details

property	value
status	complete
benchmark	w2_nt.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n091.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.84700107574 seconds
cpu usage	6.812113754
max memory	4.27638784E8

stage attributes

key	value
output-size	20743
starexec-result	WORST_CASE(NON_POLY, ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 1218 ms] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f8(A, B, B, B, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1)) :|: A >= B + 1 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f8(A, B, B, B, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1)) :|: B >= A + 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f2(A, B, C, D, E, B1, -(1) + G, 1 + H, 1 + H, -(1) + G, C1, D1, -(1) + G, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1)) :|: E >= F + 1 && G >= 1 && H >= 0 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f2(A, B, C, D, E, B1, -(1) + G, 1 + H, 1 + H, -(1) + G, C1, D1, -(1) + G, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1)) :|: F >= E + 1 && G >= 1 && H >= 0 f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f2(A, B, C, D, E, B1, 2, 1, 1, 2, K, L, M, 2, C1, D1, F1, G1, G1, G1, G1, H1, I1, 2, J1, 0, A1)) :|: E >= E1 + 1 f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f2(A, B, C, D, E, B1, 2, 1, 1, 2, K, L, M, 2, C1, D1, F1, G1, G1, G1, G1, H1, I1, 2, J1, 0, A1)) :|: E1 >= E + 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f8(A, C1, C1, C1, F, F, G, H, I, J, K, L, M, N, O, P, B1, R, S, T, D1, V, W, X, Y, Z, F1)) :|: A >= C1 + 1 && G >= 1 && H >= 0 && F >= E && F <= E f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f8(A, C1, C1, C1, F, F, G, H, I, J, K, L, M, N, O, P, B1, R, S, T, D1, V, W, X, Y, Z, F1)) :|: C1 >= A + 1 && G >= 1 && H >= 0 && F >= E && F <= E The start-symbols are:[f23_27] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f23 0: f8 -> f8 : C'=B, D'=B, [ A>=1+B ], cost: 1 1: f8 -> f8 : C'=B, D'=B, [ B>=1+A ], cost: 1 2: f2 -> f2 : F'=free_1, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free, L'=free_2, M'=-1+G, [ E>=1+F && G>=1 && H>=0 ], cost: 1 3: f2 -> f2 : F'=free_4, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free_3, L'=free_5, M'=-1+G, [ F>=1+E && G>=1 && H>=0 ], cost: 1 6: f2 -> f8 : A1'=free_24, B'=free_26, C'=free_26, D'=free_26, E'=F, Q_1'=free_25, U'=free_27, [ A>=1+free_26 && G>=1 && H>=0 && F==E ], cost: 1 7: f2 -> f8 : A1'=free_28, B'=free_30, C'=free_30, D'=free_30, E'=F, Q_1'=free_29, U'=free_31, [ free_30>=1+A && G>=1 && H>=0 && F==E ], cost: 1 4: f23 -> f2 : F'=free_11, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_7, P'=free_13, Q_1'=free_6, R'=free_12, S'=free_12, T'=free_12, U'=free_12, V'=free_8, W'=free_14, X'=2, Y'=free_10, Z'=0, [ E>=1+free_9 ], cost: 1 5: f23 -> f2 : F'=free_20, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_16, P'=free_22, Q_1'=free_15, R'=free_21, S'=free_21, T'=free_21, U'=free_21, V'=free_17, W'=free_23, X'=2, Y'=free_19, Z'=0, [ free_18>=1+E ], cost: 1 Simplified all rules, resulting in: Start location: f23 0: f8 -> f8 : C'=B, D'=B, [ A>=1+B ], cost: 1 1: f8 -> f8 : C'=B, D'=B, [ B>=1+A ], cost: 1 2: f2 -> f2 : F'=free_1, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free, L'=free_2, M'=-1+G, [ E>=1+F && G>=1 && H>=0 ], cost: 1 3: f2 -> f2 : F'=free_4, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free_3, L'=free_5, M'=-1+G, [ F>=1+E && G>=1 && H>=0 ], cost: 1 6: f2 -> f8 : A1'=free_24, B'=free_26, C'=free_26, D'=free_26, E'=F, Q_1'=free_25, U'=free_27, [ A>=1+free_26 && G>=1 && H>=0 && F==E ], cost: 1 7: f2 -> f8 : A1'=free_28, B'=free_30, C'=free_30, D'=free_30, E'=F, Q_1'=free_29, U'=free_31, [ free_30>=1+A && G>=1 && H>=0 && F==E ], cost: 1 4: f23 -> f2 : F'=free_11, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_7, P'=free_13, Q_1'=free_6, R'=free_12, S'=free_12, T'=free_12, U'=free_12, V'=free_8, W'=free_14, X'=2, Y'=free_10, Z'=0, [], cost: 1 5: f23 -> f2 : F'=free_20, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_16, P'=free_22, Q_1'=free_15, R'=free_21, S'=free_21, T'=free_21, U'=free_21, V'=free_17, W'=free_23, X'=2, Y'=free_19, Z'=0, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 0: f8 -> f8 : C'=B, D'=B, [ A>=1+B ], cost: 1 1: f8 -> f8 : C'=B, D'=B, [ B>=1+A ], cost: 1 popout

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all output return to Compl Integ Trans Syste 26843