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Compl Integ Trans Syste 26843 pair #381745312
details
property
value
status
complete
benchmark
reverse_div4.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.42824006081 seconds
cpu usage
5.369063403
max memory
3.50429184E8
stage attributes
key
value
output-size
18712
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).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, 617 ms] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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, F1, G1, H1) -> Com_1(f11(A, 1 + B, D, I1, D, J1, B, I, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: A >= B + 1 && B >= 0 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, D1, E1, F1, G1, H1) -> Com_1(f2(A, B, C, D, E, F, G, H, I, J, I1, J1, J, J1, J, Q, Q, I, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: 0 >= J + 1 && I1 >= 2 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, D1, E1, F1, G1, H1) -> Com_1(f2(A, B, C, D, E, F, G, H, I, J, I1, J1, J, J1, J, Q, Q, I, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: J >= 1 && I1 >= 2 f5(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, F1, G1, H1) -> Com_1(f5(A, B, C, D, E, F, G, H, I, J, 1, I1, J, I1, J, P, Q, R, I, U, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: 0 >= J + 1 f5(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, F1, G1, H1) -> Com_1(f5(A, B, C, D, E, F, G, H, I, J, 1, I1, J, I1, J, P, Q, R, I, U, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: J >= 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, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1) -> Com_1(f11(J1, 2, K1, L1, K1, F, G, H, I, J, J1, L, M, N, O, P, Q, R, S, T, U, I1, K1, M1, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1)) :|: J1 >= 2 f0(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, F1, G1, H1) -> Com_1(f1(K1, M1, L1, U1, T1, F, G, H, I, P1, J1, V1, W1, N, X1, P, Q, R, S, T, U, I1, S1, X, D2, Q1, R1, Y1, Z1, A2, B2, C2, E2, H1)) :|: 0 >= N1 && 0 >= J1 && 0 >= O1 && Y >= 0 && Y <= 0 f0(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, F1, G1, H1) -> Com_1(f5(J1, L1, K1, S1, R1, F, G, H, I, J, 1, T1, J, T1, J, P, Q, R, S, T, U, I1, Q1, X, Y, M1, P1, B1, C1, D1, E1, F1, G1, H1)) :|: 0 >= J + 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, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1) -> Com_1(f5(J1, L1, K1, S1, R1, F, G, H, I, J, 1, T1, J, T1, J, P, Q, R, S, T, U, I1, Q1, X, Y, M1, P1, B1, C1, D1, E1, F1, G1, H1)) :|: J >= 1 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, F1, G1, H1) -> Com_1(f2(J1, L1, K1, S1, R1, F, G, H, I, J, I1, T1, J, T1, J, P, Q, R, S, T, U, V, Q1, X, Y, M1, P1, B1, C1, D1, E1, F1, G1, H1)) :|: U1 >= 2 && H1 >= U1 && V1 >= 2 && H1 >= V1 && B >= A && B >= 0 && I1 >= 2 && 0 >= J + 1 && H1 >= 0 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, F1, G1, H1) -> Com_1(f2(J1, L1, K1, S1, R1, F, G, H, I, J, I1, T1, J, T1, J, P, Q, R, S, T, U, V, Q1, X, Y, M1, P1, B1, C1, D1, E1, F1, G1, H1)) :|: U1 >= 2 && H1 >= U1 && V1 >= 2 && H1 >= V1 && B >= A && B >= 0 && I1 >= 2 && J >= 1 && H1 >= 0 The start-symbols are:[f0_34] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f0 0: f11 -> f11 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1 9: f11 -> f2 : A'=free_62, A1'=free_63, B'=free_56, C'=free_65, D'=free_60, E'=free_58, K'=free_64, L'=free_61, M'=J, N'=free_61, O'=J, W'=free_59, Z'=free_67, [ free_57>=2 && H1>=free_57 && free_66>=2 && H1>=free_66 && B>=A && B>=0 && free_64>=2 && 0>=1+J && H1>=0 ], cost: 1 10: f11 -> f2 : A'=free_74, A1'=free_75, B'=free_68, C'=free_77, D'=free_72, E'=free_70, K'=free_76, L'=free_73, M'=J, N'=free_73, O'=J, W'=free_71, Z'=free_79, [ free_69>=2 && H1>=free_69 && free_78>=2 && H1>=free_78 && B>=A && B>=0 && free_76>=2 && J>=1 && H1>=0 ], cost: 1 1: f2 -> f2 : K'=free_3, L'=free_2, M'=J, N'=free_2, O'=J, P'=Q_1, R'=Q, [ 0>=1+J && free_3>=2 ], cost: 1 2: f2 -> f2 : K'=free_5, L'=free_4, M'=J, N'=free_4, O'=J, P'=Q_1, R'=Q, [ J>=1 && free_5>=2 ], cost: 1 3: f5 -> f5 : K'=1, L'=free_6, M'=J, N'=free_6, O'=J, S'=Q, T'=U, [ 0>=1+J ], cost: 1 4: f5 -> f5 : K'=1, L'=free_7, M'=J, N'=free_7, O'=J, S'=Q, T'=U, [ J>=1 ], cost: 1 5: f0 -> f11 : A'=free_11, B'=2, C'=free_8, D'=free_12, E'=free_8, K'=free_11, V'=free_10, W'=free_8, X'=free_9, [ free_11>=2 ], cost: 1 6: f0 -> f1 : A'=free_26, A1'=free_15, A2'=free_30, B'=free_23, B1'=free_18, B2'=F, C'=G, C1'=H, C2'=Q, D'=free_29, D1'=free_25, D2'=free_21, E'=free_33, E1'=N, E2'=free_27, F'=P, F1'=Q_1, G'=R, G1'=S, H'=T, H1'=U, Q'=free_16, Q1'=free_31, J'=X, J1'=free_24, K'=free_34, K1'=free_28, L'=free_19, L1'=free_22, M'=free_20, M1'=free_17, N'=free_14, N1'=free_35, O'=H1, [ 0>=free_32 && 0>=free_25 && 0>=free_13 && Y==0 ], cost: 1 7: f0 -> f5 : A'=free_41, A1'=free_42, B'=free_36, C'=free_44, D'=free_39, E'=free_37, K'=1, L'=free_43, M'=J, N'=free_43, O'=J, V'=free_40, W'=free_38, Z'=free_45, [ 0>=1+J ], cost: 1 8: f0 -> f5 : A'=free_51, A1'=free_52, B'=free_46, C'=free_54, D'=free_49, E'=free_47, K'=1, L'=free_53, M'=J, N'=free_53, O'=J, V'=free_50, W'=free_48, Z'=free_55, [ J>=1 ], cost: 1 Removed unreachable and leaf rules: Start location: f0 0: f11 -> f11 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, H'=Q, [ A>=1+B && B>=0 ], cost: 1 9: f11 -> f2 : A'=free_62, A1'=free_63, B'=free_56, C'=free_65, D'=free_60, E'=free_58, K'=free_64, L'=free_61, M'=J, N'=free_61, O'=J, W'=free_59, Z'=free_67, [ free_57>=2 && H1>=free_57 && free_66>=2 && H1>=free_66 && B>=A && B>=0 && free_64>=2 && 0>=1+J && H1>=0 ], cost: 1 10: f11 -> f2 : A'=free_74, A1'=free_75, B'=free_68, C'=free_77, D'=free_72, E'=free_70, K'=free_76, L'=free_73, M'=J, N'=free_73, O'=J, W'=free_71, Z'=free_79, [ free_69>=2 && H1>=free_69 && free_78>=2 && H1>=free_78 && B>=A && B>=0 && free_76>=2 && J>=1 && H1>=0 ], cost: 1 1: f2 -> f2 : K'=free_3, L'=free_2, M'=J, N'=free_2, O'=J, P'=Q_1, R'=Q, [ 0>=1+J && free_3>=2 ], cost: 1 2: f2 -> f2 : K'=free_5, L'=free_4, M'=J, N'=free_4, O'=J, P'=Q_1, R'=Q, [ J>=1 && free_5>=2 ], cost: 1 3: f5 -> f5 : K'=1, L'=free_6, M'=J, N'=free_6, O'=J, S'=Q, T'=U, [ 0>=1+J ], cost: 1 4: f5 -> f5 : K'=1, L'=free_7, M'=J, N'=free_7, O'=J, S'=Q, T'=U, [ J>=1 ], cost: 1 5: f0 -> f11 : A'=free_11, B'=2, C'=free_8, D'=free_12, E'=free_8, K'=free_11, V'=free_10, W'=free_8, X'=free_9, [ free_11>=2 ], cost: 1 7: f0 -> f5 : A'=free_41, A1'=free_42, B'=free_36, C'=free_44, D'=free_39, E'=free_37, K'=1, L'=free_43, M'=J, N'=free_43, O'=J, V'=free_40, W'=free_38, Z'=free_45, [ 0>=1+J ], cost: 1 8: f0 -> f5 : A'=free_51, A1'=free_52, B'=free_46, C'=free_54, D'=free_49, E'=free_47, K'=1, L'=free_53, M'=J, N'=free_53, O'=J, V'=free_50, W'=free_48, Z'=free_55, [ J>=1 ], cost: 1
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