/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 1328 ms] (2) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 The start-symbols are:[f19_75] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f19 0: f14 -> f18 : C'=-1+free_1, D'=1, E'=-1, F'=-1+free_1, G'=H, Q'=free, J'=1+H, K'=free_2, L'=free_4, M'=free, [ A>=2 && free_3>=A && B>=0 && C>=1 && free_1>=1 && D==1 ], cost: 1 15: f14 -> f18 : B'=free_48, C'=free_47, D'=0, H'=B, R1'=Q1_1, X1'=B, Y1'=free_48, Z'=free_49, Z1'=free_50, [ free_50>=A && A>=2 && H>=A && 0>=C && H>=0 && Q1_1==R1 && B==H && D==0 ], cost: 1 1: f15 -> f27 : D'=1, H'=G, [ A>=2 && 0>=C && H>=0 && G==H && D==1 ], cost: 1 2: f15 -> f18 : C'=-1+free_6, D'=2, G'=free_5, H'=-1+free_5, M'=free_7, N'=-1, O'=-1+free_6, P'=2, Q_1'=free_9, R'=free_8, S'=free_10, [ A>=2 && C>=1 && free_6>=1 && G>=0 ], cost: 1 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 3: f18 -> f27 : D'=free_12, H'=free_11, T'=free_12, U'=free_11, [ D>=0 && H>=0 && 0>=C ], cost: 1 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 19: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 ], cost: 1 5: f27 -> f18 : A1'=D, B1'=H, C'=free_14, Z'=free_13, [ A>=2 && D>=0 && 0>=Y && H>=0 ], cost: 1 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 6: f1 -> f1 : B'=1+B, D1'=E1, E1'=free_15, F1'=E1, [ B>=0 && C1>=1+B ], cost: 1 16: f1 -> f18 : A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, F1'=free_52, P1'=free_55, Q1_1'=D1, R1'=D1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_59>=A && free_61>=A && B>=C1 && A>=2 && H>=A && H>=0 && B>=0 && D==0 ], cost: 1 7: f10 -> f11 : G1'=free_16, H1'=Q1, J1'=-1+free_16, K1'=-1, [ G1>=0 ], cost: 1 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_19, Q2'=free_18, Q3'=J1, J'=K1, J1'=free_20, J2'=free_22, J3'=free_21, K'=free_23, K1'=free_17, 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 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 10: f11 -> f20 : A'=free_27, 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_25, Q2'=free_28, Q3'=J1, J'=K1, J1'=free_30, J2'=free_29, J3'=free_31, K'=free_24, K1'=free_26, 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 11: f12 -> f13 : H1'=Q1, T1'=free_32, U1'=-1+free_32, V1'=-1, [ T1>=0 ], cost: 1 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_35, Q2'=free_34, Q3'=J1, J'=K1, J1'=free_36, J2'=free_38, J3'=free_37, K'=free_39, K1'=free_33, 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 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 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_42, Q2'=free_41, Q3'=J1, J'=K1, J1'=free_43, J2'=free_45, J3'=free_44, K'=free_46, K1'=free_40, 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 17: f16 -> f16 : A'=1, C'=free_64, D2'=E2, E2'=free_65, F2'=free_65, R1'=Q1_1, Z'=free_63, [ 0>=C && Q1_1==R1 && A==1 ], cost: 1 24: f16 -> f20 : A'=1, A1'=B, A2'=-1+free_110, 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_107, Q2'=free_111, Q3'=J1, J'=K1, J1'=free_114, J2'=free_112, J3'=free_116, K'=free_106, K1'=free_109, K2'=0, K3'=0, 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'=free_115, O2'=F2, P'=G2, P1'=H2, P2'=Q2, Q_1'=J2, Q1_1'=K2, Q2_1'=L2, R'=M2, R1'=N2, R2'=O2, S'=-1, S1'=-1+free_110, S2'=free_105, T'=free_108, T1'=free_113, T2'=free_115, U'=V2, U1'=W2, [ C>=1 && free_110>=2 && Q1_1==0 && R1==0 && A==1 ], cost: 1 25: f16 -> f20 : A'=1, A1'=B, A2'=0, 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_122, Q2'=free_119, Q3'=J1, J'=K1, J1'=free_123, J2'=free_125, J3'=free_124, K'=free_127, K1'=free_118, K2'=0, K3'=0, 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'=free_121, O2'=F2, P'=G2, P1'=H2, P2'=Q2, Q_1'=J2, Q1_1'=K2, Q2_1'=L2, R'=M2, R1'=N2, R2'=O2, S'=-1, S1'=0, S2'=free_126, T'=free_117, T1'=T2, T2'=U2, U'=free_120, U1'=free_121, [ C>=1 && Q1_1==0 && R1==0 && A==1 ], cost: 1 21: f19 -> f1 : A'=free_71, A2'=E1, B'=2, C1'=free_71, D1'=E1, E1'=free_72, E2'=free_74, F1'=E1, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ free_71>=2 && E1==A2 ], cost: 1 22: f19 -> f16 : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 ], cost: 1 23: f19 -> f20 : A'=free_96, A1'=free_93, 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'=free_97, G2'=A1, G3'=B1, H'=free_101, H1'=free_98, H2'=free_104, H3'=free_91, Q'=G1, Q1'=free_95, Q2'=free_103, Q3'=J1, J'=K1, J1'=free_90, J2'=free_94, J3'=free_100, K'=free_99, K1'=free_102, K2'=0, K3'=0, L'=S1, L1'=T1, L2'=U1, L3'=V1, M'=W1, M1'=X1, M2'=Y1, M3'=Z1, N'=free_89, N1'=free_92, 