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Compl Integ Trans Syste 26843 pair #381744694
details
property
value
status
complete
benchmark
sudoku.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
282.615546942 seconds
cpu usage
845.616516379
max memory
1.182302208E9
stage attributes
key
value
output-size
54471
starexec-result
WORST_CASE(NON_POLY, ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 280.8 s] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f135(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f136(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= A + 1 f135(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f136(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: A >= 1 f136(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= B + 1 f136(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: B >= 1 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f26(1, 1, 3, X, 1, 1, Y, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: TRUE f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f29(A, B, C, D, E, F, G, H, 0, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= H + 1 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f29(A, B, C, D, E, F, G, H, I + 1, X, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= I + 1 f38(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f41(A, B, C, D, E, F, G, H, 0, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= H + 1 f41(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f44(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= E + 1 && D >= I + 1 f41(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f44(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: E >= 1 && D >= I + 1 f44(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f41(A, B, C, D, 1, F, G, H, I + 1, J, 1, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: TRUE f44(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f41(A, B, C, D, 0, F, G, H, I + 1, J, 0, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: TRUE f41(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f41(A, B, C, D, 0, F, G, H, I + 1, J, 0, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= I + 1 && E >= 0 && E <= 0 f56(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K, 0, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= H + 1 f59(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f62(A, B, C, D, E, F, G, H, I, J, K, L, L + 1, N, O, P, Q, R, S, T, U, V, W)) :|: D >= 2 + L f62(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f65(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= M + 1 && 0 >= A + 1 f62(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f65(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= M + 1 && A >= 1 f65(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f62(1, B, C, D, E, F, G, H, I, J, K, L, M + 1, 1, O, P, Q, R, S, T, U, V, W)) :|: X >= Y + 1 f65(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f62(1, B, C, D, E, F, G, H, I, J, K, L, M + 1, 1, O, P, Q, R, S, T, U, V, W)) :|: TRUE f65(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f62(0, B, C, D, E, F, G, H, I, J, K, L, M + 1, 0, O, P, Q, R, S, T, U, V, W)) :|: TRUE f62(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f62(0, B, C, D, E, F, G, H, I, J, K, L, M + 1, 0, O, P, Q, R, S, T, U, V, W)) :|: D >= M + 1 && A >= 0 && A <= 0 f77(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f80(A, B, C, D, E, F, G, H, I, J, K, L, M, N, 0, P, Q, R, S, T, U, V, W)) :|: D >= I + 1 f80(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f83(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, O + 1, Q, R, S, T, U, V, W)) :|: D >= 2 + O f83(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f86(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= P + 1 && 0 >= B + 1 f83(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f86(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= P + 1 && B >= 1 f86(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f83(A, 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P + 1, 1, R, S, T, U, V, W)) :|: X >= Y + 1 f86(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f83(A, 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P + 1, 1, R, S, T, U, V, W)) :|: TRUE f86(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f83(A, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P + 1, 0, R, S, T, U, V, W)) :|: TRUE f83(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f83(A, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P + 1, 0, R, S, T, U, V, W)) :|: D >= P + 1 && B >= 0 && B <= 0 f98(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f101(A, B, C, D, E, F, G, H, 0, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: C >= H + 1 f101(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f104(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, 0, S, T, U, V, W)) :|: C >= I + 1 f104(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, 0, T, U, V, W)) :|: C >= R + 1 f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, 0, U, V, W)) :|: C >= S + 1 f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f113(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, 0, V, W)) :|: C >= T + 1 f113(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f117(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= F + 1 && C * T + U >= C * R + S + 1 && C >= U + 1 f113(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f117(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: F >= 1 && C * T + U >= C * R + S + 1 && C >= U + 1 f113(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f113(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U + 1, V, W)) :|: C * R + S >= C * T + U && C >= U + 1 f117(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f113(A, B, C, D, E, 1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U + 1, 1, W)) :|: X >= Y + 1 f117(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f113(A, B, C, D, E, 1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U + 1, 1, W)) :|: TRUE f117(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f113(A, B, C, D, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U + 1, 0, W)) :|: TRUE f113(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f113(A, B, C, D, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U + 1, 0, W)) :|: C * T + U >= C * R + S + 1 && C >= U + 1 && F >= 0 && F <= 0 f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f146(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 0)) :|: 0 >= F + 1 f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f146(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 0)) :|: F >= 1 f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f146(A, B, C, D, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 1)) :|: F >= 0 && F <= 0 f136(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f146(A, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 1)) :|: B >= 0 && B <= 0 f135(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f146(0, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 1)) :|: A >= 0 && A <= 0 f113(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T + 1, U, V, W)) :|: U >= C f110(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S + 1, T, U, V, W)) :|: T >= C f107(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f104(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R + 1, S, T, U, V, W)) :|: S >= C f104(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f101(A, B, C, D, E, F, G, H, I + 1, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: R >= C f101(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f98(A, B, C, D, E, F, G, H + 1, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: I >= C f98(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f135(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= E + 1 && H >= C f98(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f135(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: E >= 1 && H >= C f98(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f146(A, B, C, D, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 1)) :|: H >= C && E >= 0 && E <= 0 f83(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f80(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O + 1, P, Q, R, S, T, U, V, W)) :|: P >= D f80(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f77(A, B, C, D, E, F, G, H, I + 1, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: O + 1 >= D f77(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f98(A, B, C, D, E, F, G, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: I >= D f62(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K, L + 1, M, N, O, P, Q, R, S, T, U, V, W)) :|: M >= D f59(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f56(A, B, C, D, E, F, G, H + 1, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: L + 1 >= D f56(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f77(A, B, C, D, E, F, G, H, 0, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: H >= D f41(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f38(A, B, C, D, E, F, G, H + 1, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: I >= D f38(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f56(A, B, C, D, E, F, G, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: H >= D f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f26(A, B, C, D, E, F, G, H + 1, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: I >= D f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f38(A, B, C, D, E, F, G, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: H >= D The start-symbols are:[f0_23] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ###
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