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Complexity_ITS 2019-03-21 04.46 pair #429990898
details
property
value
status
complete
benchmark
slayer-n5-filtered.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)
3.31099 seconds
cpu usage
9.18799
user time
8.75239
system time
0.435605
max virtual memory
1.8811976E7
max residence set size
292536.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
8.92/3.23 WORST_CASE(NON_POLY, ?) 8.92/3.24 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 8.92/3.24 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.92/3.24 8.92/3.24 8.92/3.24 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 8.92/3.24 8.92/3.24 (0) CpxIntTrs 8.92/3.24 (1) Loat Proof [FINISHED, 1282 ms] 8.92/3.24 (2) BOUNDS(INF, INF) 8.92/3.24 8.92/3.24 8.92/3.24 ---------------------------------------- 8.92/3.24 8.92/3.24 (0) 8.92/3.24 Obligation: 8.92/3.24 Complexity Int TRS consisting of the following rules: 8.92/3.24 f14(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f18(A, B, -(1) + Y2, 1, -(1), -(1) + Y2, H, H, Z2, 1 + H, A3, B3, Z2, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: A >= 2 && X2 >= A && B >= 0 && C >= 1 && Y2 >= 1 && D >= 1 && D <= 1 8.92/3.24 f15(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f27(A, B, C, 1, E, F, G, G, 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: A >= 2 && 0 >= C && H >= 0 && G >= H && G <= H && D >= 1 && D <= 1 8.92/3.24 f15(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f18(A, B, -(1) + Y2, 2, E, F, Z2, -(1) + Z2, I, J, K, L, A3, -(1), -(1) + Y2, 2, B3, X2, C3, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: A >= 2 && C >= 1 && Y2 >= 1 && G >= 0 8.92/3.24 f18(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f27(A, B, C, Z2, E, F, G, Y2, I, J, K, L, M, N, O, P, Q, R, S, Z2, Y2, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: D >= 0 && H >= 0 && 0 >= C 8.92/3.24 f18(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f18(A, B, -(1) + C, 1 + D, E, F, G, -(1) + H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 1 + D, -(1) + H, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: A >= 2 && D >= 0 && V >= 1 && H >= 0 && C >= V && C <= V 8.92/3.24 f27(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f18(A, B, Y2, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z2, D, H, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: A >= 2 && D >= 0 && 0 >= Y && H >= 0 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f1(A, 1 + 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, E1, Y2, E1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: B >= 0 && C1 >= B + 1 8.92/3.24 f10(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_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, Y2, I1, I1, -(1) + Y2, -(1), L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: G1 >= 0 8.92/3.24 f10(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f20(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, D3, X2, J1, K1, B3, Y2, Z2, A3, C3, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: G1 >= 0 && L1 >= I1 && L1 <= I1 8.92/3.24 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, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_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, I1, I1, -(1) + J1, K1, 0, R1, 0, R1, P1, 0, R1, -(1) + J1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: A >= 2 && J1 >= 0 && C >= 1 && Q1 >= 0 && Q1 <= 0 && R1 >= O1 && R1 <= O1 && N1 >= 0 && N1 <= 0 && M1 >= O1 && M1 <= O1 && L1 >= 0 && L1 <= 0 8.92/3.24 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, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f20(Y2, 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, E3, C3, J1, K1, X2, Z2, A3, B3, D3, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: