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Complexity_ITS 2019-03-21 04.46 pair #429990386
details
property
value
status
complete
benchmark
toeplz.c.i.toeplz.pl.t2.fixed.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
56.6297 seconds
cpu usage
82.2368
user time
81.2737
system time
0.963069
max virtual memory
3.6531436E7
max residence set size
259072.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
82.17/56.60 WORST_CASE(?, O(n^1)) 82.17/56.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 82.17/56.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 82.17/56.61 82.17/56.61 82.17/56.61 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 82.17/56.61 82.17/56.61 (0) CpxIntTrs 82.17/56.61 (1) Koat Proof [FINISHED, 1344 ms] 82.17/56.61 (2) BOUNDS(1, n^1) 82.17/56.61 82.17/56.61 82.17/56.61 ---------------------------------------- 82.17/56.61 82.17/56.61 (0) 82.17/56.61 Obligation: 82.17/56.61 Complexity Int TRS consisting of the following rules: 82.17/56.61 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(1, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= 1 && A <= 1 82.17/56.61 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: 0 >= A 82.17/56.61 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= 2 82.17/56.61 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f20(A, B, B + 1, S, T, 1, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= B 82.17/56.61 f20(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f20(A, B, C, D + S * T, E + U * V, F + 1, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= F 82.17/56.61 f31(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f31(A, B, C, D, E, F + 1, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= F 82.17/56.61 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f45(A, B, C, D, E, F + 1, G + S * T, H + U * V, I + W * X, J, K, L, M, N, O, P, Q, R)) :|: B >= F 82.17/56.61 f60(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f60(A, B, C, D, E, F + 1, G, H, I, J, K - 1, S, T, U, V, K, Q, R)) :|: J >= F 82.17/56.61 f60(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: F >= 1 + J 82.17/56.61 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f60(A, B, C, D, E, 1, G, H, I, S, B, L, M, N, O, P, T, U)) :|: B + 1 >= 2 * V && 3 * V >= B + 2 && V >= S && B + 1 >= 2 * W && 3 * W >= B + 2 && S >= W && F >= 1 + B 82.17/56.61 f31(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, A, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: F >= 1 + B && A >= C && A <= C 82.17/56.61 f31(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f45(A, B, C, D, E, 1, S, T, U, J, K, L, M, N, O, P, Q, R)) :|: A >= C + 1 && F >= 1 + B 82.17/56.61 f31(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f45(A, B, C, D, E, 1, S, T, U, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 + A && F >= 1 + B 82.17/56.61 f20(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f31(A, B, C, D, E, 1, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: 0 >= E + 1 && F >= 1 + B 82.17/56.61 f20(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f31(A, B, C, D, E, 1, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: E >= 1 && F >= 1 + B 82.17/56.61 f20(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f31(A, B, C, D, 0, 1, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: F >= 1 + B && E >= 0 && E <= 0 82.17/56.61 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= 1 + A 82.17/56.61 82.17/56.61 The start-symbols are:[f2_18] 82.17/56.61 82.17/56.61 82.17/56.61 ---------------------------------------- 82.17/56.61 82.17/56.61 (1) Koat Proof (FINISHED) 82.17/56.61 YES(?, 285*ar_0 + 575) 82.17/56.61 82.17/56.61 82.17/56.61 82.17/56.61 Initial complexity problem: 82.17/56.61 82.17/56.61 1: T: 82.17/56.61 82.17/56.61 (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, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f1(1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 = 1 ] 82.17/56.61 82.17/56.61 (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, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f13(ar_0, 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 >= ar_0 ] 82.17/56.61 82.17/56.61 (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, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f13(ar_0, 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= 2 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f20(ar_0, ar_1, ar_1 + 1, s, t, 1, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_1 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f20(ar_0, ar_1, ar_2, ar_3 + s*t, ar_4 + u*v, ar_5 + 1, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_5 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_5 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6 + s*t, ar_7 + u*v, ar_8 + w*x, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_5 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f60(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f60(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7, ar_8, ar_9, ar_10 - 1, s, t, u, v, ar_10, ar_16, ar_17)) [ ar_9 >= ar_5 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f60(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f13(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_5 >= ar_9 + 1 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f60(ar_0, ar_1, ar_2, ar_3, ar_4, 1, ar_6, ar_7, ar_8, s, ar_1, ar_11, ar_12, ar_13, ar_14, ar_15, t, u)) [ ar_1 + 1 >= 2*v /\ 3*v >= ar_1 + 2 /\ v >= s /\ ar_1 + 1 >= 2*w /\ 3*w >= ar_1 + 2 /\ s >= w /\ ar_5 >= ar_1 + 1 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f1(ar_0, ar_1, ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_5 >= ar_1 + 1 /\ ar_0 = ar_2 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4, 1, s, t, u, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_2 + 1 /\ ar_5 >= ar_1 + 1 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4, 1, s, t, u, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_2 >= ar_0 + 1 /\ ar_5 >= ar_1 + 1 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4, 1, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 >= ar_4 + 1 /\ ar_5 >= ar_1 + 1 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4, 1, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_4 >= 1 /\ ar_5 >= ar_1 + 1 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, 0, 1, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_5 >= ar_1 + 1 /\ ar_4 = 0 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_1 >= ar_0 + 1 ] 82.17/56.61 82.17/56.61 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 <= 0 ] 82.17/56.61 82.17/56.61 start location: koat_start 82.17/56.61 82.17/56.61 leaf cost: 0 82.17/56.61 82.17/56.61 82.17/56.61 82.17/56.61 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_4, ar_5, ar_9]. 82.17/56.61 82.17/56.61 We thus obtain the following problem: 82.17/56.61 82.17/56.61 2: T: 82.17/56.61 82.17/56.61 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_4, ar_5, ar_9) -> Com_1(f2(ar_0, ar_1, ar_2, ar_4, ar_5, ar_9)) [ 0 <= 0 ] 82.17/56.61 82.17/56.61 (Comp: ?, Cost: 1) f13(ar_0, ar_1, ar_2, ar_4, ar_5, ar_9) -> Com_1(f1(ar_0, ar_1, ar_2, ar_4, ar_5, ar_9)) [ ar_1 >= ar_0 + 1 ]
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