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Complexity_ITS 2019-03-21 04.46 pair #429990660
details
property
value
status
complete
benchmark
fun5.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
289.681 seconds
cpu usage
329.944
user time
326.081
system time
3.86335
max virtual memory
1.8749988E7
max residence set size
316640.0
stage attributes
key
value
starexec-result
MAYBE
output
329.85/289.64 MAYBE 329.85/289.66 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 329.85/289.66 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 329.85/289.66 329.85/289.66 329.85/289.66 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). 329.85/289.66 329.85/289.66 (0) CpxIntTrs 329.85/289.66 (1) Loat Proof [FINISHED, 288.5 s] 329.85/289.66 (2) BOUNDS(1, INF) 329.85/289.66 329.85/289.66 329.85/289.66 ---------------------------------------- 329.85/289.66 329.85/289.66 (0) 329.85/289.66 Obligation: 329.85/289.66 Complexity Int TRS consisting of the following rules: 329.85/289.66 f0(A, B, C, D, E, F, G) -> Com_1(f1(A, B, C, D, E, F, G)) :|: A >= 0 && 3 >= A && B >= 0 && 3 >= B && 3 >= C && D >= 0 && 3 >= E && E >= 0 329.85/289.66 f1(A, B, C, D, E, F, G) -> Com_1(f2(A, B, C, D, E, D + 1, G)) :|: 1 + B >= 2 * D 329.85/289.66 f1(A, B, C, D, E, F, G) -> Com_1(f2(A, B, C, D, E, D - 1, G)) :|: 2 * D >= 4 + B 329.85/289.66 f1(A, B, C, D, E, F, G) -> Com_1(f2(A, B, C, D, E, D, G)) :|: B + 2 >= 2 * D && B + 2 <= 2 * D 329.85/289.66 f1(A, B, C, D, E, F, G) -> Com_1(f2(A, B, C, D, E, D, G)) :|: B + 3 >= 2 * D && B + 3 <= 2 * D 329.85/289.66 f2(A, B, C, D, E, F, G) -> Com_1(f3(A, B, C, D, E, F, E + 1)) :|: D + A >= 2 * E + 1 329.85/289.66 f2(A, B, C, D, E, F, G) -> Com_1(f3(A, B, C, D, E, F, E - 1)) :|: 2 * E >= 2 + D + A 329.85/289.66 f2(A, B, C, D, E, F, G) -> Com_1(f3(A, B, C, D, E, F, E)) :|: D + A >= 2 * E && D + A <= 2 * E 329.85/289.66 f2(A, B, C, D, E, F, G) -> Com_1(f3(A, B, C, D, E, F, E)) :|: D + A + 1 >= 2 * E && D + A + 1 <= 2 * E 329.85/289.66 f3(A, B, C, D, E, F, G) -> Com_1(f1(A, B, C, F, G, F, G)) :|: D >= F + 1 329.85/289.66 f3(A, B, C, D, E, F, G) -> Com_1(f1(A, B, C, F, G, F, G)) :|: F >= D + 1 329.85/289.66 f3(A, B, C, D, E, F, G) -> Com_1(f1(A, B, C, F, G, F, G)) :|: E >= G + 1 329.85/289.66 f3(A, B, C, D, E, F, G) -> Com_1(f1(A, B, C, F, G, F, G)) :|: G >= E + 1 329.85/289.66 329.85/289.66 The start-symbols are:[f0_7] 329.85/289.66 329.85/289.66 329.85/289.66 ---------------------------------------- 329.85/289.66 329.85/289.66 (1) Loat Proof (FINISHED) 329.85/289.66 329.85/289.66 329.85/289.66 ### Pre-processing the ITS problem ### 329.85/289.66 329.85/289.66 329.85/289.66 329.85/289.66 Initial linear ITS problem 329.85/289.66 329.85/289.66 Start location: f0 329.85/289.66 329.85/289.66 0: f0 -> f1 : [ A>=0 && 3>=A && B>=0 && 3>=B && 3>=C && D>=0 && 3>=E && E>=0 ], cost: 1 329.85/289.66 329.85/289.66 1: f1 -> f2 : F'=1+D, [ 1+B>=2*D ], cost: 1 329.85/289.66 329.85/289.66 2: f1 -> f2 : F'=-1+D, [ 2*D>=4+B ], cost: 1 329.85/289.66 329.85/289.66 3: f1 -> f2 : F'=D, [ 2+B==2*D ], cost: 1 329.85/289.66 329.85/289.66 4: f1 -> f2 : F'=D, [ 3+B==2*D ], cost: 1 329.85/289.66 329.85/289.66 5: f2 -> f3 : G'=1+E, [ D+A>=1+2*E ], cost: 1 329.85/289.66 329.85/289.66 6: f2 -> f3 : G'=-1+E, [ 2*E>=2+D+A ], cost: 1 329.85/289.66 329.85/289.66 7: f2 -> f3 : G'=E, [ D+A==2*E ], cost: 1 329.85/289.66 329.85/289.66 8: f2 -> f3 : G'=E, [ 1+D+A==2*E ], cost: 1 329.85/289.66 329.85/289.66 9: f3 -> f1 : D'=F, E'=G, [ D>=1+F ], cost: 1 329.85/289.66 329.85/289.66 10: f3 -> f1 : D'=F, E'=G, [ F>=1+D ], cost: 1 329.85/289.66 329.85/289.66 11: f3 -> f1 : D'=F, E'=G, [ E>=1+G ], cost: 1 329.85/289.66 329.85/289.66 12: f3 -> f1 : D'=F, E'=G, [ G>=1+E ], cost: 1 329.85/289.66 329.85/289.66 329.85/289.66 329.85/289.66 ### Simplification by acceleration and chaining ### 329.85/289.66 329.85/289.66 329.85/289.66 329.85/289.66 Eliminated locations (on tree-shaped paths): 329.85/289.66 329.85/289.66 Start location: f0 329.85/289.66 329.85/289.66 0: f0 -> f1 : [ A>=0 && 3>=A && B>=0 && 3>=B && 3>=C && D>=0 && 3>=E && E>=0 ], cost: 1 329.85/289.66 329.85/289.66 13: f1 -> f3 : F'=1+D, G'=1+E, [ 1+B>=2*D && D+A>=1+2*E ], cost: 2 329.85/289.66 329.85/289.66 14: f1 -> f3 : F'=1+D, G'=-1+E, [ 1+B>=2*D && 2*E>=2+D+A ], cost: 2 329.85/289.66 329.85/289.66 15: f1 -> f3 : F'=1+D, G'=E, [ 1+B>=2*D && D+A==2*E ], cost: 2 329.85/289.66 329.85/289.66 16: f1 -> f3 : F'=1+D, G'=E, [ 1+B>=2*D && 1+D+A==2*E ], cost: 2 329.85/289.66 329.85/289.66 17: f1 -> f3 : F'=-1+D, G'=1+E, [ 2*D>=4+B && D+A>=1+2*E ], cost: 2 329.85/289.66 329.85/289.66 18: f1 -> f3 : F'=-1+D, G'=-1+E, [ 2*D>=4+B && 2*E>=2+D+A ], cost: 2 329.85/289.66 329.85/289.66 19: f1 -> f3 : F'=-1+D, G'=E, [ 2*D>=4+B && D+A==2*E ], cost: 2 329.85/289.66 329.85/289.66 20: f1 -> f3 : F'=-1+D, G'=E, [ 2*D>=4+B && 1+D+A==2*E ], cost: 2
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