details

property	value
status	complete
benchmark	5.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n099.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.83443 seconds
cpu usage	7.22641
user time	6.86355
system time	0.362866
max virtual memory	1.8642528E7
max residence set size	234324.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

6.92/2.79 WORST_CASE(NON_POLY, ?) 6.92/2.80 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 6.92/2.80 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.92/2.80 6.92/2.80 6.92/2.80 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 6.92/2.80 6.92/2.80 (0) CpxIntTrs 6.92/2.80 (1) Loat Proof [FINISHED, 1122 ms] 6.92/2.80 (2) BOUNDS(INF, INF) 6.92/2.80 6.92/2.80 6.92/2.80 ---------------------------------------- 6.92/2.80 6.92/2.80 (0) 6.92/2.80 Obligation: 6.92/2.80 Complexity Int TRS consisting of the following rules: 6.92/2.80 f0(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M)) :|: TRUE 6.92/2.80 f1(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f2(0, O, P, 3, N, 0, O, P, 3, N, 2, L, M)) :|: 7 >= N && N >= 1 6.92/2.80 f4(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f2(0, O, P, N, Q, 0, O, P, N, Q, 2, L, M)) :|: L >= 1 && L >= P + 1 && M >= 1 && M >= O + 1 && 7 >= Q && 7 >= N && Q >= 1 && N >= 1 6.92/2.80 f1(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f1(O, P, N, 2, Q, O, P, N, 2, Q, 1, L, M)) :|: R >= 1 && 7 >= R && S >= 1 && 7 >= S && Q >= 1 && 7 >= Q && 1 >= O && O >= 0 6.92/2.80 f2(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f1(O, P, N, 2, Q, O, P, N, 2, Q, 1, L, M)) :|: R >= 1 && 7 >= R && S >= 1 && 7 >= S && Q >= 1 && 7 >= Q && 1 >= O && O >= 0 6.92/2.80 f4(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f1(O, P, N, 2, Q, O, P, N, 2, Q, 1, L, M)) :|: R >= L && S >= M && T >= 1 && 7 >= T && U >= 1 && 7 >= U && Q >= 1 && 7 >= Q && 1 >= O && O >= 0 6.92/2.80 f4(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f1(O, P, N, 2, Q, O, P, N, 2, Q, 1, L, M)) :|: R >= 1 && 7 >= R && S >= 1 && 7 >= S && Q >= 1 && 7 >= Q && 1 >= O && O >= 0 6.92/2.80 f2(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f4(O, P, N, Q, 2, O, P, N, Q, 2, 4, L, M)) :|: R >= 1 && 7 >= R && S >= 1 && 7 >= S && T >= 1 && 7 >= T && U >= 1 && 7 >= U && Q >= 1 && 7 >= Q && 1 >= O && O >= 0 6.92/2.80 f2(A, B, C, D, E, F, G, H, I, J, K, L, M) -> Com_1(f4(O, P, N, Q, 7, O, P, N, Q, 7, 4, L, M)) :|: R >= 1 && 7 >= R && S >= 1 && 7 >= S && T >= 1 && 7 >= T && U >= 1 && 7 >= U && Q >= 1 && 7 >= Q && 1 >= O && O >= 0 6.92/2.80 6.92/2.80 The start-symbols are:[f0_13] 6.92/2.80 6.92/2.80 6.92/2.80 ---------------------------------------- 6.92/2.80 6.92/2.80 (1) Loat Proof (FINISHED) 6.92/2.80 6.92/2.80 6.92/2.80 ### Pre-processing the ITS problem ### 6.92/2.80 6.92/2.80 6.92/2.80 6.92/2.80 Initial linear ITS problem 6.92/2.80 6.92/2.80 Start location: f0 6.92/2.80 6.92/2.80 0: f0 -> f1 : [], cost: 1 6.92/2.80 6.92/2.80 1: f1 -> f2 : A'=0, B'=free_2, C'=free, D'=3, E'=free_1, F'=0, G'=free_2, H'=free, Q'=3, J'=free_1, K'=2, [ 7>=free_1 && free_1>=1 ], cost: 1 6.92/2.80 6.92/2.80 3: f1 -> f1 : A'=free_12, B'=free_8, C'=free_10, D'=2, E'=free_9, F'=free_12, G'=free_8, H'=free_10, Q'=2, J'=free_9, K'=1, [ free_11>=1 && 7>=free_11 && free_7>=1 && 7>=free_7 && free_9>=1 && 7>=free_9 && 1>=free_12 && free_12>=0 ], cost: 1 6.92/2.80 6.92/2.80 2: f4 -> f2 : A'=0, B'=free_6, C'=free_3, D'=free_5, E'=free_4, F'=0, G'=free_6, H'=free_3, Q'=free_5, J'=free_4, K'=2, [ L>=1 && L>=1+free_3 && M>=1 && M>=1+free_6 && 7>=free_4 && 7>=free_5 && free_4>=1 && free_5>=1 ], cost: 1 6.92/2.80 6.92/2.80 5: f4 -> f1 : A'=free_26, B'=free_20, C'=free_23, D'=2, E'=free_22, F'=free_26, G'=free_20, H'=free_23, Q'=2, J'=free_22, K'=1, [ free_25>=L && free_19>=M && free_21>=1 && 7>=free_21 && free_24>=1 && 7>=free_24 && free_22>=1 && 7>=free_22 && 1>=free_26 && free_26>=0 ], cost: 1 6.92/2.80 6.92/2.80 6: f4 -> f1 : A'=free_32, B'=free_28, C'=free_30, D'=2, E'=free_29, F'=free_32, G'=free_28, H'=free_30, Q'=2, J'=free_29, K'=1, [ free_31>=1 && 7>=free_31 && free_27>=1 && 7>=free_27 && free_29>=1 && 7>=free_29 && 1>=free_32 && free_32>=0 ], cost: 1 6.92/2.80 6.92/2.80 4: f2 -> f1 : A'=free_18, B'=free_14, C'=free_16, D'=2, E'=free_15, F'=free_18, G'=free_14, H'=free_16, Q'=2, J'=free_15, K'=1, [ free_17>=1 && 7>=free_17 && free_13>=1 && 7>=free_13 && free_15>=1 && 7>=free_15 && 1>=free_18 && free_18>=0 ], cost: 1 6.92/2.80 6.92/2.80 7: f2 -> f4 : A'=free_40, B'=free_34, C'=free_37, D'=free_36, E'=2, F'=free_40, G'=free_34, H'=free_37, Q'=free_36, J'=2, K'=4, [ free_39>=1 && 7>=free_39 && free_33>=1 && 7>=free_33 && free_35>=1 && 7>=free_35 && free_38>=1 && 7>=free_38 && free_36>=1 && 7>=free_36 && 1>=free_40 && free_40>=0 ], cost: 1 6.92/2.80 6.92/2.80 8: f2 -> f4 : A'=free_48, B'=free_42, C'=free_45, D'=free_44, E'=7, F'=free_48, G'=free_42, H'=free_45, Q'=free_44, J'=7, K'=4, [ free_47>=1 && 7>=free_47 && free_41>=1 && 7>=free_41 && free_43>=1 && 7>=free_43 && free_46>=1 && 7>=free_46 && free_44>=1 && 7>=free_44 && 1>=free_48 && free_48>=0 ], cost: 1 6.92/2.80 6.92/2.80 6.92/2.80 6.92/2.80 Simplified all rules, resulting in: 6.92/2.80 6.92/2.80 Start location: f0 6.92/2.80 6.92/2.80 0: f0 -> f1 : [], cost: 1 6.92/2.80 6.92/2.80 1: f1 -> f2 : A'=0, B'=free_2, C'=free, D'=3, E'=free_1, F'=0, G'=free_2, H'=free, Q'=3, J'=free_1, K'=2, [ 7>=free_1 && free_1>=1 ], cost: 1 6.92/2.80 6.92/2.80 3: f1 -> f1 : A'=free_12, B'=free_8, C'=free_10, D'=2, E'=free_9, F'=free_12, G'=free_8, H'=free_10, Q'=2, J'=free_9, K'=1, [ free_9>=1 && 7>=free_9 && 1>=free_12 && free_12>=0 ], cost: 1 6.92/2.80 6.92/2.80 2: f4 -> f2 : A'=0, B'=free_6, C'=free_3, D'=free_5, E'=free_4, F'=0, G'=free_6, H'=free_3, Q'=free_5, J'=free_4, K'=2, [ L>=1 && L>=1+free_3 && M>=1 && M>=1+free_6 && 7>=free_4 && 7>=free_5 && free_4>=1 && free_5>=1 ], cost: 1 6.92/2.80 6.92/2.80 5: f4 -> f1 : A'=free_26, B'=free_20, C'=free_23, D'=2, E'=free_22, F'=free_26, G'=free_20, H'=free_23, Q'=2, J'=free_22, K'=1, [ free_22>=1 && 7>=free_22 && 1>=free_26 && free_26>=0 ], cost: 1 6.92/2.80 6.92/2.80 6: f4 -> f1 : A'=free_32, B'=free_28, C'=free_30, D'=2, E'=free_29, F'=free_32, G'=free_28, H'=free_30, Q'=2, J'=free_29, K'=1, [ free_29>=1 && 7>=free_29 && 1>=free_32 && free_32>=0 ], cost: 1 6.92/2.80 6.92/2.80 4: f2 -> f1 : A'=free_18, B'=free_14, C'=free_16, D'=2, E'=free_15, F'=free_18, G'=free_14, H'=free_16, Q'=2, J'=free_15, K'=1, [ free_15>=1 && 7>=free_15 && 1>=free_18 && free_18>=0 ], cost: 1 6.92/2.80 6.92/2.80 7: f2 -> f4 : A'=free_40, B'=free_34, C'=free_37, D'=free_36, E'=2, F'=free_40, G'=free_34, H'=free_37, Q'=free_36, J'=2, K'=4, [ free_36>=1 && 7>=free_36 && 1>=free_40 && free_40>=0 ], cost: 1 6.92/2.80 6.92/2.80 8: f2 -> f4 : A'=free_48, B'=free_42, C'=free_45, D'=free_44, E'=7, F'=free_48, G'=free_42, H'=free_45, Q'=free_44, J'=7, K'=4, [ free_44>=1 && 7>=free_44 && 1>=free_48 && free_48>=0 ], cost: 1 6.92/2.80 6.92/2.80 6.92/2.80 6.92/2.80 ### Simplification by acceleration and chaining ### 6.92/2.80 6.92/2.80 6.92/2.80 6.92/2.80 Accelerating simple loops of location 1. 6.92/2.80 6.92/2.80 Accelerating the following rules: 6.92/2.80 6.92/2.80 3: f1 -> f1 : A'=free_12, B'=free_8, C'=free_10, D'=2, E'=free_9, F'=free_12, G'=free_8, H'=free_10, Q'=2, J'=free_9, K'=1, [ free_9>=1 && 7>=free_9 && 1>=free_12 && free_12>=0 ], cost: 1 6.92/2.80 6.92/2.80 6.92/2.80 6.92/2.80 Accelerated rule 3 with NONTERM, yielding the new rule 9. popout

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actions

all output return to Complexity_ITS 2019-03-21 04.46