J1 >= 0 && L1 >= I1 && L1 <= I1 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_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, I1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, Y2, -(1) + Y2, -(1), W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: T1 >= 0 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f20(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, D3, X2, J1, K1, B3, Y2, Z2, A3, C3, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: T1 >= 0 && L1 >= I1 && L1 <= I1 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_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, I1, I1, J1, K1, 0, R1, 0, R1, P1, 0, R1, S1, T1, -(1) + U1, V1, -(1) + U1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: A >= 2 && U1 >= 0 && 0 >= C && Q1 >= 0 && Q1 <= 0 && R1 >= O1 && R1 <= O1 && N1 >= 0 && N1 <= 0 && M1 >= O1 && M1 <= O1 && L1 >= 0 && L1 <= 0 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f20(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, D3, X2, J1, K1, B3, Y2, Z2, A3, C3, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: U1 >= 0 && L1 >= I1 && L1 <= I1 8.92/3.24 f14(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f18(A, Y2, Z2, 0, E, F, G, B, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, A3, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, Q1, S1, T1, U1, V1, W1, B, Y2, B3, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: B3 >= A && A >= 2 && H >= A && 0 >= C && H >= 0 && Q1 >= R1 && Q1 <= R1 && B >= H && B <= H && D >= 0 && D <= 0 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f18(A, Y2, Z2, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, A3, A1, B1, X2, C3, E3, D3, G1, H1, I1, J1, K1, L1, M1, N1, O1, I3, D1, D1, S1, T1, U1, V1, W1, X1, Y2, B3, G3, H3, H, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: F3 >= A && B3 >= A && B >= C1 && A >= 2 && H >= A && H >= 0 && B >= 0 && D >= 0 && D <= 0 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f16(1, B, Y2, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, A3, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, Q1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, E2, Z2, Z2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: 0 >= C && Q1 >= R1 && Q1 <= R1 && A >= 1 && A <= 1 8.92/3.24 f15(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f11(A, B, C, J1 + 1, E, F, 0, 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, J1, R1, R1, J1, K1, 0, R1, 0, R1, P1, 0, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, Y2, -(1), I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: Y2 >= 0 && A >= 2 && C >= 1 && Q1 >= 0 && Q1 <= 0 && G >= 0 && G <= 0 && D >= 1 && D <= 1 8.92/3.24 f18(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f11(A, B, C, J1 + 1, 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, J1, R1, R1, J1, K1, 0, R1, 0, R1, P1, 0, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, Z2, -(1), Y2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: Z2 >= 0 && Y2 >= 0 && A >= 2 && C >= 1 && D >= 0 && H >= 0 && Q1 >= 0 && Q1 <= 0 8.92/3.24 f27(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f13(A, B, C, U1 + 1, 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, R1, R1, J1, K1, 0, R1, 0, R1, P1, 0, R1, S1, U1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, Y2, -(1), L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: Y2 >= 0 && A >= 2 && 0 >= C && D >= 0 && H >= 0 && Q1 >= 0 && Q1 <= 0 8.92/3.24 f19(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f1(Y2, 2, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, A3, A1, B1, Y2, E1, B3, E1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, E1, B2, C2, D2, Z2, F2, G2, H2, I2, J2, K2, X2, 