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Complexity_ITS 2019-03-21 04.46 pair #429990416
details
property
value
status
complete
benchmark
zeroconf_withassume.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n017.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
71.7489 seconds
cpu usage
161.566
user time
158.285
system time
3.28066
max virtual memory
1.8880624E7
max residence set size
281988.0
stage attributes
key
value
starexec-result
MAYBE
output
161.44/71.72 MAYBE 161.44/71.73 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 161.44/71.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 161.44/71.73 161.44/71.73 161.44/71.73 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). 161.44/71.73 161.44/71.73 (0) CpxIntTrs 161.44/71.73 (1) Loat Proof [FINISHED, 21.8 s] 161.44/71.73 (2) BOUNDS(1, INF) 161.44/71.73 161.44/71.73 161.44/71.73 ---------------------------------------- 161.44/71.73 161.44/71.73 (0) 161.44/71.73 Obligation: 161.44/71.73 Complexity Int TRS consisting of the following rules: 161.44/71.73 f0(A, B, C, D, E, F, G, H, I, J) -> Com_1(f15(1, 4, K, 0, L, 0, 0, 0, 0, 0)) :|: K >= 0 && L >= 0 161.44/71.73 f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C, D + 1, E, 0, 0, 0, 0, 0)) :|: 0 >= D && 0 >= C && B >= 1 && I >= 0 && I <= 0 161.44/71.73 f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B - 1, C, 0, E, K, 0, 0, 0, 0)) :|: D >= 1 && 0 >= C && K >= 0 && B >= 1 && 1 >= K && I >= 0 && I <= 0 161.44/71.73 f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A + 1, A + 4, K, 0, E, L, 0, 0, 0, 0)) :|: 0 >= C && L >= 0 && 1 >= L && 0 >= B && K >= 0 && I >= 0 && I <= 0 161.44/71.73 f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C - 1, D, E, K, 0, 0, 0, 0)) :|: C >= 1 && 1 >= K && K >= 0 && I >= 0 && I <= 0 161.44/71.73 f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f78(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= H && J >= 1 + E 161.44/71.73 f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f78(A, B, C, D, E, F, G, H, I, J)) :|: H >= 1 161.44/71.73 f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f48(A, B, C, D + 1, E, F, 0, H, I, J)) :|: E >= J && 0 >= H && 0 >= D && 0 >= C && B >= 1 161.44/71.73 f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f48(A, B - 1, C, 0, E, F, K, H, I, J)) :|: E >= J && 0 >= H && D >= 1 && 0 >= C && K >= 0 && B >= 1 && 1 >= K 161.44/71.73 f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f48(A + 1, A + 4, K, 0, E, F, L, H, I, J)) :|: E >= J && 0 >= H && 0 >= C && L >= 0 && 1 >= L && 0 >= B && K >= 0 161.44/71.73 f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f48(A, B, C - 1, D, E, F, K, H, I, J)) :|: E >= J && 0 >= H && C >= 1 && 1 >= K && K >= 0 161.44/71.73 f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C, D, E, F, G, H, I, J + 1)) :|: E + 1 >= A && 0 >= G 161.44/71.73 f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C, D, E, F, G, H, I, J + 1)) :|: G >= 1 && E + 1 >= A && F >= 1 161.44/71.73 f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C, D + 1, E, F, G, 0, I, J + 1)) :|: G >= 1 && 0 >= F && E + 1 >= A && 0 >= D && 0 >= C && B >= 1 161.44/71.73 f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B - 1, C, 0, E, F, G, K, I, J + 1)) :|: G >= 1 && 0 >= F && E + 1 >= A && D >= 1 && 0 >= C && K >= 0 && B >= 1 && 1 >= K 161.44/71.73 f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A + 1, A + 4, K, 0, E, F, G, L, I, J + 1)) :|: G >= 1 && 0 >= F && E >= A && 0 >= C && L >= 0 && 1 >= L && 0 >= B && K >= 0 161.44/71.73 f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C - 1, D, E, F, G, K, I, J + 1)) :|: G >= 1 && 0 >= F && E + 1 >= A && C >= 1 && 1 >= K && K >= 0 161.44/71.73 f78(A, B, C, D, E, F, G, H, I, J) -> Com_1(f15(A, B, C, D, E, F, G, H, I, J)) :|: E + 1 >= A && H >= 1 161.44/71.73 f78(A, B, C, D, E, F, G, H, I, J) -> Com_1(f15(A, B, C, D, E, F, G, H, 1, J)) :|: E + 1 >= A && 0 >= H 161.44/71.73 f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f83(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= I + 1 161.44/71.73 f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f83(A, B, C, D, E, F, G, H, I, J)) :|: I >= 1 161.44/71.73 161.44/71.73 The start-symbols are:[f0_10] 161.44/71.73 161.44/71.73 161.44/71.73 ---------------------------------------- 161.44/71.73 161.44/71.73 (1) Loat Proof (FINISHED) 161.44/71.73 161.44/71.73 161.44/71.73 ### Pre-processing the ITS problem ### 161.44/71.73 161.44/71.73 161.44/71.73 161.44/71.73 Initial linear ITS problem 161.44/71.73 161.44/71.73 Start location: f0 161.44/71.73 161.44/71.73 0: f0 -> f15 : A'=1, B'=4, C'=free_1, D'=0, E'=free, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free_1>=0 && free>=0 ], cost: 1 161.44/71.73 161.44/71.73 1: f15 -> f36 : D'=1+D, F'=0, G'=0, H'=0, Q'=0, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 ], cost: 1 161.44/71.73 161.44/71.73 2: f15 -> f36 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=0, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 ], cost: 1 161.44/71.73 161.44/71.73 3: f15 -> f36 : A'=1+A, B'=4+A, C'=free_4, D'=0, F'=free_3, G'=0, H'=0, Q'=0, J'=0, [ 0>=C && free_3>=0 && 1>=free_3 && 0>=B && free_4>=0 && Q==0 ], cost: 1 161.44/71.73 161.44/71.73 4: f15 -> f36 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=0, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 ], cost: 1 161.44/71.73 161.44/71.73 19: f15 -> f83 : [ 0>=1+Q ], cost: 1 161.44/71.73 161.44/71.73 20: f15 -> f83 : [ Q>=1 ], cost: 1 161.44/71.73 161.44/71.73 5: f36 -> f78 : [ 0>=H && J>=1+E ], cost: 1 161.44/71.73 161.44/71.73 6: f36 -> f78 : [ H>=1 ], cost: 1 161.44/71.73 161.44/71.73 7: f36 -> f48 : D'=1+D, G'=0, [ E>=J && 0>=H && 0>=D && 0>=C && B>=1 ], cost: 1 161.44/71.73 161.44/71.73 8: f36 -> f48 : B'=-1+B, D'=0, G'=free_6, [ E>=J && 0>=H && D>=1 && 0>=C && free_6>=0 && B>=1 && 1>=free_6 ], cost: 1 161.44/71.73 161.44/71.73 9: f36 -> f48 : A'=1+A, B'=4+A, C'=free_8, D'=0, G'=free_7, [ E>=J && 0>=H && 0>=C && free_7>=0 && 1>=free_7 && 0>=B && free_8>=0 ], cost: 1 161.44/71.73 161.44/71.73 10: f36 -> f48 : C'=-1+C, G'=free_9, [ E>=J && 0>=H && C>=1 && 1>=free_9 && free_9>=0 ], cost: 1 161.44/71.73 161.44/71.73 11: f48 -> f36 : J'=1+J, [ 1+E>=A && 0>=G ], cost: 1 161.44/71.73 161.44/71.73 12: f48 -> f36 : J'=1+J, [ G>=1 && 1+E>=A && F>=1 ], cost: 1 161.44/71.73 161.44/71.73 13: f48 -> f36 : D'=1+D, H'=0, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && 0>=D && 0>=C && B>=1 ], cost: 1 161.44/71.73 161.44/71.73 14: f48 -> f36 : B'=-1+B, D'=0, H'=free_10, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && D>=1 && 0>=C && free_10>=0 && B>=1 && 1>=free_10 ], cost: 1 161.44/71.73 161.44/71.73 15: f48 -> f36 : A'=1+A, B'=4+A, C'=free_12, D'=0, H'=free_11, J'=1+J, [ G>=1 && 0>=F && E>=A && 0>=C && free_11>=0 && 1>=free_11 && 0>=B && free_12>=0 ], cost: 1 161.44/71.73 161.44/71.73 16: f48 -> f36 : C'=-1+C, H'=free_13, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && C>=1 && 1>=free_13 && free_13>=0 ], cost: 1 161.44/71.73 161.44/71.73 17: f78 -> f15 : [ 1+E>=A && H>=1 ], cost: 1 161.44/71.73 161.44/71.73 18: f78 -> f15 : Q'=1, [ 1+E>=A && 0>=H ], cost: 1 161.44/71.73 161.44/71.73 161.44/71.73 161.44/71.73 Removed unreachable and leaf rules:
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