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Complexity_ITS 2019-03-21 04.46 pair #429990446
details
property
value
status
complete
benchmark
tqli.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n171.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
146.912 seconds
cpu usage
178.939
user time
175.88
system time
3.05878
max virtual memory
1.8980084E7
max residence set size
346696.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
178.81/146.87 WORST_CASE(Omega(n^1), ?) 178.81/146.88 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 178.81/146.88 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 178.81/146.88 178.81/146.88 178.81/146.88 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). 178.81/146.88 178.81/146.88 (0) CpxIntTrs 178.81/146.88 (1) Loat Proof [FINISHED, 13.0 s] 178.81/146.88 (2) BOUNDS(n^1, INF) 178.81/146.88 178.81/146.88 178.81/146.88 ---------------------------------------- 178.81/146.88 178.81/146.88 (0) 178.81/146.88 Obligation: 178.81/146.88 Complexity Int TRS consisting of the following rules: 178.81/146.88 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f0(A, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: A >= B 178.81/146.88 f74(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= D + 1 178.81/146.88 f74(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: D >= 1 + C 178.81/146.88 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f16(A, B, C, D, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: A >= C 178.81/146.88 f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: D >= A 178.81/146.88 f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f26(A, B, C, D, E, V, W, V + W, 0, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: A >= 1 + D 178.81/146.88 f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f16(A, B, C, D + 1, E, V, W, V + W, X, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 0 >= X + 1 && A >= 1 + D 178.81/146.88 f16(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f16(A, B, C, D + 1, E, V, W, V + W, X, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: X >= 1 && A >= 1 + D 178.81/146.88 f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f74(A, B, C, C, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= D && C <= D 178.81/146.88 f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f29(A, B, C, D, E + 1, F, G, H, I, E, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= D + 1 178.81/146.88 f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f29(A, B, C, D, E + 1, F, G, H, I, E, K, L, M, N, O, P, Q, R, S, T, U)) :|: D >= 1 + C 178.81/146.88 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f33(A, B, C, D, E, F, G, H, I, J, V, W, M, N, O, P, Q, R, S, T, U)) :|: 29 >= J 178.81/146.88 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f33(A, B, C, D, E, F, G, H, I, J, V, W, M, N, O, P, Q, R, S, T, U)) :|: J >= 31 178.81/146.88 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f33(A, B, C, D, E, F, G, H, I, 30, V, W, M, N, O, P, Q, R, S, T, U)) :|: J >= 30 && J <= 30 178.81/146.88 f33(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f42(A, B, C, D, E, F, G, H, I, J, V, L, W, W, 1, 1, 0, R, S, T, U)) :|: K >= 0 178.81/146.88 f33(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f42(A, B, C, D, E, F, G, H, I, J, V, L, M, -(W), 1, 1, 0, W, S, T, U)) :|: 0 >= K + 1 178.81/146.88 f42(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= B + 1 178.81/146.88 f42(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f68(A, B, C, D, E, F, G, H, I, J, K, 0, M, N, O, P, Q, R, V, W, U)) :|: B >= C 178.81/146.88 f42(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, V, W, M, N, X, Z, A1, R, B1, C1, U)) :|: B >= C && 0 >= Y + 1 178.81/146.88 f42(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, V, W, M, N, X, Z, A1, R, B1, C1, U)) :|: B >= C && Y >= 1 178.81/146.88 f59(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, V, T, U + 1)) :|: A >= U 178.81/146.88 f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f74(A, B, C, D, E, F, G, H, I, J, K, 0, M, N, O, P, Q, R, S, T, U)) :|: B >= C && L >= 0 && L <= 0 178.81/146.88 f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f74(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 0 >= L + 1 178.81/146.88 f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f74(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: L >= 1 178.81/146.88 f68(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f74(A, B, C, D, E, F, G, H, I, J, K, 0, M, N, O, P, Q, R, S, T, U)) :|: C >= B + 1 && L >= 0 && L <= 0 178.81/146.88 f74(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f13(A, B, C + 1, C, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= D && C <= D 178.81/146.88 f59(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f42(A, B - 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: U >= 1 + A 178.81/146.88 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f80(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= 1 + A 178.81/146.88 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: B >= 1 + A 178.81/146.88 start(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: TRUE 178.81/146.88 178.81/146.88 The start-symbols are:[start_21] 178.81/146.88 178.81/146.88 178.81/146.88 ---------------------------------------- 178.81/146.88 178.81/146.88 (1) Loat Proof (FINISHED) 178.81/146.88 178.81/146.88 178.81/146.88 ### Pre-processing the ITS problem ### 178.81/146.88 178.81/146.88 178.81/146.88 178.81/146.88 Initial linear ITS problem 178.81/146.88 178.81/146.88 Start location: start 178.81/146.88 178.81/146.88 0: f0 -> f0 : B'=1+B, [ A>=B ], cost: 1 178.81/146.88 178.81/146.88 28: f0 -> f13 : [ B>=1+A ], cost: 1 178.81/146.88 178.81/146.88 1: f74 -> f16 : [ C>=1+D ], cost: 1 178.81/146.88 178.81/146.88 2: f74 -> f16 : [ D>=1+C ], cost: 1 178.81/146.88 178.81/146.88 25: f74 -> f13 : C'=1+C, D'=C, [ C==D ], cost: 1 178.81/146.88 178.81/146.88 3: f13 -> f16 : E'=0, [ A>=C ], cost: 1 178.81/146.88 178.81/146.88 27: f13 -> f80 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, E'=H, F'=Q, G'=J, H'=K, Q'=L, J'=M, K'=N, L'=O, M'=P, N'=Q_1, O'=R, P'=S, Q_1'=T, R'=U, [ C>=1+A ], cost: 1 178.81/146.88 178.81/146.88 4: f16 -> f26 : [ D>=A ], cost: 1 178.81/146.88 178.81/146.88 5: f16 -> f26 : F'=free, G'=free_1, H'=free_1+free, Q'=0, [ A>=1+D ], cost: 1 178.81/146.88 178.81/146.88 6: f16 -> f16 : D'=1+D, F'=free_2, G'=free_3, H'=free_2+free_3, Q'=free_4, [ 0>=1+free_4 && A>=1+D ], cost: 1 178.81/146.88 178.81/146.88 7: f16 -> f16 : D'=1+D, F'=free_5, G'=free_6, H'=free_5+free_6, Q'=free_7, [ free_7>=1 && A>=1+D ], cost: 1 178.81/146.88 178.81/146.88 8: f26 -> f74 : D'=C, [ C==D ], cost: 1 178.81/146.88 178.81/146.88 9: f26 -> f29 : E'=1+E, J'=E, [ C>=1+D ], cost: 1 178.81/146.88 178.81/146.88 10: f26 -> f29 : E'=1+E, J'=E, [ D>=1+C ], cost: 1 178.81/146.88 178.81/146.88 11: f29 -> f33 : K'=free_8, L'=free_9, [ 29>=J ], cost: 1 178.81/146.88 178.81/146.88 12: f29 -> f33 : K'=free_10, L'=free_11, [ J>=31 ], cost: 1 178.81/146.88 178.81/146.88 13: f29 -> f33 : J'=30, K'=free_12, L'=free_13, [ J==30 ], cost: 1 178.81/146.88 178.81/146.88 14: f33 -> f42 : K'=free_14, M'=free_15, N'=free_15, O'=1, P'=1, Q_1'=0, [ K>=0 ], cost: 1 178.81/146.88
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