, B, C, D, E + 1, H, I)) :|: B >= E + 1 4.29/1.95 f71(A, B, C, D, E, F, G) -> Com_1(f77(A, B, C, D, E, H, I)) :|: B >= D + 1 4.29/1.95 f71(A, B, C, D, E, F, G) -> Com_1(f71(A, B, C, D + 1, E, H, I)) :|: B >= D + 1 4.29/1.95 f81(A, B, C, D, E, F, G) -> Com_1(f81(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 4.29/1.95 f81(A, B, C, D, E, F, G) -> Com_1(f77(A, B, C, D, E, F, G)) :|: D >= A 4.29/1.95 f71(A, B, C, D, E, F, G) -> Com_1(f81(A, B, C, 0, E, F, G)) :|: D >= B 4.29/1.95 f60(A, B, C, D, E, F, G) -> Com_1(f57(A, B, C, D + 1, E, F, G)) :|: E >= B 4.29/1.95 f57(A, B, C, D, E, F, G) -> Com_1(f71(A, B, C, 0, E, F, G)) :|: D >= A 4.29/1.95 f49(A, B, C, D, E, F, G) -> Com_1(f57(A, B, C, 0, E, F, G)) :|: D >= A 4.29/1.95 4.29/1.95 The start-symbols are:[f0_7] 4.29/1.95 4.29/1.95 4.29/1.95 ---------------------------------------- 4.29/1.95 4.29/1.95 (1) Koat Proof (FINISHED) 4.29/1.95 YES(?, 1858) 4.29/1.95 4.29/1.95 4.29/1.95 4.29/1.95 Initial complexity problem: 4.29/1.95 4.29/1.95 1: T: 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f49(5, 13, 0, 0, ar_4, ar_5, ar_6)) 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f49(ar_0, ar_1, ar_2, ar_2 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f49(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 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f49(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 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f57(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f60(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f60(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f60(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, h, i)) [ ar_1 >= ar_4 + 1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f71(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f81(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f81(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f60(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_4 >= ar_1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f57(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f71(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.29/1.95 4.29/1.95 (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 ] 4.29/1.95 4.29/1.95 start location: koat_start 4.29/1.95 4.29/1.95 leaf cost: 0 4.29/1.95 4.29/1.95 4.29/1.95 4.29/1.95 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4]. 4.29/1.95 4.29/1.95 We thus obtain the following problem: 4.29/1.95 4.29/1.95 2: T: 4.29/1.95 4.29/1.95 (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 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f71(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f60(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f71(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f81(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.29/1.95 4.29/1.95 (Comp: ?, Cost: 1) f81(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.29/1.95
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