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Compl Integ Trans Syste 26843 pair #381745494
details
property
value
status
complete
benchmark
ludcmp.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
20.493281126 seconds
cpu usage
37.846613989
max memory
5.5898112E8
stage attributes
key
value
output-size
92090
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(max(3 * Arg_1 + nat(6 + 6 * Arg_0 + -6 * Arg_1), 3 * Arg_1) + max(min(-3 * Arg_3 + min(-6 + -6 * Arg_0 + 6 * Arg_3, 0), -3 * Arg_3), -3 * Arg_3)) + nat(1 + 2 * Arg_0 + max(min(-2 * Arg_3 + min(-4 + -4 * Arg_0 + 4 * Arg_3, 0), -2 * Arg_3), -2 * Arg_3)) + nat(2 + 2 * Arg_0 + -2 * Arg_1) + nat(-1 * Arg_7 + max(Arg_1 + nat(2 + 2 * Arg_0 + -2 * Arg_1), Arg_1)) + nat(2 * Arg_0 + max(min(-2 * Arg_3 + min(-4 + -4 * Arg_0 + 4 * Arg_3, 0), -2 * Arg_3), -2 * Arg_3)) + max(1, 7 + 6 * Arg_0 + -6 * Arg_3) + nat(-3 * Arg_3 + max(3 * Arg_1 + nat(6 + 6 * Arg_0 + -6 * Arg_1), 3 * Arg_1)) + max(2, 4 + 2 * Arg_0 + -2 * Arg_1) + nat(3 * Arg_0 + max(-3 * Arg_3, min(-3 * Arg_3 + min(-6 + -6 * Arg_0 + 6 * Arg_3, 0), -3 * Arg_3)))). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 13.1 s] (2) BOUNDS(1, nat(max(3 * Arg_1 + nat(6 + 6 * Arg_0 + -6 * Arg_1), 3 * Arg_1) + max(min(-3 * Arg_3 + min(-6 + -6 * Arg_0 + 6 * Arg_3, 0), -3 * Arg_3), -3 * Arg_3)) + nat(1 + 2 * Arg_0 + max(min(-2 * Arg_3 + min(-4 + -4 * Arg_0 + 4 * Arg_3, 0), -2 * Arg_3), -2 * Arg_3)) + nat(2 + 2 * Arg_0 + -2 * Arg_1) + nat(-1 * Arg_7 + max(Arg_1 + nat(2 + 2 * Arg_0 + -2 * Arg_1), Arg_1)) + nat(2 * Arg_0 + max(min(-2 * Arg_3 + min(-4 + -4 * Arg_0 + 4 * Arg_3, 0), -2 * Arg_3), -2 * Arg_3)) + max(1, 7 + 6 * Arg_0 + -6 * Arg_3) + nat(-3 * Arg_3 + max(3 * Arg_1 + nat(6 + 6 * Arg_0 + -6 * Arg_1), 3 * Arg_1)) + max(2, 4 + 2 * Arg_0 + -2 * Arg_1) + nat(3 * Arg_0 + max(-3 * Arg_3, min(-3 * Arg_3 + min(-6 + -6 * Arg_0 + 6 * Arg_3, 0), -3 * Arg_3)))) (3) Loat Proof [FINISHED, 18.8 s] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f69(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= L + 1 f69(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f71(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f12(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE f12(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f15(A, B, 0, D, E, F, G, H, I, J, K)) :|: A >= B f15(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f15(A, B, C, D + 1, L, L, G, H, I, J, K)) :|: C >= L && A >= D f15(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f15(A, B, L, D + 1, L, L, G, H, I, J, K)) :|: L >= 1 + C && A >= D f28(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f30(A, B, C, D, E, F, G, H, I, J, K)) :|: A >= D f30(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f33(A, B, C, D, E, F, L, H, I, J, K)) :|: D >= B + 1 f33(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f33(A, B, C, D, E, F, L, H + 1, I, J, K)) :|: B >= H + 1 f42(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f45(A, B, C, D, E, F, L, H, I, J, K)) :|: A >= B f45(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f45(A, B, C, D, E, F, L, H + 1, I, J, K)) :|: D >= H + 1 f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H + 1, L, J, K)) :|: A >= H f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f73(A, B, C, D, E, F, G, H, L, J, K)) :|: A >= D + 1 f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f73(A, B, C, D, E, F, G, H, L, J, K)) :|: D >= 1 + A f73(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f73(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: A >= B f71(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f28(A, B, C, A + 1, E, F, G, H, I, J, K)) :|: A >= D && A <= D f73(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f28(A, B, C, D + 1, E, F, G, H, I, J, K)) :|: B >= 1 + A f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, K)) :|: H >= 1 + A f45(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f42(A, B + 1, C, D, E, F, G, H, M, L, K)) :|: C >= M + 1 && H >= D f45(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f42(A, B + 1, L, D, E, F, G, H, L, M, B)) :|: L >= C && H >= D f42(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A && K >= D + 1 f42(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A && D >= 1 + K f42(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, D)) :|: B >= 1 + A && D >= K && D <= K f33(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f30(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: H >= B f30(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f42(A, B, 0, D, E, F, G, H, I, J, K)) :|: B >= D f28(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f82(A, B, C, D, E, F, G, H, I, J, K)) :|: D >= 1 + A f15(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f12(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: 0 >= C + 1 && D >= 1 + A f15(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f12(A, B + 1, C, D, E, F, G, H, I, J, K)) :|: C >= 1 && D >= 1 + A f15(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f12(A, B + 1, 0, D, E, F, G, H, I, J, K)) :|: D >= 1 + A && C >= 0 && C <= 0 f12(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f28(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= 1 + A The start-symbols are:[f0_11] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 1+2*2*max([0, 1+Arg_0-Arg_3])+max([0, 3*Arg_0+max([-3*Arg_3, -3*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_1])+max([0, 2*Arg_0+max([-2*Arg_3, -2*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+Arg_0-Arg_3])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([2, 2+2+2*Arg_0+-2*Arg_1])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_3])+max([0, -(Arg_3)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([0, 1+Arg_0-Arg_1])+max([0, max([3*Arg_1, 3*max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])])+max([-3*Arg_3, -3*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, 1+2*Arg_0+max([-2*Arg_3, -2*max([Arg_3, Arg_3+2*max([0, 1+Arg_0-Arg_3])])])])+max([0, -(Arg_7)+max([Arg_1, Arg_1+2*max([0, 1+Arg_0-Arg_1])])]) {O(n)}) Initial Complexity Problem: Start: f0 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7, Arg_8, Arg_9, Arg_10 Temp_Vars: L Locations: f0, f12, f15, f28, f30, f42, f59, f69, f71, f73, f82 Transitions: f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|: f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f15(Arg_0,Arg_1,0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:Arg_1 <= Arg_0 f12(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f28(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_0 <= Arg_1 f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f12(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:0 <= Arg_2 && Arg_1 <= Arg_0 && 1 <= Arg_2 && 1+Arg_0 <= Arg_3 f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f12(Arg_0,Arg_1+1,0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:0 <= Arg_2 && Arg_1 <= Arg_0 && 1+Arg_0 <= Arg_3 && Arg_2 <= 0 && 0 <= Arg_2 f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f15(Arg_0,Arg_1,Arg_2,Arg_3+1,L,L,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:0 <= Arg_2 && Arg_1 <= Arg_0 && L <= Arg_2 && Arg_3 <= Arg_0 f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f15(Arg_0,Arg_1,L,Arg_3+1,L,L,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:0 <= Arg_2 && Arg_1 <= Arg_0 && 1+Arg_2 <= L && Arg_3 <= Arg_0 f28(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f30(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_0 <= Arg_1 && Arg_3 <= Arg_0 f28(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_0 <= Arg_1 && 1+Arg_0 <= Arg_3 f30(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f42(Arg_0,Arg_1,0,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 1+Arg_0 <= Arg_1 && Arg_3 <= Arg_1 f42(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10) -> f59(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9,Arg_10):|:1+Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2 && 1+Arg_0 <= Arg_1 && 1+Arg_0 <= Arg_1 && Arg_3+1 <= Arg_10
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