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, [ 0>=free_96 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 21: f19 -> f1 : A'=free_71, A2'=E1, B'=2, C1'=free_71, D1'=E1, E1'=free_72, E2'=free_74, F1'=E1, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ free_71>=2 && E1==A2 ], cost: 1 Removed unreachable and leaf rules: Start location: f19 3: f18 -> f27 : D'=free_12, H'=free_11, T'=free_12, U'=free_11, [ D>=0 && H>=0 && 0>=C ], cost: 1 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 19: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 ], cost: 1 5: f27 -> f18 : A1'=D, B1'=H, C'=free_14, Z'=free_13, [ A>=2 && D>=0 && 0>=Y && H>=0 ], cost: 1 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 6: f1 -> f1 : B'=1+B, D1'=E1, E1'=free_15, F1'=E1, [ B>=0 && C1>=1+B ], cost: 1 16: f1 -> f18 : A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, F1'=free_52, P1'=free_55, Q1_1'=D1, R1'=D1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_59>=A && free_61>=A && B>=C1 && A>=2 && H>=A && H>=0 && B>=0 && D==0 ], cost: 1 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 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 17: f16 -> f16 : A'=1, C'=free_64, D2'=E2, E2'=free_65, F2'=free_65, R1'=Q1_1, Z'=free_63, [ 0>=C && Q1_1==R1 && A==1 ], cost: 1 21: f19 -> f1 : A'=free_71, A2'=E1, B'=2, C1'=free_71, D1'=E1, E1'=free_72, E2'=free_74, F1'=E1, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ free_71>=2 && E1==A2 ], cost: 1 22: f19 -> f16 : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 ], cost: 1 Removed unreachable and leaf rules: Start location: f19 3: f18 -> f27 : D'=free_12, H'=free_11, T'=free_12, U'=free_11, [ D>=0 && H>=0 && 0>=C ], cost: 1 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 19: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 ], cost: 1 5: f27 -> f18 : A1'=D, B1'=H, C'=free_14, Z'=free_13, [ A>=2 && D>=0 && 0>=Y && H>=0 ], cost: 1 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 6: f1 -> f1 : B'=1+B, D1'=E1, E1'=free_15, F1'=E1, [ B>=0 && C1>=1+B ], cost: 1 16: f1 -> f18 : A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, F1'=free_52, P1'=free_55, Q1_1'=D1, R1'=D1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_59>=A && free_61>=A && B>=C1 && A>=2 && H>=A && H>=0 && B>=0 && D==0 ], cost: 1 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 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 17: f16 -> f16 : A'=1, C'=free_64, D2'=E2, E2'=free_65, F2'=free_65, R1'=Q1_1, Z'=free_63, [ 0>=C && Q1_1==R1 && A==1 ], cost: 1 21: f19 -> f1 : A'=free_71, A2'=E1, B'=2, C1'=free_71, D1'=E1, E1'=free_72, E2'=free_74, F1'=E1, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ free_71>=2 && E1==A2 ], cost: 1 22: f19 -> f16 : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 ], cost: 1 Simplified all rules, resulting in: Start location: f19 3: f18 -> f27 : D'=free_12, H'=free_11, T'=free_12, U'=free_11, [ D>=0 && H>=0 && 0>=C ], cost: 1 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 19: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 ], cost: 1 5: f27 -> f18 : A1'=D, B1'=H, C'=free_14, Z'=free_13, [ A>=2 && D>=0 && 0>=Y && H>=0 ], cost: 1 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 6: f1 -> f1 : B'=1+B, D1'=E1, E1'=free_15, F1'=E1, [ B>=0 && C1>=1+B ], cost: 1 16: f1 -> f18 : A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, F1'=free_52, P1'=free_55, Q1_1'=D1, R1'=D1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_61>=A && B>=C1 && A>=2 && H>=A && B>=0 && D==0 ], cost: 1 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 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 17: f16 -> f16 : A'=1, C'=free_64, D2'=E2, E2'=free_65, F2'=free_65, R1'=Q1_1, Z'=free_63, [ 0>=C && Q1_1==R1 && A==1 ], cost: 1 21: f19 -> f1 : A'=free_71, A2'=E1, B'=2, C1'=free_71, D1'=E1, E1'=free_72, E2'=free_74, F1'=E1, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ free_71>=2 && E1==A2 ], cost: 1 22: f19 -> f16 : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 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 Accelerated rule 4 with metering function C-V, yielding the new rule 26. Removing the simple loops: 