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Complexity_ITS 2019-03-21 04.46 pair #429990920
details
property
value
status
complete
benchmark
ludcmp.c.i.ludcmp.pl.t2.fixed.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n014.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
14.0852 seconds
cpu usage
30.4426
user time
29.108
system time
1.33462
max virtual memory
1.8898604E7
max residence set size
301908.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
30.35/14.04 WORST_CASE(Omega(n^1), O(n^1)) 30.35/14.05 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 30.35/14.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.35/14.05 30.35/14.05 30.35/14.05 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 30.35/14.05 30.35/14.05 (0) CpxIntTrs 30.35/14.05 (1) Koat Proof [FINISHED, 1597 ms] 30.35/14.05 (2) BOUNDS(1, n^1) 30.35/14.05 (3) Loat Proof [FINISHED, 12.3 s] 30.35/14.05 (4) BOUNDS(n^1, INF) 30.35/14.05 30.35/14.05 30.35/14.05 ---------------------------------------- 30.35/14.05 30.35/14.05 (0) 30.35/14.05 Obligation: 30.35/14.05 Complexity Int TRS consisting of the following rules: 30.35/14.05 f69(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= L + 1 30.35/14.05 f69(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K)) :|: L >= 1 30.35/14.05 f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f5(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE 30.35/14.05 f5(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f9(A, B, 0, D, E, F, G, H, I, J, K)) :|: A >= B 30.35/14.05 f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f9(A, B, C, D + 1, L, L, G, H, I, J, K)) :|: C >= L && A >= D 30.35/14.05 f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f9(A, B, L, D + 1, L, L, G, H, I, J, K)) :|: L >= 1 + C && A >= D 30.35/14.05 f23(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f26(A, B, C, D, E, F, G, H, I, J, K)) :|: A >= D 30.35/14.05 f26(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f30(A, B, C, D, E, F, L, H, I, J, K)) :|: D >= B + 1 30.35/14.05 f30(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f30(A, B, C, D, E, F, G - L * M, H + 1, I, J, K)) :|: B >= H + 1 30.35/14.05 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f44(A, B, C, D, E, F, L, H, I, J, K)) :|: A >= B 30.35/14.05 f44(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f44(A, B, C, D, E, F, G - L * M, H + 1, I, J, K)) :|: D >= H + 1 30.35/14.05 f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H + 1, L, J, K)) :|: A >= H 30.35/14.05 f69(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE 30.35/14.05 f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f74(A, B, C, D, E, F, G, H, L, J, K)) :|: A >= D + 1 30.35/14.05 f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f74(A, B, C, D, E, F, G, H, L, J, K)) :|: D >= 1 + A 30.35/14.05 f74(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f74(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: A >= B 30.35/14.05 f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f23(A, B, C, A + 1, E, F, G, H, I, J, K)) :|: A >= D && A <= D 30.35/14.05 f74(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f23(A, B, C, D + 1, E, F, G, H, I, J, K)) :|: B >= 1 + A 30.35/14.05 f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, K)) :|: H >= 1 + A 30.35/14.05 f44(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B + 1, C, D, E, F, G, H, L * M, L, K)) :|: C >= L * M + 1 && H >= D 30.35/14.05 f44(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B + 1, L * M, D, E, F, G, H, L * M, M, B)) :|: L * M >= C && H >= D 30.35/14.05 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A && K >= D + 1 30.35/14.05 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A && D >= 1 + K 30.35/14.05 f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, D)) :|: B >= 1 + A && D >= K && D <= K 30.35/14.05 f30(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f26(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: H >= B 30.35/14.05 f26(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B, 0, D, E, F, G, H, I, J, K)) :|: B >= D 30.35/14.05 f23(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K)) :|: D >= 1 + A 30.35/14.05 f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f5(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: 0 >= C + 1 && D >= 1 + A 30.35/14.05 f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f5(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: C >= 1 && D >= 1 + A 30.35/14.05 f9(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f5(A, B + 1, 0, D, E, F, G, H, I, J, K)) :|: D >= 1 + A && C >= 0 && C <= 0 30.35/14.05 f5(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f23(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A 30.35/14.05 30.35/14.05 The start-symbols are:[f2_11] 30.35/14.05 30.35/14.05 30.35/14.05 ---------------------------------------- 30.35/14.05 30.35/14.05 (1) Koat Proof (FINISHED) 30.35/14.05 YES(?, 147*ar_0 + 144*ar_3 + 2*ar_1 + ar_7 + 152) 30.35/14.05 30.35/14.05 30.35/14.05 30.35/14.05 Initial complexity problem: 30.35/14.05 30.35/14.05 1: T: 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ 0 >= l + 1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ l >= 1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_0 >= ar_1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, ar_2, ar_3 + 1, l, l, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_2 >= l /\ ar_0 >= ar_3 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f9(ar_0, ar_1, l, ar_3 + 1, l, l, ar_6, ar_7, ar_8, ar_9, ar_10)) [ l >= ar_2 + 1 /\ ar_0 >= ar_3 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_0 >= ar_3 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, l, ar_7, ar_8, ar_9, ar_10)) [ ar_3 >= ar_1 + 1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - l*m, ar_7 + 1, ar_8, ar_9, ar_10)) [ ar_1 >= ar_7 + 1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f44(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, l, ar_7, ar_8, ar_9, ar_10)) [ ar_0 >= ar_1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f44(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f44(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - l*m, ar_7 + 1, ar_8, ar_9, ar_10)) [ ar_3 >= ar_7 + 1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f59(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, l, ar_9, ar_10)) [ ar_0 >= ar_7 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f74(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, l, ar_9, ar_10)) [ ar_0 >= ar_3 + 1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f74(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, l, ar_9, ar_10)) [ ar_3 >= ar_0 + 1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f74(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f74(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_0 >= ar_1 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f23(ar_0, ar_1, ar_2, ar_0 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_0 = ar_3 ] 30.35/14.05 30.35/14.05 (Comp: ?, Cost: 1) f74(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10) -> Com_1(f23(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10)) [ ar_1 >= ar_0 + 1 ]
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