details

property	value
status	complete
benchmark	eric2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.507597923 seconds
cpu usage	588.865343069
max memory	8.4146176E8

stage attributes

key	value
output-size	42344
starexec-result	WORST_CASE(Omega(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), ?) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 4032 ms] (2) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f2(0, 0, 0, D + C, E + B - 1, F + A - 1, G + 1, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: A >= 1 && B >= 1 f999(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(1, 1, H - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, C1)) :|: H >= 1 && C >= 0 && C <= 0 && B >= 0 && B <= 0 && A >= 0 && A <= 0 && D >= 0 && D <= 0 && E >= 0 && E <= 0 && F >= 0 && F <= 0 && G >= 0 && G <= 0 && I >= 0 && I <= 0 && J >= 0 && J <= 0 && K >= 0 && K <= 0 && L >= 0 && L <= 0 && M >= 0 && M <= 0 && N >= 0 && N <= 0 && O >= 0 && O <= 0 && P >= 0 && P <= 0 && Q >= 0 && Q <= 0 && R >= 0 && R <= 0 && S >= 0 && S <= 0 && T >= 0 && T <= 0 && U >= 0 && U <= 0 && V >= 0 && V <= 0 && W >= 0 && W <= 0 && X >= 0 && X <= 0 && Y >= 0 && Y <= 0 && Z >= 0 && Z <= 0 && A1 >= 0 && A1 <= 0 && B1 >= 0 && B1 <= 0 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(A + 1, B + 1, H + C - 1, D, E, F, G, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: H + C >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(A + 1, B + 1, C + H + D - 1, 0, E, F, G, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: H + D >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f2(A, B, C, I + D - 1, K + E, M + F, N + G, H, 0, J + 1, 0, L + 1, 0, 0, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: D >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(A + L + 1, B + J + 1, C + I + D - 1, 0, 0, 0, 0, H, 0, 0, K + E, 0, M + F, N + G, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: D >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(A + 1, B + 1, C + H + I + D - 2, 0, 0, 0, 0, 0, 0, J + 1, K + E, L + 1, M + F, N + G, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: H + I + D >= 2 && D >= 1 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(R + A + S + 1, P + B + Q + 1, O + C - 1, D, E, F, G, H, I, J, K, L, M, N, 0, 0, 0, 0, 0, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: C >= 1 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f2(A, B, C, T + D + U + 1, V + E + W - 1, X + F + Z + B1, Y + G + A1, H, I, J, K, L, M, N, O, P, Q, R, S, 0, 0, 0, 0, 0, 0, 0, 0, 0, D1)) :|: G >= 1 && F >= C1 && C1 >= 1 && E >= C1 The start-symbols are:[f999_29] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f999 0: f1 -> f2 : A'=0, B'=0, C'=0, D'=D+C, E'=-1+E+B, F'=-1+F+A, G'=1+G, [ A>=1 && B>=1 ], cost: 1 2: f1 -> f1 : A'=1+A, B'=1+B, C'=-1+H+C, H'=0, [ H+C>=1 ], cost: 1 7: f1 -> f1 : A'=1+R+S+A, B'=1+B+P+Q_1, C'=-1+O+C, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ C>=1 ], cost: 1 1: f999 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ H>=1 && C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 ], cost: 1 3: f2 -> f1 : A'=1+A, B'=1+B, C'=-1+H+D+C, D'=0, H'=0, [ H+D>=1 ], cost: 1 4: f2 -> f2 : D'=-1+Q+D, E'=E+K, F'=F+M, G'=G+N, Q'=0, J'=1+J, K'=0, L'=1+L, M'=0, N'=0, [ D>=1 ], cost: 1 5: f2 -> f1 : A'=1+L+A, B'=1+B+J, C'=-1+Q+D+C, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=E+K, L'=0, M'=F+M, N'=G+N, [ D>=1 ], cost: 1 6: f2 -> f1 : A'=1+A, B'=1+B, C'=-2+H+Q+D+C, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=E+K, L'=1+L, M'=F+M, N'=G+N, [ H+Q+D>=2 && D>=1 ], cost: 1 8: f2 -> f2 : A1'=0, B1'=0, C1'=free, D'=1+U+D+T, E'=-1+E+V+W, F'=X+F+B1+Z, G'=Y+G+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ G>=1 && F>=C1 && C1>=1 && E>=C1 ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 2: f1 -> f1 : A'=1+A, B'=1+B, C'=-1+H+C, H'=0, [ H+C>=1 ], cost: 1 7: f1 -> f1 : A'=1+R+S+A, B'=1+B+P+Q_1, C'=-1+O+C, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ C>=1 ], cost: 1 Accelerated rule 2 with metering function H+C, yielding the new rule 9. Accelerated rule 7 with backward acceleration, yielding the new rule 10. Removing the simple loops: 2 7. Accelerating simple loops of location 2. Accelerating the following rules: 4: f2 -> f2 : D'=-1+Q+D, E'=E+K, F'=F+M, G'=G+N, Q'=0, J'=1+J, K'=0, L'=1+L, M'=0, N'=0, [ D>=1 ], cost: 1 8: f2 -> f2 : A1'=0, B1'=0, C1'=free, D'=1+U+D+T, E'=-1+E+V+W, F'=X+F+B1+Z, G'=Y+G+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ G>=1 && F>=C1 && C1>=1 && E>=C1 ], cost: 1 popout

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all output return to Compl Integ Trans Syste 26843