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Compl Integ Trans Syste 26843 pair #381745378
details
property
value
status
complete
benchmark
s1-saved.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n020.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
14.5596499443 seconds
cpu usage
39.34816064
max memory
7.40724736E8
stage attributes
key
value
output-size
97063
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).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, 12.7 s] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f12(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, I1, J1, K1) -> Com_1(f16(A, B, 1, L1, N1, O1, 1 + H, H, P1, H, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: A >= 0 && L1 >= 2 && 0 >= B + 1 && M1 >= L1 && 0 >= N1 + 1 && C >= 1 && C <= 1 f12(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, I1, J1, K1) -> Com_1(f16(A, B, 1, L1, N1, O1, 1 + H, H, P1, H, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: A >= 0 && L1 >= 2 && 0 >= B + 1 && M1 >= L1 && N1 >= 1 && C >= 1 && C <= 1 f12(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, I1, J1, K1) -> Com_1(f16(A, B, 1, L1, N1, O1, 1 + H, H, P1, H, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: A >= 0 && L1 >= 2 && B >= 1 && M1 >= L1 && 0 >= N1 + 1 && C >= 1 && C <= 1 f12(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, I1, J1, K1) -> Com_1(f16(A, B, 1, L1, N1, O1, 1 + H, H, P1, H, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: A >= 0 && L1 >= 2 && B >= 1 && M1 >= L1 && N1 >= 1 && C >= 1 && C <= 1 f13(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, I1, J1, K1) -> Com_1(f16(A, B, C, L1, N1, F, G, H, I, J, O1, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: J >= 0 && L1 >= 2 && 0 >= B + 1 && 0 >= N1 + 1 && 0 >= P1 + 1 f13(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, I1, J1, K1) -> Com_1(f16(A, B, C, L1, N1, F, G, H, I, J, O1, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: J >= 0 && L1 >= 2 && 0 >= B + 1 && 0 >= N1 + 1 && P1 >= 1 f13(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, I1, J1, K1) -> Com_1(f16(A, B, C, L1, N1, F, G, H, I, J, O1, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: J >= 0 && L1 >= 2 && 0 >= B + 1 && N1 >= 1 && 0 >= P1 + 1 f13(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, I1, J1, K1) -> Com_1(f16(A, B, C, L1, N1, F, G, H, I, J, O1, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: J >= 0 && L1 >= 2 && 0 >= B + 1 && N1 >= 1 && P1 >= 1 f13(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, I1, J1, K1) -> Com_1(f16(A, B, C, L1, N1, F, G, H, I, J, O1, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: J >= 0 && L1 >= 2 && B >= 1 && 0 >= N1 + 1 && 0 >= P1 + 1 f13(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, I1, J1, K1) -> Com_1(f16(A, B, C, L1, N1, F, G, H, I, J, O1, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: J >= 0 && L1 >= 2 && B >= 1 && 0 >= N1 + 1 && P1 >= 1 f13(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, I1, J1, K1) -> Com_1(f16(A, B, C, L1, N1, F, G, H, I, J, O1, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: J >= 0 && L1 >= 2 && B >= 1 && N1 >= 1 && 0 >= P1 + 1 f13(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, I1, J1, K1) -> Com_1(f16(A, B, C, L1, N1, F, G, H, I, J, O1, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: J >= 0 && L1 >= 2 && B >= 1 && N1 >= 1 && P1 >= 1 