details

property	value
status	complete
benchmark	rev_nt3.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.2647 seconds
cpu usage	7.59258
user time	7.19571
system time	0.396867
max virtual memory	1.874626E7
max residence set size	230832.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

7.47/3.22 WORST_CASE(NON_POLY, ?) 7.47/3.23 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 7.47/3.23 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.47/3.23 7.47/3.23 7.47/3.23 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 7.47/3.23 7.47/3.23 (0) CpxIntTrs 7.47/3.23 (1) Loat Proof [FINISHED, 1406 ms] 7.47/3.23 (2) BOUNDS(INF, INF) 7.47/3.23 7.47/3.23 7.47/3.23 ---------------------------------------- 7.47/3.23 7.47/3.23 (0) 7.47/3.23 Obligation: 7.47/3.23 Complexity Int TRS consisting of the following rules: 7.47/3.23 f12(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, B1, C1, D1, E1) -> Com_1(f11(A, B, A, A, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: A >= B + 1 7.47/3.23 f12(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, B1, C1, D1, E1) -> Com_1(f11(A, B, A, A, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: B >= A + 1 7.47/3.23 f11(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, B1, C1, D1, E1) -> Com_1(f11(A, B, A, A, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: A >= B + 1 7.47/3.23 f11(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, B1, C1, D1, E1) -> Com_1(f11(A, B, A, A, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: B >= A + 1 7.47/3.23 f6(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, B1, C1, D1, E1) -> Com_1(f6(A, B, C, D, H1, F, 1 + G, -(1) + H, 1 + G, -(1) + H, F1, G1, -(1) + H, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: E >= F + 1 && G >= 0 && H >= 1 7.47/3.23 f6(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, B1, C1, D1, E1) -> Com_1(f6(A, B, C, D, H1, F, 1 + G, -(1) + H, 1 + G, -(1) + H, F1, G1, -(1) + H, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: F >= E + 1 && G >= 0 && H >= 1 7.47/3.23 f26(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, B1, C1, D1, E1) -> Com_1(f6(A, B, C, D, L1, F, 1, 4, 1, 4, K, L, M, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, E1)) :|: I1 >= F + 1 7.47/3.23 f26(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, B1, C1, D1, E1) -> Com_1(f6(A, B, C, D, L1, F, 1, 4, 1, 4, K, L, M, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, E1)) :|: F >= I1 + 1 7.47/3.23 f6(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, B1, C1, D1, E1) -> Com_1(f12(J1, B, J1, J1, E, E, G, H, I, J, K, L, M, F1, O, P, Q, R, S, T, U, V, W, X, Y, G1, A1, B1, C1, D1, H1)) :|: J1 >= B + 1 && G >= 0 && H >= 1 && E >= F && E <= F 7.47/3.23 f6(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, B1, C1, D1, E1) -> Com_1(f12(J1, B, J1, J1, E, E, G, H, I, J, K, L, M, F1, O, P, Q, R, S, T, U, V, W, X, Y, G1, A1, B1, C1, D1, H1)) :|: B >= J1 + 1 && G >= 0 && H >= 1 && E >= F && E <= F 7.47/3.23 7.47/3.23 The start-symbols are:[f26_31] 7.47/3.23 7.47/3.23 7.47/3.23 ---------------------------------------- 7.47/3.23 7.47/3.23 (1) Loat Proof (FINISHED) 7.47/3.23 7.47/3.23 7.47/3.23 ### Pre-processing the ITS problem ### 7.47/3.23 7.47/3.23 7.47/3.23 7.47/3.23 Initial linear ITS problem 7.47/3.23 7.47/3.23 Start location: f26 7.47/3.23 7.47/3.23 0: f12 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1 