2, C3, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: Y2 >= 2 && E1 >= A2 && E1 <= A2 8.92/3.24 f19(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f16(1, Y2, Z2, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, B3, A1, B1, X2, C3, E3, D3, G1, H1, I1, J1, K1, L1, M1, N1, O1, F3, E1, E1, S1, T1, U1, V1, W1, X1, Y1, Z1, H3, I3, C2, D2, A3, A3, G2, H2, I2, J2, K2, G3, M2, N2, J3, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: E1 >= A2 && E1 <= A2 8.92/3.24 f19(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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f20(Z2, Y2, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, E3, A1, B1, G3, H3, F3, I3, G1, M3, D3, J1, K1, C3, A3, B3, X2, L3, 0, 0, S1, T1, U1, V1, W1, X1, Y1, Z1, J3, K3, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2)) :|: 0 >= Z2 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f20(1, B, -(1) + Y2, 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, F3, H3, J1, K1, G3, C3, D3, E3, I3, 0, 0, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, Z2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, -(1), -(1) + Y2, A3, B3, X2, Z2, V2, W2)) :|: C >= 1 && Y2 >= 2 && Q1 >= 0 && Q1 <= 0 && R1 >= 0 && R1 <= 0 && A >= 1 && A <= 1 8.92/3.24 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, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2) -> Com_1(f20(1, B, 0, 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, I3, G3, J1, K1, E3, X2, C3, D3, H3, 0, 0, S1, T1, U1, V1, W1, X1, Y1, Z1, A2, B2, C2, D2, Y2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2, -(1), 0, Z2, A3, T2, U2, B3, Y2)) :|: C >= 1 && Q1 >= 0 && Q1 <= 0 && R1 >= 0 && R1 <= 0 && A >= 1 && A <= 1 8.92/3.24 8.92/3.24 The start-symbols are:[f19_75] 8.92/3.24 8.92/3.24 8.92/3.24 ---------------------------------------- 8.92/3.24 8.92/3.24 (1) Loat Proof (FINISHED) 8.92/3.24 8.92/3.24 8.92/3.24 ### Pre-processing the ITS problem ### 8.92/3.24 8.92/3.24 8.92/3.24 8.92/3.24 Initial linear ITS problem 8.92/3.24 8.92/3.24 Start location: f19 8.92/3.24 8.92/3.24 0: f14 -> f18 : C'=-1+free, D'=1, E'=-1, F'=-1+free, G'=H, Q'=free_4, J'=1+H, K'=free_2, L'=free_3, M'=free_4, [ A>=2 && free_1>=A && B>=0 && C>=1 && free>=1 && D==1 ], cost: 1 8.92/3.24 8.92/3.24 15: f14 -> f18 : B'=free_47, C'=free_50, D'=0, H'=B, R1'=Q1_1, X1'=B, Y1'=free_47, Z'=free_48, Z1'=free_49, [ free_49>=A && A>=2 && H>=A && 0>=C && H>=0 && Q1_1==R1 && B==H && D==0 ], cost: 1 8.92/3.24 8.92/3.24 1: f15 -> f27 : D'=1, H'=G, [ A>=2 && 0>=C && H>=0 && G==H && D==1 ], cost: 1 8.92/3.24 8.92/3.24 2: f15 -> f18 : C'=-1+free_5, D'=2, G'=free_10, H'=-1+free_10, M'=free_8, N'=-1, O'=-1+free_5, P'=2, Q_1'=free_9, R'=free_7, S'=free_6, [ A>=2 && C>=1 && free_5>=1 && G>=0 ], cost: 1 8.92/3.24 8.92/3.24 18: f15 -> f11 : D'=1+J1, G'=0, G1'=J1, G2'=free_66, H1'=R1, H2'=-1, Q1'=R1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, [ free_66>=0 && A>=2 && C>=1 && Q1_1==0 && G==0 && D==1 ], cost: 1 8.92/3.24 8.92/3.24 3: f18 -> f27 : D'=free_11, H'=free_12, T'=free_11, U'=free_12, [ D>=0 && H>=0 && 0>=C ], cost: 1 8.92/3.24 8.92/3.24 4: f18 -> f18 : C'=-1+C, D'=1+D, H'=-1+H, W'=1+D, X'=-1+H, [ A>=2 && D>=0 && V>=1 && H>=0 && C==V ], cost: 1 8.92/3.24 8.92/3.24 19: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_67, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_68, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, [ free_67>=0 && free_68>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 ], cost: 1 8.92/3.24 8.92/3.24 5: f27 -> f18 : A1'=D, B1'=H, C'=free_13, Z'=free_14, [ A>=2 && D>=0 && 0>=Y && H>=0 ], cost: 1 8.92/3.24 8.92/3.24 20: f27 -> f13 : D'=1+U1, H1'=R1, Q1'=R1, J2'=free_69, K2'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, T1'=U1, [ free_69>=0 && A>=2 && 0>=C && D>=0 && H>=0 && Q1_1==0 ], cost: 1 8.92/3.24 8.92/3.24 6: f1 -> f1 : B'=1+B, D1'=E1, E1'=free_15, F1'=E1, [ B>=0 && C1>=1+B ], cost: 1 8.92/3.24 8.92/3.24 16: f1 -> f18 : A2'=free_56, B'=free_51, B2'=free_59, C'=free_62, C1'=free_61, C2'=H, D'=0, D1'=free_54, E1'=free_53, F1'=free_55, P1'=free_57, Q1_1'=D1, R1'=D1, Y1'=free_51, Z'=free_58, Z1'=free_52, [ free_60>=A && free_52>=A && B>=C1 && A>=2 && H>=A && H>=0 && B>=0 && D==0 ], cost: 1 8.92/3.24 8.92/3.24 7: f10 -> f11 : G1'=free_16, H1'=Q1, J1'=-1+free_16, K1'=-1, [ G1>=0 ], cost: 1 8.92/3.24 8.92/3.24 8: f10 -> f20 : A1'=B, A2'=C, A3'=D, B'=E, B1'=F, B2'=G, B3'=H, C'=Q, C1'=J, C2'=K, C3'=L, D'=M, D1'=N, D2'=O, D3'=P, E'=Q_1, E1'=R, E2'=S, E3'=T, F'=U, F1'=V, F2'=W, F3'=X, G'=Y, G1'=Z, G2'=A1, G3'=B1, H'=C1, H1'=D1, H2'=E1, H3'=F1, Q'=G1, Q1'=free_17, Q2'=free_23, Q3'=J1, J'=K1, J1'=free_21, J2'=free_22, J3'=free_19, K'=free_18, K1'=free_20, K2'=Q1_1, K3'=R1, L'=S1, L1'=T1, L2'=U1, L3'=V1, M'=W1, M1'=X1, M2'=Y1, M3'=Z1, N'=A2, N1'=B2, N2'=C2, O'=D2, O1'=E2, O2'=F2, P'=G2, P1'=H2, P2'=Q2, Q_1'=J2, Q1_1'=K2, Q2_1'=L2, R'=M2, R1'=N2, R2'=O2, S'=P2, S1'=Q2_1, S2'=R2, T'=S2, T1'=T2, T2'=U2, U'=V2, U1'=W2, [ G1>=0 && L1==Q1 ], cost: 1 8.92/3.24 8.92/3.24 9: f11 -> f11 : H1'=Q1, J1'=-1+J1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, S1'=-1+J1, [ A>=2 && J1>=0 && C>=1 && Q1_1==0 && R1==O1 && N1==0 && M1==O1 && L1==0 ], cost: 1 8.92/3.24 8.92/3.24 10: f11 -> f20 : A'=free_24, A1'=B, A2'=C, A3'=D, B'=E, B1'=F, B2'=G, B3'=H, C'=Q, C1'=J, C2'=K, C3'=L, D'=M, D1'=N, D2'=O, D3'=P, E'=Q_1, E1'=R, E2'=S, E3'=T, F'=U, F1'=V, F2'=W, F3'=X, G'=Y, G1'=Z, G2'=A1, G3'=B1, H'=C1, H1'=D1, H2'=E1, H3'=F1, Q'=G1, Q1'=free_31, Q2'=free_29, Q3'=J1, J'=K1, J1'=free_30, J2'=free_26, J3'=free_25, K'=free_27, K1'=free_28, K2'=Q1_1, K3'=R1, L'=S1, L1'=T1, L2'=U1, L3'=V1, M'=W1, M1'=X1, M2'=Y1, M3'=Z1, N'=A2, N1'=B2, N2'=C2, O'=D2, O1'=E2, O2'=F2, P'=G2, P1'=H2, P2'=Q2, Q_1'=J2, Q1_1'=K2, Q2_1'=L2, R'=M2, R1'=N2, R2'=O2, S'=P2, S1'=Q2_1, S2'=R2, T'=S2, T1'=T2, T2'=U2, U'=V2, U1'=W2, [ J1>=0 && L1==Q1 ], cost: 1 8.92/3.24 8.92/3.24 11: f12 -> f13 : H1'=Q1, T1'=free_32, U1'=-1+free_32, V1'=-1, [ T1>=0 ], cost: 1 8.92/3.24 8.92/3.24 12: f12 -> f20 : A1'=B, A2'=C, A3'=D, B'=E, B1'=F, B2'=G, B3'=H, C'=Q, C1'=J, C2'=K, C3'=L, D'=M, D1'=N, D2'=O, D3'=P, E'=Q_1, E1'=R, E2'=S, E3'=T, F'=U, F1'=V, F2'=W, F3'=X, G'=Y, G1'=Z, G2'=A1, G3'=B1, H'=C1, H1'=D1, H2'=E1, H3'=F1, Q'=G1, Q1'=free_33, Q2'=free_39, Q3'=J1, J'=K1, J1'=free_37, J2'=free_38, J3'=free_35, K'=free_34, K1'=free_36, K2'=Q1_1, K3'=R1, L'=S1, L1'=T1, L2'=U1, L3'=V1, M'=W1, M1'=X1, M2'=Y1, M3'=Z1, N'=A2, N1'=B2, N2'=C2, O'=D2, O1'=E2, O2'=F2, P'=G2, P1'=H2, P2'=Q2, Q_1'=J2, Q1_1'=K2, Q2_1'=L2, R'=M2, R1'=N2, R2'=O2, S'=P2, S1'=Q2_1, S2'=R2, T'=S2, T1'=T2, T2'=U2, U'=V2, U1'=W2, [ T1>=0 && L1==Q1 ], cost: 1 8.92/3.24 8.92/3.24 13: f13 -> f13 : H1'=Q1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, U1'=-1+U1, W1'=-1+U1, [ A>=2 && U1>=0 && 0>=C && Q1_1==0 && R1==O1 && N1==0 && M1==O1 && L1==0 ], cost: 1 8.92/3.24 8.92/3.24 14: f13 -> f20 : A1'=B, A2'=C, A3'=D, B'=E, B1'=F, B2'=G, B3'=H, C'=Q, C1'=J, C2'=K, C3'=L, D'=M, D1'=N, D2'=O, D3'=P, E'=Q_1, E1'=R, E2'=S, E3'=T, F'=U, F1'=V, F2'=W, F3'=X, G'=Y, G1'=Z, G2'=A1, G3'=B1, H'=C1, H1'=D1, H2'=E1, H3'=F1, Q'=G1, Q1'=free_40, Q2'=free_46, Q3'=J1, J'=K1, J1'=free_44, J2'=free_45, J3'=free_42, K'=free_41, K1'=free_43, K2'=Q1_1, K3'=R1, L'=S1, L1'=T1, L2'=U1, L3'=V1, M'=W1, M1'=X1, M2'=Y1, M3'=Z1, N'=A2, N1'=B2, N2'=C2, O'=D2, O1'=E2, O2'=F2, P'=G2, P1'=H2, P2'=Q2, Q_1'=J2, Q1_1'=K2, Q2_1'=L2, R'=M2, R1'=N2, R2'=O2, S'=P2, S1'=Q2_1, S2'=R2, T'=S2, T1'=T2, T2'=U2, U'=V2, U1'=W2, [ U1>=0 && L1==Q1 ], cost: 1 8.92/3.24
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