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Complexity_ITS 2019-03-21 04.46 pair #429990488
details
property
value
status
complete
benchmark
nakata.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.4483 seconds
cpu usage
59.3291
user time
57.356
system time
1.97314
max virtual memory
1.8852996E7
max residence set size
264732.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
29.59/10.38 WORST_CASE(NON_POLY, ?) 29.59/10.39 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 29.59/10.39 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 29.59/10.39 29.59/10.39 29.59/10.39 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 29.59/10.39 29.59/10.39 (0) CpxIntTrs 29.59/10.39 (1) Loat Proof [FINISHED, 8576 ms] 29.59/10.39 (2) BOUNDS(INF, INF) 29.59/10.39 29.59/10.39 29.59/10.39 ---------------------------------------- 29.59/10.39 29.59/10.39 (0) 29.59/10.39 Obligation: 29.59/10.39 Complexity Int TRS consisting of the following rules: 29.59/10.39 f25(A, B, C, D, E, F, G, H, I, J) -> Com_1(f16(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= A 29.59/10.39 f0(A, B, C, D, E, F, G, H, I, J) -> Com_1(f16(A, 1, 0, 1, N, 0, M, L, K, J)) :|: K >= 0 && L >= K && L >= 0 && M >= L && N >= 0 && M >= 0 29.59/10.39 f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f25(0, B, C, D, E, F + 1, G, H, I, J)) :|: I >= 1 && 0 >= F && 0 >= E 29.59/10.39 f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f25(N, B, C, D, E, F, G, H, I, J)) :|: I >= 1 && F >= 2 && 0 >= E && 1 >= N && N >= 0 29.59/10.39 f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f25(1, B, C + 1, D, E, F, G, H, I, J)) :|: I >= 1 && 0 >= E && 0 >= C && F >= 1 && F <= 1 29.59/10.40 f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f25(0, B, 0, D - 1, E, F, G, H, I, J)) :|: I >= 1 && 0 >= E && D >= 1 && F >= 1 && F <= 1 && C >= 1 && C <= 1 29.59/10.40 f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f25(M, B + 1, 0, B + 1, N, 0, G, H, I, J)) :|: I >= 1 && 0 >= E && M >= 0 && 1 >= M && C >= 2 && N >= 0 && F >= 1 && F <= 1 29.59/10.40 f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f25(M, B + 1, 0, B + 1, N, 0, G, H, I, J)) :|: I >= 1 && 0 >= E && 0 >= D && M >= 0 && 1 >= M && N >= 0 && F >= 1 && F <= 1 && C >= 1 && C <= 1 29.59/10.40 f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f25(N, B, C, D, E - 1, F, G, H, I, J)) :|: I >= 1 && E >= 1 && 1 >= N && N >= 0 29.59/10.40 f25(A, B, C, D, E, F, G, H, I, J) -> Com_1(f50(A, B, C, D, E, F + 1, G, H, I, 0)) :|: A >= 1 && 0 >= F && 0 >= E 29.59/10.40 f25(A, B, C, D, E, F, G, H, I, J) -> Com_1(f50(A, B, C, D, E, F, G, H, I, N)) :|: A >= 1 && F >= 2 && 0 >= E && 1 >= N && N >= 0 29.59/10.40 f25(A, B, C, D, E, F, G, H, I, J) -> Com_1(f50(A, B, C + 1, D, E, F, G, H, I, 1)) :|: A >= 1 && 0 >= E && 0 >= C && F >= 1 && F <= 1 29.59/10.40 f25(A, B, C, D, E, F, G, H, I, J) -> Com_1(f50(A, B, 0, D - 1, E, F, G, H, I, 0)) :|: A >= 1 && 0 >= E && D >= 1 && F >= 1 && F <= 1 && C >= 1 && C <= 1 29.59/10.40 f25(A, B, C, D, E, F, G, H, I, J) -> Com_1(f50(A, B + 1, 0, B + 1, N, 0, G, H, I, M)) :|: A >= 1 && 0 >= E && M >= 0 && 1 >= M && C >= 2 && N >= 0 && F >= 1 && F <= 1 29.59/10.40 f25(A, B, C, D, E, F, G, H, I, J) -> Com_1(f50(A, B + 1, 0, B + 1, N, 0, G, H, I, M)) :|: A >= 1 && 0 >= E && 0 >= D && M >= 0 && 1 >= M && N >= 0 && F >= 1 && F <= 1 && C >= 1 && C <= 1 29.59/10.40 f25(A, B, C, D, E, F, G, H, I, J) -> Com_1(f50(A, B, C, D, E - 1, F, G, H, I, N)) :|: A >= 1 && E >= 1 && 1 >= N && N >= 0 29.59/10.40 f50(A, B, C, D, E, F, G, H, I, J) -> Com_1(f16(A, B, C, D, E, F, G, H, I, J)) :|: I >= H && J >= 1 29.59/10.40 f50(A, B, C, D, E, F, G, H, I, J) -> Com_1(f16(A, B, C, D, E, F, G, H, I + 1, J)) :|: H >= I + 1 && J >= 1 29.59/10.40 f50(A, B, C, D, E, F, G, H, I, J) -> Com_1(f16(A, B, C, D, E, F, G, H, I - 1, J)) :|: 0 >= J 29.59/10.40 f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f73(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= I 29.59/10.40 29.59/10.40 The start-symbols are:[f0_10] 29.59/10.40 29.59/10.40 29.59/10.40 ---------------------------------------- 29.59/10.40 29.59/10.40 (1) Loat Proof (FINISHED) 29.59/10.40 29.59/10.40 29.59/10.40 ### Pre-processing the ITS problem ### 29.59/10.40 29.59/10.40 29.59/10.40 29.59/10.40 Initial linear ITS problem 29.59/10.40 29.59/10.40 Start location: f0 29.59/10.40 29.59/10.40 0: f25 -> f16 : [ 0>=A ], cost: 1 29.59/10.40 29.59/10.40 9: f25 -> f50 : F'=1+F, J'=0, [ A>=1 && 0>=F && 0>=E ], cost: 1 29.59/10.40 29.59/10.40 10: f25 -> f50 : J'=free_10, [ A>=1 && F>=2 && 0>=E && 1>=free_10 && free_10>=0 ], cost: 1 29.59/10.40 29.59/10.40 11: f25 -> f50 : C'=1+C, J'=1, [ A>=1 && 0>=E && 0>=C && F==1 ], cost: 1 29.59/10.40 29.59/10.40 12: f25 -> f50 : C'=0, D'=-1+D, J'=0, [ A>=1 && 0>=E && D>=1 && F==1 && C==1 ], cost: 1 29.59/10.40 29.59/10.40 13: f25 -> f50 : B'=1+B, C'=0, D'=1+B, E'=free_12, F'=0, J'=free_11, [ A>=1 && 0>=E && free_11>=0 && 1>=free_11 && C>=2 && free_12>=0 && F==1 ], cost: 1 29.59/10.40 29.59/10.40 14: f25 -> f50 : B'=1+B, C'=0, D'=1+B, E'=free_14, F'=0, J'=free_13, [ A>=1 && 0>=E && 0>=D && free_13>=0 && 1>=free_13 && free_14>=0 && F==1 && C==1 ], cost: 1 29.59/10.40 29.59/10.40 15: f25 -> f50 : E'=-1+E, J'=free_15, [ A>=1 && E>=1 && 1>=free_15 && free_15>=0 ], cost: 1 29.59/10.40 29.59/10.40 1: f0 -> f16 : B'=1, C'=0, D'=1, E'=free_2, F'=0, G'=free_1, H'=free, Q'=free_3, [ free_3>=0 && free>=free_3 && free>=0 && free_1>=free && free_2>=0 && free_1>=0 ], cost: 1 29.59/10.40 29.59/10.40 2: f16 -> f25 : A'=0, F'=1+F, [ Q>=1 && 0>=F && 0>=E ], cost: 1 29.59/10.40 29.59/10.40 3: f16 -> f25 : A'=free_4, [ Q>=1 && F>=2 && 0>=E && 1>=free_4 && free_4>=0 ], cost: 1 29.59/10.40 29.59/10.40 4: f16 -> f25 : A'=1, C'=1+C, [ Q>=1 && 0>=E && 0>=C && F==1 ], cost: 1 29.59/10.40 29.59/10.40 5: f16 -> f25 : A'=0, C'=0, D'=-1+D, [ Q>=1 && 0>=E && D>=1 && F==1 && C==1 ], cost: 1 29.59/10.40 29.59/10.40 6: f16 -> f25 : A'=free_6, B'=1+B, C'=0, D'=1+B, E'=free_5, F'=0, [ Q>=1 && 0>=E && free_6>=0 && 1>=free_6 && C>=2 && free_5>=0 && F==1 ], cost: 1 29.59/10.40 29.59/10.40 7: f16 -> f25 : A'=free_8, B'=1+B, C'=0, D'=1+B, E'=free_7, F'=0, [ Q>=1 && 0>=E && 0>=D && free_8>=0 && 1>=free_8 && free_7>=0 && F==1 && C==1 ], cost: 1 29.59/10.40 29.59/10.40 8: f16 -> f25 : A'=free_9, E'=-1+E, [ Q>=1 && E>=1 && 1>=free_9 && free_9>=0 ], cost: 1 29.59/10.40 29.59/10.40 19: f16 -> f73 : [ 0>=Q ], cost: 1 29.59/10.40 29.59/10.40 16: f50 -> f16 : [ Q>=H && J>=1 ], cost: 1 29.59/10.40 29.59/10.40 17: f50 -> f16 : Q'=1+Q, [ H>=1+Q && J>=1 ], cost: 1 29.59/10.40 29.59/10.40 18: f50 -> f16 : Q'=-1+Q, [ 0>=J ], cost: 1 29.59/10.40 29.59/10.40 29.59/10.40 29.59/10.40 Removed unreachable and leaf rules: 29.59/10.40 29.59/10.40 Start location: f0 29.59/10.40
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