7.47/3.23 7.47/3.23 1: f12 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1 7.47/3.23 7.47/3.23 2: f11 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1 7.47/3.23 7.47/3.23 3: f11 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1 7.47/3.23 7.47/3.23 4: f6 -> f6 : E'=free, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_2, L'=free_1, M'=-1+H, [ E>=1+F && G>=0 && H>=1 ], cost: 1 7.47/3.23 7.47/3.23 5: f6 -> f6 : E'=free_3, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_5, L'=free_4, M'=-1+H, [ F>=1+E && G>=0 && H>=1 ], cost: 1 7.47/3.23 7.47/3.23 8: f6 -> f12 : A'=free_28, C'=free_28, D'=free_28, E1'=free_30, F'=E, N'=free_31, Z'=free_29, [ free_28>=1+B && G>=0 && H>=1 && E==F ], cost: 1 7.47/3.23 7.47/3.23 9: f6 -> f12 : A'=free_32, C'=free_32, D'=free_32, E1'=free_34, F'=E, N'=free_35, Z'=free_33, [ B>=1+free_32 && G>=0 && H>=1 && E==F ], cost: 1 7.47/3.23 7.47/3.23 6: f26 -> f6 : A1'=free_6, B1'=free_15, C1'=free_11, D1'=4, E'=free_7, G'=1, H'=4, Q'=1, J'=4, N'=free_13, O'=2, P'=3, Q_1'=free_9, R'=free_12, S'=4, T'=free_8, U'=0, V'=free_14, W'=free_10, X'=free_10, Y'=free_10, Z'=free_10, [ free_16>=1+F ], cost: 1 7.47/3.23 7.47/3.23 7: f26 -> f6 : A1'=free_17, B1'=free_26, C1'=free_22, D1'=4, E'=free_18, G'=1, H'=4, Q'=1, J'=4, N'=free_24, O'=2, P'=3, Q_1'=free_20, R'=free_23, S'=4, T'=free_19, U'=0, V'=free_25, W'=free_21, X'=free_21, Y'=free_21, Z'=free_21, [ F>=1+free_27 ], cost: 1 7.47/3.23 7.47/3.23 7.47/3.23 7.47/3.23 Simplified all rules, resulting in: 7.47/3.23 7.47/3.23 Start location: f26 7.47/3.23 7.47/3.23 0: f12 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1 7.47/3.23 7.47/3.23 1: f12 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1 7.47/3.23 7.47/3.23 2: f11 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1 7.47/3.23 7.47/3.23 3: f11 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1 7.47/3.23 7.47/3.23 4: f6 -> f6 : E'=free, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_2, L'=free_1, M'=-1+H, [ E>=1+F && G>=0 && H>=1 ], cost: 1 7.47/3.23 7.47/3.23 5: f6 -> f6 : E'=free_3, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_5, L'=free_4, M'=-1+H, [ F>=1+E && G>=0 && H>=1 ], cost: 1 7.47/3.23 7.47/3.23 8: f6 -> f12 : A'=free_28, C'=free_28, D'=free_28, E1'=free_30, F'=E, N'=free_31, Z'=free_29, [ free_28>=1+B && G>=0 && H>=1 && E==F ], cost: 1 7.47/3.23 7.47/3.23 9: f6 -> f12 : A'=free_32, C'=free_32, D'=free_32, E1'=free_34, F'=E, N'=free_35, Z'=free_33, [ B>=1+free_32 && G>=0 && H>=1 && E==F ], cost: 1 7.47/3.23 7.47/3.23 6: f26 -> f6 : A1'=free_6, B1'=free_15, C1'=free_11, D1'=4, E'=free_7, G'=1, H'=4, Q'=1, J'=4, N'=free_13, O'=2, P'=3, Q_1'=free_9, R'=free_12, S'=4, T'=free_8, U'=0, V'=free_14, W'=free_10, X'=free_10, Y'=free_10, Z'=free_10, [], cost: 1 7.47/3.23 7.47/3.23 7: f26 -> f6 : A1'=free_17, B1'=free_26, C1'=free_22, D1'=4, E'=free_18, G'=1, H'=4, Q'=1, J'=4, N'=free_24, O'=2, P'=3, Q_1'=free_20, R'=free_23, S'=4, T'=free_19, U'=0, V'=free_25, W'=free_21, X'=free_21, Y'=free_21, Z'=free_21, [], cost: 1 7.47/3.23 7.47/3.23 7.47/3.23 7.47/3.23 ### Simplification by acceleration and chaining ### 7.47/3.23 7.47/3.23 7.47/3.23 7.47/3.23 Accelerating simple loops of location 1. 7.47/3.23 7.47/3.23 Accelerating the following rules: 7.47/3.23 popout

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all output return to Complexity_ITS 2019-03-21 04.46