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Complexity_ITS 2019-03-21 04.46 pair #429990430
details
property
value
status
complete
benchmark
rev_nt2.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n121.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.91251 seconds
cpu usage
6.81366
user time
6.50528
system time
0.308383
max virtual memory
1.8752604E7
max residence set size
225012.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
6.56/2.86 WORST_CASE(NON_POLY, ?) 6.56/2.87 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 6.56/2.87 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.56/2.87 6.56/2.87 6.56/2.87 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 6.56/2.87 6.56/2.87 (0) CpxIntTrs 6.56/2.87 (1) Loat Proof [FINISHED, 1230 ms] 6.56/2.87 (2) BOUNDS(INF, INF) 6.56/2.87 6.56/2.87 6.56/2.87 ---------------------------------------- 6.56/2.87 6.56/2.87 (0) 6.56/2.87 Obligation: 6.56/2.87 Complexity Int TRS consisting of the following rules: 6.56/2.87 f11(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, D1, E1) -> Com_1(f11(A, B, B, B, 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, D1, E1)) :|: A >= B + 1 6.56/2.87 f11(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, D1, E1) -> Com_1(f11(A, B, B, B, 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, D1, E1)) :|: B >= A + 1 6.56/2.87 f6(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, D1, E1) -> Com_1(f6(A, B, C, D, E, H1, 1 + G, -(1) + H, 1 + G, -(1) + H, F1, G1, -(1) + H, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: E >= F + 1 && G >= 0 && H >= 1 6.56/2.87 f6(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, D1, E1) -> Com_1(f6(A, B, C, D, E, H1, 1 + G, -(1) + H, 1 + G, -(1) + H, F1, G1, -(1) + H, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: F >= E + 1 && G >= 0 && H >= 1 6.56/2.87 f26(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, D1, E1) -> Com_1(f6(A, B, C, D, E, L1, 1, 4, 1, 4, K, L, M, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, E1)) :|: E >= I1 + 1 6.56/2.87 f26(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, D1, E1) -> Com_1(f6(A, B, C, D, E, L1, 1, 4, 1, 4, K, L, M, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, E1)) :|: I1 >= E + 1 6.56/2.87 f6(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, D1, E1) -> Com_1(f11(A, J1, J1, J1, F, F, G, H, I, J, K, L, M, F1, O, P, Q, R, S, T, U, V, W, X, Y, G1, A1, B1, C1, D1, H1)) :|: A >= J1 + 1 && G >= 0 && H >= 1 && F >= E && F <= E 6.56/2.87 f6(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, D1, E1) -> Com_1(f11(A, J1, J1, J1, F, F, G, H, I, J, K, L, M, F1, O, P, Q, R, S, T, U, V, W, X, Y, G1, A1, B1, C1, D1, H1)) :|: J1 >= A + 1 && G >= 0 && H >= 1 && F >= E && F <= E 6.56/2.87 6.56/2.87 The start-symbols are:[f26_31] 6.56/2.87 6.56/2.87 6.56/2.87 ---------------------------------------- 6.56/2.87 6.56/2.87 (1) Loat Proof (FINISHED) 6.56/2.87 6.56/2.87 6.56/2.87 ### Pre-processing the ITS problem ### 6.56/2.87 6.56/2.87 6.56/2.87 6.56/2.87 Initial linear ITS problem 6.56/2.87 6.56/2.87 Start location: f26 6.56/2.87 6.56/2.87 0: f11 -> f11 : C'=B, D'=B, [ A>=1+B ], cost: 1 6.56/2.87 6.56/2.87 1: f11 -> f11 : C'=B, D'=B, [ B>=1+A ], cost: 1 6.56/2.87 6.56/2.87 2: f6 -> f6 : F'=free, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_2, L'=free_1, M'=-1+H, [ E>=1+F && G>=0 && H>=1 ], cost: 1 6.56/2.87 6.56/2.87 3: f6 -> f6 : F'=free_3, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_5, L'=free_4, M'=-1+H, [ F>=1+E && G>=0 && H>=1 ], cost: 1 6.56/2.87 6.56/2.87 6: f6 -> f11 : B'=free_28, C'=free_28, D'=free_28, E'=F, E1'=free_30, N'=free_31, Z'=free_29, [ A>=1+free_28 && G>=0 && H>=1 && F==E ], cost: 1 6.56/2.87 6.56/2.87 7: f6 -> f11 : B'=free_32, C'=free_32, D'=free_32, E'=F, E1'=free_34, N'=free_35, Z'=free_33, [ free_32>=1+A && G>=0 && H>=1 && F==E ], cost: 1 6.56/2.87 6.56/2.87 4: f26 -> f6 : A1'=free_6, B1'=free_15, C1'=free_11, D1'=4, F'=free_7, G'=1, H'=4, Q'=1, J'=4, N'=free_13, O'=2, P'=3, Q_1'=free_9, R'=free_12, S'=4, T'=free_8, U'=0, V'=free_14, W'=free_10, X'=free_10, Y'=free_10, Z'=free_10, [ E>=1+free_16 ], cost: 1 6.56/2.87 6.56/2.87 5: f26 -> f6 : A1'=free_17, B1'=free_26, C1'=free_22, D1'=4, F'=free_18, G'=1, H'=4, Q'=1, J'=4, N'=free_24, O'=2, P'=3, Q_1'=free_20, R'=free_23, S'=4, T'=free_19, U'=0, V'=free_25, W'=free_21, X'=free_21, Y'=free_21, Z'=free_21, [ free_27>=1+E ], cost: 1 6.56/2.87 6.56/2.87 6.56/2.87 6.56/2.87 Simplified all rules, resulting in: 6.56/2.87 6.56/2.87 Start location: f26 6.56/2.87 6.56/2.87 0: f11 -> f11 : C'=B, D'=B, [ A>=1+B ], cost: 1 6.56/2.87 6.56/2.87 1: f11 -> f11 : C'=B, D'=B, [ B>=1+A ], cost: 1 6.56/2.87 6.56/2.87 2: f6 -> f6 : F'=free, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_2, L'=free_1, M'=-1+H, [ E>=1+F && G>=0 && H>=1 ], cost: 1 6.56/2.87 6.56/2.87 3: f6 -> f6 : F'=free_3, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_5, L'=free_4, M'=-1+H, [ F>=1+E && G>=0 && H>=1 ], cost: 1 6.56/2.87 6.56/2.87 6: f6 -> f11 : B'=free_28, C'=free_28, D'=free_28, E'=F, E1'=free_30, N'=free_31, Z'=free_29, [ A>=1+free_28 && G>=0 && H>=1 && F==E ], cost: 1 6.56/2.87 6.56/2.87 7: f6 -> f11 : B'=free_32, C'=free_32, D'=free_32, E'=F, E1'=free_34, N'=free_35, Z'=free_33, [ free_32>=1+A && G>=0 && H>=1 && F==E ], cost: 1 6.56/2.87 6.56/2.87 4: f26 -> f6 : A1'=free_6, B1'=free_15, C1'=free_11, D1'=4, F'=free_7, G'=1, H'=4, Q'=1, J'=4, N'=free_13, O'=2, P'=3, Q_1'=free_9, R'=free_12, S'=4, T'=free_8, U'=0, V'=free_14, W'=free_10, X'=free_10, Y'=free_10, Z'=free_10, [], cost: 1 6.56/2.87 6.56/2.87 5: f26 -> f6 : A1'=free_17, B1'=free_26, C1'=free_22, D1'=4, F'=free_18, G'=1, H'=4, Q'=1, J'=4, N'=free_24, O'=2, P'=3, Q_1'=free_20, R'=free_23, S'=4, T'=free_19, U'=0, V'=free_25, W'=free_21, X'=free_21, Y'=free_21, Z'=free_21, [], cost: 1 6.56/2.87 6.56/2.87 6.56/2.87 6.56/2.87 ### Simplification by acceleration and chaining ### 6.56/2.87 6.56/2.87 6.56/2.87 6.56/2.87 Accelerating simple loops of location 0. 6.56/2.87 6.56/2.87 Accelerating the following rules: 6.56/2.87 6.56/2.87 0: f11 -> f11 : C'=B, D'=B, [ A>=1+B ], cost: 1 6.56/2.87 6.56/2.87 1: f11 -> f11 : C'=B, D'=B, [ B>=1+A ], cost: 1 6.56/2.87 6.56/2.87 6.56/2.87 6.56/2.87 Accelerated rule 0 with NONTERM, yielding the new rule 8. 6.56/2.87 6.56/2.87 Accelerated rule 1 with NONTERM, yielding the new rule 9. 6.56/2.87
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