f16(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, I1, J1, K1) -> Com_1(f16(A, B, 1 + C, L1, N1, O1, G, -(1) + H, I, J, K, L, B, P1, 1 + C, -(1) + H, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: C >= 0 && H >= 0 && L1 >= 2 && 0 >= M1 + 1 && 0 >= N1 + 1 && 0 >= P1 + 1 f16(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, I1, J1, K1) -> Com_1(f16(A, B, 1 + C, L1, N1, O1, G, -(1) + H, I, J, K, L, B, P1, 1 + C, -(1) + H, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: C >= 0 && H >= 0 && L1 >= 2 && 0 >= M1 + 1 && 0 >= N1 + 1 && P1 >= 1 f16(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, I1, J1, K1) -> Com_1(f16(A, B, 1 + C, L1, N1, O1, G, -(1) + H, I, J, K, L, B, P1, 1 + C, -(1) + H, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: C >= 0 && H >= 0 && L1 >= 2 && 0 >= M1 + 1 && N1 >= 1 && 0 >= P1 + 1 f16(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, I1, J1, K1) -> Com_1(f16(A, B, 1 + C, L1, N1, O1, G, -(1) + H, I, J, K, L, B, P1, 1 + C, -(1) + H, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: C >= 0 && H >= 0 && L1 >= 2 && 0 >= M1 + 1 && N1 >= 1 && P1 >= 1 f16(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, I1, J1, K1) -> Com_1(f16(A, B, 1 + C, L1, N1, O1, G, -(1) + H, I, J, K, L, B, P1, 1 + C, -(1) + H, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: C >= 0 && H >= 0 && L1 >= 2 && M1 >= 1 && 0 >= N1 + 1 && 0 >= P1 + 1 f16(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, I1, J1, K1) -> Com_1(f16(A, B, 1 + C, L1, N1, O1, G, -(1) + H, I, J, K, L, B, P1, 1 + C, -(1) + H, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: C >= 0 && H >= 0 && L1 >= 2 && M1 >= 1 && 0 >= N1 + 1 && P1 >= 1 f16(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, I1, J1, K1) -> Com_1(f16(A, B, 1 + C, L1, N1, O1, G, -(1) + H, I, J, K, L, B, P1, 1 + C, -(1) + H, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: C >= 0 && H >= 0 && L1 >= 2 && M1 >= 1 && N1 >= 1 && 0 >= P1 + 1 f16(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, I1, J1, K1) -> Com_1(f16(A, B, 1 + C, L1, N1, O1, G, -(1) + H, I, J, K, L, B, P1, 1 + C, -(1) + H, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: C >= 0 && H >= 0 && L1 >= 2 && M1 >= 1 && N1 >= 1 && P1 >= 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, D1, E1, F1, G1, H1, I1, J1, K1) -> Com_1(f1(1 + A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, S, L1, S, N1, A, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: Q >= A + 1 && A >= 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, D1, E1, F1, G1, H1, I1, J1, K1) -> Com_1(f16(H, R, 0, L1, R, F, G, H, I, J, K, L, M, N, O, P, N1, O1, R1, M1, U, V, P1, S1, T1, Q1, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: A >= Q && A >= 0 && L1 >= 2 && 0 >= R + 1 && Q1 >= L1 && H >= L1 && C >= 0 && C <= 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, D1, E1, F1, G1, H1, I1, J1, K1) -> Com_1(f16(H, R, 0, L1, R, F, G, H, I, J, K, L, M, N, O, P, N1, O1, R1, M1, U, V, P1, S1, T1, Q1, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1)) :|: A >= Q && A >= 0 && L1 >= 2 && R >= 1 && Q1 >= L1 && H >= L1 && C >= 0 && C <= 0 f7(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, H1, I1, J1, K1)) :|: O1 >= A1 + 1 && B1 >= 0 && L1 >= 2 && N1 >= O1 + 1 && 0 >= N1 + 1 && C1 >= 0 && C1 <= 0 f7(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, H1, I1, J1, K1)) :|: O1 >= A1 + 1 && B1 >= 0 && L1 >= 2 && N1 >= O1 + 1 && N1 >= 1 && C1 >= 0 && C1 <= 0 