details

property	value
status	complete
benchmark	n-36.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n128.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.23973 seconds
cpu usage	5.08029
user time	4.77884
system time	0.301451
max virtual memory	1.86884E7
max residence set size	235804.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

4.99/2.20 WORST_CASE(NON_POLY, ?) 4.99/2.21 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 4.99/2.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.99/2.21 4.99/2.21 4.99/2.21 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 4.99/2.21 4.99/2.21 (0) CpxIntTrs 4.99/2.21 (1) Loat Proof [FINISHED, 386 ms] 4.99/2.21 (2) BOUNDS(INF, INF) 4.99/2.21 4.99/2.21 4.99/2.21 ---------------------------------------- 4.99/2.21 4.99/2.21 (0) 4.99/2.21 Obligation: 4.99/2.21 Complexity Int TRS consisting of the following rules: 4.99/2.21 f300(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f1(V, W, X, Y, Z, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: TRUE 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f1(A, B, C, D, E, F, G, 256, V, W, X, Y, Z, B1, C1, D1, Q, R, S, T, U)) :|: A1 >= 1 && F + 1 >= G && F + 1 <= G && H >= 256 && H <= 256 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f1(A, B, C, D, E, F, G, H, V, W, X, Y, Z, B1, C1, P, Q, R, S, T, U)) :|: 0 >= H && F + 1 >= G && F + 1 <= G 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f1(A, B, C, D, E, F, G, H, V, W, X, Y, Z, B1, C1, D1, 256, R, S, T, U)) :|: A1 >= 1 && G >= 1 + F && G >= 2 + F && Q >= 256 && Q <= 256 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f1(A, B, C, D, E, F, G, H, V, W, X, Y, Z, B1, C1, P, Q, R, S, T, U)) :|: 0 >= Q && G >= 1 + F && G >= 2 + F 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f2(A, B, C, D, E, F, G, H, V, W, K, L, M, N, O, P, Q, 0, 0, 0, U)) :|: F >= G 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f3(A, B, C, D, E, F, G, H, V, W, X, Y, Z, B1, C1, D1, Q, H, H, H, A1)) :|: H >= 1 && H >= 257 && F + 1 >= G && F + 1 <= G 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f3(A, B, C, D, E, F, G, H, V, W, X, Y, Z, B1, C1, D1, Q, H, H, H, A1)) :|: H >= 1 && 255 >= H && F + 1 >= G && F + 1 <= G 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f3(A, B, C, D, E, F, G, H, V, W, X, Y, Z, B1, C1, D1, Q, Q, Q, Q, A1)) :|: Q >= 1 && Q >= 257 && G >= 1 + F && G >= 2 + F 4.99/2.21 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f3(A, B, C, D, E, F, G, H, V, W, X, Y, Z, B1, C1, D1, Q, Q, Q, Q, A1)) :|: Q >= 1 && 255 >= Q && G >= 1 + F && G >= 2 + F 4.99/2.21 4.99/2.21 The start-symbols are:[f300_21] 4.99/2.21 4.99/2.21 4.99/2.21 ---------------------------------------- 4.99/2.21 4.99/2.21 (1) Loat Proof (FINISHED) 4.99/2.21 4.99/2.21 4.99/2.21 ### Pre-processing the ITS problem ### 4.99/2.21 4.99/2.21 4.99/2.21 4.99/2.21 Initial linear ITS problem 4.99/2.21 4.99/2.21 Start location: f300 4.99/2.21 4.99/2.21 0: f300 -> f1 : A'=free_2, B'=free_3, C'=free, D'=free_1, E'=free_4, [], cost: 1 4.99/2.21 4.99/2.21 1: f1 -> f1 : H'=256, Q'=free_8, J'=free_10, K'=free_5, L'=free_7, M'=free_12, N'=free_9, O'=free_6, P'=free_11, [ free_13>=1 && 1+F==G && H==256 ], cost: 1 4.99/2.21 4.99/2.21 2: f1 -> f1 : Q'=free_17, J'=free_19, K'=free_14, L'=free_16, M'=free_20, N'=free_18, O'=free_15, [ 0>=H && 1+F==G ], cost: 1 4.99/2.21 4.99/2.21 3: f1 -> f1 : Q'=free_24, J'=free_26, K'=free_21, L'=free_23, M'=free_28, N'=free_25, O'=free_22, P'=free_27, Q_1'=256, [ free_29>=1 && G>=1+F && G>=2+F && Q_1==256 ], cost: 1 4.99/2.21 4.99/2.21 4: f1 -> f1 : Q'=free_33, J'=free_35, K'=free_30, L'=free_32, M'=free_36, N'=free_34, O'=free_31, [ 0>=Q_1 && G>=1+F && G>=2+F ], cost: 1 4.99/2.21 4.99/2.21 5: f1 -> f2 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_37, F'=free_38, G'=K, H'=L, Q'=M, J'=N, K'=O, L'=P, M'=Q_1, N'=0, O'=0, P'=0, Q_1'=U, [ F>=G ], cost: 1 4.99/2.21 4.99/2.21 6: f1 -> f3 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_42, F'=free_44, G'=free_39, H'=free_41, Q'=free_46, J'=free_43, K'=free_40, L'=free_45, M'=Q_1, N'=H, O'=H, P'=H, Q_1'=free_47, [ H>=1 && H>=257 && 1+F==G ], cost: 1 4.99/2.21 4.99/2.21 7: f1 -> f3 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_51, F'=free_53, G'=free_48, H'=free_50, Q'=free_55, J'=free_52, K'=free_49, L'=free_54, M'=Q_1, N'=H, O'=H, P'=H, Q_1'=free_56, [ H>=1 && 255>=H && 1+F==G ], cost: 1 4.99/2.21 4.99/2.21 8: f1 -> f3 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_60, F'=free_62, G'=free_57, H'=free_59, Q'=free_64, J'=free_61, K'=free_58, L'=free_63, M'=Q_1, N'=Q_1, O'=Q_1, P'=Q_1, Q_1'=free_65, [ Q_1>=1 && Q_1>=257 && G>=1+F && G>=2+F ], cost: 1 4.99/2.21 4.99/2.21 9: f1 -> f3 : A1'=B, B'=C, B1'=D, C'=E, C1'=F, D'=G, D1'=H, E'=free_69, F'=free_71, G'=free_66, H'=free_68, Q'=free_73, J'=free_70, K'=free_67, L'=free_72, M'=Q_1, N'=Q_1, O'=Q_1, P'=Q_1, Q_1'=free_74, [ Q_1>=1 && 255>=Q_1 && G>=1+F && G>=2+F ], cost: 1 4.99/2.21 4.99/2.21 4.99/2.21 4.99/2.21 Removed unreachable and leaf rules: 4.99/2.21 4.99/2.21 Start location: f300 4.99/2.21 4.99/2.21 0: f300 -> f1 : A'=free_2, B'=free_3, C'=free, D'=free_1, E'=free_4, [], cost: 1 4.99/2.21 4.99/2.21 1: f1 -> f1 : H'=256, Q'=free_8, J'=free_10, K'=free_5, L'=free_7, M'=free_12, N'=free_9, O'=free_6, P'=free_11, [ free_13>=1 && 1+F==G && H==256 ], cost: 1 4.99/2.21 4.99/2.21 2: f1 -> f1 : Q'=free_17, J'=free_19, K'=free_14, L'=free_16, M'=free_20, N'=free_18, O'=free_15, [ 0>=H && 1+F==G ], cost: 1 4.99/2.21 4.99/2.21 3: f1 -> f1 : Q'=free_24, J'=free_26, K'=free_21, L'=free_23, M'=free_28, N'=free_25, O'=free_22, P'=free_27, Q_1'=256, [ free_29>=1 && G>=1+F && G>=2+F && Q_1==256 ], cost: 1 4.99/2.21 4.99/2.21 4: f1 -> f1 : Q'=free_33, J'=free_35, K'=free_30, L'=free_32, M'=free_36, N'=free_34, O'=free_31, [ 0>=Q_1 && G>=1+F && G>=2+F ], cost: 1 4.99/2.21 4.99/2.21 4.99/2.21 4.99/2.21 Simplified all rules, resulting in: 4.99/2.21 4.99/2.21 Start location: f300 4.99/2.21 4.99/2.21 0: f300 -> f1 : A'=free_2, B'=free_3, C'=free, D'=free_1, E'=free_4, [], cost: 1 4.99/2.21 4.99/2.21 1: f1 -> f1 : H'=256, Q'=free_8, J'=free_10, K'=free_5, L'=free_7, M'=free_12, N'=free_9, O'=free_6, P'=free_11, [ 1+F==G && H==256 ], cost: 1 4.99/2.21 4.99/2.21 2: f1 -> f1 : Q'=free_17, J'=free_19, K'=free_14, L'=free_16, M'=free_20, N'=free_18, O'=free_15, [ 0>=H && 1+F==G ], cost: 1 4.99/2.21 4.99/2.21 3: f1 -> f1 : Q'=free_24, J'=free_26, K'=free_21, L'=free_23, M'=free_28, N'=free_25, O'=free_22, P'=free_27, Q_1'=256, [ G>=2+F && Q_1==256 ], cost: 1 4.99/2.21 4.99/2.21 4: f1 -> f1 : Q'=free_33, J'=free_35, K'=free_30, L'=free_32, M'=free_36, N'=free_34, O'=free_31, [ 0>=Q_1 && G>=2+F ], cost: 1 4.99/2.21 4.99/2.21 4.99/2.21 4.99/2.21 ### Simplification by acceleration and chaining ### 4.99/2.21 popout

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all output return to Complexity_ITS 2019-03-21 04.46