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	n161.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.651 seconds
cpu usage	589.86
user time	588.384
system time	1.47637
max virtual memory	1.9004416E7
max residence set size	457236.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

589.56/291.60 WORST_CASE(Omega(n^1), ?) 589.77/291.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 589.77/291.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 589.77/291.61 589.77/291.61 589.77/291.61 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). 589.77/291.61 589.77/291.61 (0) CpxIntTrs 589.77/291.61 (1) Loat Proof [FINISHED, 4048 ms] 589.77/291.61 (2) BOUNDS(n^1, INF) 589.77/291.61 589.77/291.61 589.77/291.61 ---------------------------------------- 589.77/291.61 589.77/291.61 (0) 589.77/291.61 Obligation: 589.77/291.61 Complexity Int TRS consisting of the following rules: 589.77/291.61 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 >= 1 589.77/291.61 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 <= 0 589.77/291.61 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 >= 1 589.77/291.61 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 >= 1 589.77/291.61 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 >= 1 589.77/291.61 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 >= 1 589.77/291.61 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 >= 1 589.77/291.61 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 >= 1 589.77/291.61 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 589.77/291.61 589.77/291.61 The start-symbols are:[f999_29] 589.77/291.61 589.77/291.61 589.77/291.61 ---------------------------------------- 589.77/291.61 589.77/291.61 (1) Loat Proof (FINISHED) 589.77/291.61 589.77/291.61 589.77/291.61 ### Pre-processing the ITS problem ### 589.77/291.61 589.77/291.61 589.77/291.61 589.77/291.61 Initial linear ITS problem 589.77/291.61 589.77/291.61 Start location: f999 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 2: f1 -> f1 : A'=1+A, B'=1+B, C'=-1+H+C, H'=0, [ H+C>=1 ], cost: 1 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 3: f2 -> f1 : A'=1+A, B'=1+B, C'=-1+H+D+C, D'=0, H'=0, [ H+D>=1 ], cost: 1 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 589.77/291.61 589.77/291.61 ### Simplification by acceleration and chaining ### 589.77/291.61 589.77/291.61 589.77/291.61 589.77/291.61 Accelerating simple loops of location 0. 589.77/291.61 589.77/291.61 Accelerating the following rules: 589.77/291.61 589.77/291.61 2: f1 -> f1 : A'=1+A, B'=1+B, C'=-1+H+C, H'=0, [ H+C>=1 ], cost: 1 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 589.77/291.61 589.77/291.61 Accelerated rule 2 with metering function H+C, yielding the new rule 9. 589.77/291.61 589.77/291.61 Accelerated rule 7 with backward acceleration, yielding the new rule 10. 589.77/291.61 589.77/291.61 Removing the simple loops: 2 7. 589.77/291.61 589.77/291.61 589.77/291.61 589.77/291.61 Accelerating simple loops of location 2. 589.77/291.61 589.77/291.61 Accelerating the following rules: 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 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: 1 589.77/291.61 589.77/291.61 589.77/291.61 589.77/291.61 Accelerated rule 4 with backward acceleration, yielding the new rule 11. 589.77/291.61 589.77/291.61 During metering: Instantiating temporary variables by {free==X+F+B1+Z} 589.77/291.61 589.77/291.61 Found no metering function for rule 8. popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Complexity_ITS 2019-03-21 04.46