f7(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, H1, I1, J1, K1)) :|: O1 >= A1 + 1 && B1 >= 0 && L1 >= 2 && O1 >= N1 + 1 && 0 >= N1 + 1 && C1 >= 0 && C1 <= 0 f7(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, H1, I1, J1, K1)) :|: O1 >= A1 + 1 && B1 >= 0 && L1 >= 2 && O1 >= N1 + 1 && N1 >= 1 && C1 >= 0 && C1 <= 0 f7(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, H1, I1, J1, K1)) :|: A1 >= O1 + 1 && B1 >= 0 && L1 >= 2 && N1 >= O1 + 1 && 0 >= N1 + 1 && C1 >= 0 && C1 <= 0 f7(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, H1, I1, J1, K1)) :|: A1 >= O1 + 1 && B1 >= 0 && L1 >= 2 && N1 >= O1 + 1 && N1 >= 1 && C1 >= 0 && C1 <= 0 f7(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, H1, I1, J1, K1)) :|: A1 >= O1 + 1 && B1 >= 0 && L1 >= 2 && O1 >= N1 + 1 && 0 >= N1 + 1 && C1 >= 0 && C1 <= 0 f7(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, H1, I1, J1, K1)) :|: A1 >= O1 + 1 && B1 >= 0 && L1 >= 2 && O1 >= N1 + 1 && N1 >= 1 && C1 >= 0 && C1 <= 0 f7(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, I1, J1, K1) -> Com_1(f10(A, B, C, L1, S1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, T1, Z, R1, B1, M1, N1, O1, P1, Q1, H1, I1, J1, K1)) :|: B1 >= 0 && 0 >= S1 + 1 && L1 >= 2 && C1 >= A1 && C1 <= A1 f7(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, I1, J1, K1) -> Com_1(f10(A, B, C, L1, S1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, T1, Z, R1, B1, M1, N1, O1, P1, Q1, H1, I1, J1, K1)) :|: B1 >= 0 && S1 >= 1 && L1 >= 2 && C1 >= A1 && C1 <= A1 f8(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, O1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, -(1) + H1, -(1) + H1, J1, K1)) :|: P1 >= A1 + 1 && H1 >= 0 && L1 >= 2 && N1 >= P1 + 1 && 0 >= N1 + 1 && C1 >= 0 && C1 <= 0 f8(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, O1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, -(1) + H1, -(1) + H1, J1, K1)) :|: P1 >= A1 + 1 && H1 >= 0 && L1 >= 2 && N1 >= P1 + 1 && N1 >= 1 && C1 >= 0 && C1 <= 0 f8(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, O1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, -(1) + H1, -(1) + H1, J1, K1)) :|: P1 >= A1 + 1 && H1 >= 0 && L1 >= 2 && P1 >= N1 + 1 && 0 >= N1 + 1 && C1 >= 0 && C1 <= 0 f8(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, O1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, -(1) + H1, -(1) + H1, J1, K1)) :|: P1 >= A1 + 1 && H1 >= 0 && L1 >= 2 && P1 >= N1 + 1 && N1 >= 1 && C1 >= 0 && C1 <= 0 f8(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, O1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, -(1) + H1, -(1) + H1, J1, K1)) :|: A1 >= P1 + 1 && H1 >= 0 && L1 >= 2 && N1 >= P1 + 1 && 0 >= N1 + 1 && C1 >= 0 && C1 <= 0 f8(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, O1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, -(1) + H1, -(1) + H1, J1, K1)) :|: A1 >= P1 + 1 && H1 >= 0 && L1 >= 2 && N1 >= P1 + 1 && N1 >= 1 && C1 >= 0 && C1 <= 0 f8(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, O1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, -(1) + H1, -(1) + H1, J1, K1)) :|: A1 >= P1 + 1 && H1 >= 0 && L1 >= 2 && P1 >= N1 + 1 && 0 >= N1 + 1 && C1 >= 0 && C1 <= 0 f8(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, I1, J1, K1) -> Com_1(f8(A, 0, C, L1, N1, O1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, 0, N1, 0, N1, A1, -(1) + H1, -(1) + H1, J1, K1)) :|: A1 >= P1 + 1 && H1 >= 0 && L1 >= 2 && P1 >= N1 + 1 && N1 >= 1 && C1 >= 0 && C1 <= 0 f8(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, I1, J1, K1) -> Com_1(f10(A, B, C, L1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, S1, Z, R1, B1, M1, N1, O1, P1, T1, H1, I1, J1, K1)) :|: L1 >= 2 && H1 >= 0 && C1 >= A1 && C1 <= A1 f13(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, I1, J1, K1) -> Com_1(f8(A, 0, H1 + 1, L1, E, F, G, H, I, 0, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, E, H1, 0, E, 0, E, E, H1, I1, J1, K1)) :|: N1 >= 2 && E >= 1 && L1 >= 2 && 0 >= E + 1 && B >= 0 && B <= 0 && J >= 0 && J <= 0 && C >= 1 && C <= 1 f13(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, I1, J1, K1) -> Com_1(f8(A, 0, H1 + 1, L1, E, F, G, H, I, 0, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, E, H1, 0, E, 0, E, E, H1, I1, J1, K1)) :|: N1 >= 2 && E >= 1 && L1 >= 2 && B >= 0 && B <= 0 && J >= 0 && J <= 0 && C >= 1 && C <= 1 f13(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, I1, J1, K1) -> Com_1(f8(A, 0, H1 + 1, L1, E, F, G, H, I, 0, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, E, H1, 0, E, 0, E, E, H1, I1, J1, K1)) :|: N1 >= 2 && 0 >= E + 1 && L1 >= 2 && B >= 0 && B <= 0 && J >= 0 && J <= 0 && C >= 1 && C <= 1 f16(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, I1, J1, K1) -> Com_1(f8(A, 0, H1 + 1, L1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, E, H1, 0, E, 0, E, E, H1, I1, J1, K1)) :|: N1 >= 2 && E >= 1 && L1 >= 2 && C >= 0 && H >= 0 && 0 >= E + 1 && B >= 0 && B <= 0 f16(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, I1, J1, K1) -> Com_1(f8(A, 0, H1 + 1, L1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, E, H1, 0, E, 0, E, E, H1, I1, J1, K1)) :|: N1 >= 2 && E >= 1 && L1 >= 2 && C >= 0 && H >= 0 && B >= 0 && B <= 0 f16(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, I1, J1, K1) -> Com_1(f8(A, 0, H1 + 1, L1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, E, H1, 0, E, 0, E, E, H1, I1, J1, K1)) :|: N1 >= 2 && 0 >= E + 1 && L1 >= 2 && C >= 0 && H >= 0 && B >= 0 && B <= 0 f9(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, I1, J1, K1) -> Com_1(f1(2, B, C, L1, E, F, G, H, I, J, K, L, M, N, O, P, L1, O1, P1, O1, U, V, O1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, N1, M1)) :|: L1 >= 2 f9(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, I1, J1, K1) -> Com_1(f10(S1, 0, C, L1, 0, F, G, H, I, J, K, L, M, N, O, P, Q1, X1, A2, Z1, U, V, Y1, B2, C2, Z, R1, B1, M1, N1, O1, P1, D2, H1, I1, T1, K1)) :|: 0 >= U1 && 0 >= V1 && 0 >= L1 && 0 >= W1 The start-symbols are:[f9_37] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f9 0: f12 -> f16 : C'=1, D'=free, E'=free_2, F'=free_1, G'=1+H, Q'=free_3, J'=H, [ A>=0 && free>=2 && 0>=1+B && free_4>=free && 0>=1+free_2 && C==1 ], cost: 1 1: f12 -> f16 : C'=1, D'=free_5, E'=free_7, F'=free_6, G'=1+H, Q'=free_8, J'=H, [ A>=0 && free_5>=2 && 0>=1+B && free_9>=free_5 && free_7>=1 && C==1 ], cost: 1 2: f12 -> f16 : C'=1, D'=free_10, E'=free_12, F'=free_11, G'=1+H, Q'=free_13, J'=H, [ A>=0 && free_10>=2 && B>=1 && free_14>=free_10 && 0>=1+free_12 && C==1 ], cost: 1 3: f12 -> f16 : C'=1, D'=free_15, E'=free_17, F'=free_16, G'=1+H, Q'=free_18, J'=H, [ A>=0 && free_15>=2 && B>=1 && free_19>=free_15 && free_17>=1 && C==1 ], cost: 1 4: f13 -> f16 : D'=free_20, E'=free_22, K'=free_21, L'=free_23, [ J>=0 && free_20>=2 && 0>=1+B && 0>=1+free_22 && 0>=1+free_23 ], cost: 1
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