details

property	value
status	complete
benchmark	huh.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n057.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.04562 seconds
cpu usage	4.59152
user time	4.3036
system time	0.287914
max virtual memory	1.8451996E7
max residence set size	225056.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

4.09/2.02 WORST_CASE(NON_POLY, ?) 4.09/2.03 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.09/2.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.09/2.03 4.09/2.03 4.09/2.03 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 4.09/2.03 4.09/2.03 (0) CpxIntTrs 4.09/2.03 (1) Loat Proof [FINISHED, 302 ms] 4.09/2.03 (2) BOUNDS(INF, INF) 4.09/2.03 4.09/2.03 4.09/2.03 ---------------------------------------- 4.09/2.03 4.09/2.03 (0) 4.09/2.03 Obligation: 4.09/2.03 Complexity Int TRS consisting of the following rules: 4.09/2.03 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f9(A, 1 + B, 1 + C, S, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= 1 + B && C >= 0 4.09/2.03 f5(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f0(A, B, C, D, E, F, S, G, V, W, X, L, M, N, O, P, Q, R)) :|: U >= T + 1 && E >= 1 && F >= 0 4.09/2.03 f5(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f5(A, B, C, D, 1 + E, -(1) + F, M, 0, W, X, K, M, N, V, S, E, Q, R)) :|: T >= U && E >= 0 && F >= 0 && H >= 0 && H <= 0 4.09/2.03 f5(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f12(A, B, C, D, E, F, G, 0, V, W, K, M, M, 0, O, E, S, R)) :|: X >= T && E >= 0 && F >= 0 && N >= 0 && N <= 0 && H >= 0 && H <= 0 4.09/2.03 f9(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f5(A, B, C, D, 1, T - 3 + C, S, 0, U, A1, K, S, V, X, W, P, D, -(2) + C)) :|: C >= 2 && B >= A && Y >= Z 4.09/2.03 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f9(17, 1, 0, S, E, F, G, H, I, J, K, V, M, N, O, P, Q, R)) :|: TRUE 4.09/2.03 4.09/2.03 The start-symbols are:[f6_18] 4.09/2.03 4.09/2.03 4.09/2.03 ---------------------------------------- 4.09/2.03 4.09/2.03 (1) Loat Proof (FINISHED) 4.09/2.03 4.09/2.03 4.09/2.03 ### Pre-processing the ITS problem ### 4.09/2.03 4.09/2.03 4.09/2.03 4.09/2.03 Initial linear ITS problem 4.09/2.03 4.09/2.03 Start location: f6 4.09/2.03 4.09/2.03 0: f9 -> f9 : B'=1+B, C'=1+C, D'=free, [ A>=1+B && C>=0 ], cost: 1 4.09/2.03 4.09/2.03 4: f9 -> f5 : E'=1, F'=-3+free_22+C, G'=free_21, H'=0, Q'=free_24, J'=free_18, L'=free_25, M'=free_21, N'=free_19, O'=free_26, Q_1'=D, R'=-2+C, [ C>=2 && B>=A && free_20>=free_23 ], cost: 1 4.09/2.03 4.09/2.03 1: f5 -> f0 : A1'=B, B'=C, C'=D, D'=E, E'=F, F'=free_4, H'=free_3, Q'=free_5, J'=free_1, K'=L, L'=M, M'=N, N'=O, O'=P, P'=Q_1, Q_1'=R, [ free_6>=1+free_2 && E>=1 && F>=0 ], cost: 1 4.09/2.03 4.09/2.03 2: f5 -> f5 : E'=1+E, F'=-1+F, G'=L, H'=0, Q'=free_10, J'=free_9, L'=N, M'=L, N'=free_11, O'=free_7, P'=E, [ free_12>=free_8 && E>=0 && F>=0 && H==0 ], cost: 1 4.09/2.03 4.09/2.03 3: f5 -> f12 : A1'=B, B'=C, C'=D, D'=E, E'=F, F'=G, G'=0, H'=free_15, Q'=free_14, J'=K, K'=L, M'=0, N'=O, O'=E, P'=free_16, Q_1'=R, [ free_13>=free_17 && E>=0 && F>=0 && N==0 && H==0 ], cost: 1 4.09/2.03 4.09/2.03 5: f6 -> f9 : A'=17, B'=1, C'=0, D'=free_28, M'=free_27, [], cost: 1 4.09/2.03 4.09/2.03 4.09/2.03 4.09/2.03 Removed unreachable and leaf rules: 4.09/2.03 4.09/2.03 Start location: f6 4.09/2.03 4.09/2.03 0: f9 -> f9 : B'=1+B, C'=1+C, D'=free, [ A>=1+B && C>=0 ], cost: 1 4.09/2.03 4.09/2.03 4: f9 -> f5 : E'=1, F'=-3+free_22+C, G'=free_21, H'=0, Q'=free_24, J'=free_18, L'=free_25, M'=free_21, N'=free_19, O'=free_26, Q_1'=D, R'=-2+C, [ C>=2 && B>=A && free_20>=free_23 ], cost: 1 4.09/2.03 4.09/2.03 2: f5 -> f5 : E'=1+E, F'=-1+F, G'=L, H'=0, Q'=free_10, J'=free_9, L'=N, M'=L, N'=free_11, O'=free_7, P'=E, [ free_12>=free_8 && E>=0 && F>=0 && H==0 ], cost: 1 4.09/2.03 4.09/2.03 5: f6 -> f9 : A'=17, B'=1, C'=0, D'=free_28, M'=free_27, [], cost: 1 4.09/2.03 4.09/2.03 4.09/2.03 4.09/2.03 Simplified all rules, resulting in: 4.09/2.03 4.09/2.03 Start location: f6 4.09/2.03 4.09/2.03 0: f9 -> f9 : B'=1+B, C'=1+C, D'=free, [ A>=1+B && C>=0 ], cost: 1 4.09/2.03 4.09/2.03 4: f9 -> f5 : E'=1, F'=-3+free_22+C, G'=free_21, H'=0, Q'=free_24, J'=free_18, L'=free_25, M'=free_21, N'=free_19, O'=free_26, Q_1'=D, R'=-2+C, [ C>=2 && B>=A ], cost: 1 4.09/2.03 4.09/2.03 2: f5 -> f5 : E'=1+E, F'=-1+F, G'=L, H'=0, Q'=free_10, J'=free_9, L'=N, M'=L, N'=free_11, O'=free_7, P'=E, [ E>=0 && F>=0 && H==0 ], cost: 1 4.09/2.03 4.09/2.03 5: f6 -> f9 : A'=17, B'=1, C'=0, D'=free_28, M'=free_27, [], cost: 1 4.09/2.03 4.09/2.03 4.09/2.03 4.09/2.03 ### Simplification by acceleration and chaining ### 4.09/2.03 4.09/2.03 4.09/2.03 4.09/2.03 Accelerating simple loops of location 0. 4.09/2.03 4.09/2.03 Accelerating the following rules: 4.09/2.03 4.09/2.03 0: f9 -> f9 : B'=1+B, C'=1+C, D'=free, [ A>=1+B && C>=0 ], cost: 1 4.09/2.03 4.09/2.03 4.09/2.03 4.09/2.03 Accelerated rule 0 with metering function -B+A, yielding the new rule 6. 4.09/2.03 4.09/2.03 Removing the simple loops: 0. 4.09/2.03 4.09/2.03 4.09/2.03 popout

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all output return to Complexity_ITS 2019-03-21 04.46