4. Accelerating simple loops of location 4. Accelerating the following rules: 6: f1 -> f1 : B'=1+B, D1'=E1, E1'=free_15, F1'=E1, [ B>=0 && C1>=1+B ], cost: 1 Accelerated rule 6 with metering function C1-B, yielding the new rule 27. Removing the simple loops: 6. Accelerating simple loops of location 6. Accelerating the following rules: 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 Accelerated rule 9 with metering function 1+J1, yielding the new rule 28. Removing the simple loops: 9. Accelerating simple loops of location 8. Accelerating the following rules: 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 Accelerated rule 13 with metering function 1+U1, yielding the new rule 29. Removing the simple loops: 13. Accelerating simple loops of location 9. Accelerating the following rules: 17: f16 -> f16 : A'=1, C'=free_64, D2'=E2, E2'=free_65, F2'=free_65, R1'=Q1_1, Z'=free_63, [ 0>=C && Q1_1==R1 && A==1 ], cost: 1 Accelerated rule 17 with NONTERM (after strengthening guard), yielding the new rule 30. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: f19 3: f18 -> f27 : D'=free_12, H'=free_11, T'=free_12, U'=free_11, [ D>=0 && H>=0 && 0>=C ], cost: 1 19: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 ], cost: 1 26: f18 -> f18 : C'=V, D'=D+C-V, H'=H-C+V, W'=D+C-V, X'=H-C+V, [ A>=2 && D>=0 && V>=1 && H>=0 && C==V && C-V>=1 ], cost: C-V 5: f27 -> f18 : A1'=D, B1'=H, C'=free_14, Z'=free_13, [ A>=2 && D>=0 && 0>=Y && H>=0 ], cost: 1 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 16: f1 -> f18 : A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, F1'=free_52, P1'=free_55, Q1_1'=D1, R1'=D1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_61>=A && B>=C1 && A>=2 && H>=A && B>=0 && D==0 ], cost: 1 27: f1 -> f1 : B'=C1, D1'=free_15, E1'=free_15, F1'=free_15, [ B>=0 && C1>=1+B ], cost: C1-B 28: f11 -> f11 : H1'=Q1, J1'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, S1'=-1, [ A>=2 && J1>=0 && C>=1 && Q1_1==0 && R1==O1 && N1==0 && M1==O1 && L1==0 ], cost: 1+J1 29: f13 -> f13 : H1'=Q1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, U1'=-1, W1'=-1, [ A>=2 && U1>=0 && 0>=C && Q1_1==0 && R1==O1 && N1==0 && M1==O1 && L1==0 ], cost: 1+U1 17: f16 -> f16 : A'=1, C'=free_64, D2'=E2, E2'=free_65, F2'=free_65, R1'=Q1_1, Z'=free_63, [ 0>=C && Q1_1==R1 && A==1 ], cost: 1 30: f16 -> [16] : [ 0>=C && Q1_1==R1 && A==1 && 0>=free_64 ], cost: NONTERM 21: f19 -> f1 : A'=free_71, A2'=E1, B'=2, C1'=free_71, D1'=E1, E1'=free_72, E2'=free_74, F1'=E1, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ free_71>=2 && E1==A2 ], cost: 1 22: f19 -> f16 : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 ], cost: 1 Chained accelerated rules (with incoming rules): Start location: f19 3: f18 -> f27 : D'=free_12, H'=free_11, T'=free_12, U'=free_11, [ D>=0 && H>=0 && 0>=C ], cost: 1 19: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 ], cost: 1 32: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, J1'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, S1'=-1, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 && J1>=0 ], cost: 2+J1 5: f27 -> f18 : A1'=D, B1'=H, C'=free_14, Z'=free_13, [ A>=2 && D>=0 && 0>=Y && H>=0 ], cost: 1 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 33: 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, U1'=-1, W1'=-1, [ free_69>=0 && A>=2 && 0>=C && D>=0 && H>=0 && Q1_1==0 && U1>=0 ], cost: 2+U1 16: f1 -> f18 : A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, F1'=free_52, P1'=free_55, Q1_1'=D1, R1'=D1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_61>=A && B>=C1 && A>=2 && H>=A && B>=0 && D==0 ], cost: 1 21: f19 -> f1 : A'=free_71, A2'=E1, B'=2, C1'=free_71, D1'=E1, E1'=free_72, E2'=free_74, F1'=E1, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ free_71>=2 && E1==A2 ], cost: 1 22: f19 -> f16 : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 ], cost: 1 31: f19 -> f1 : A'=free_71, A2'=E1, B'=free_71, C1'=free_71, D1'=free_15, E1'=free_15, E2'=free_74, F1'=free_15, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ E1==A2 && free_71>=3 ], cost: -1+free_71 34: f19 -> f16 : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_64, C1'=free_86, D1'=free_83, D2'=free_79, E1'=free_88, E2'=free_65, F1'=free_77, F2'=free_65, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_63, [ E1==A2 ], cost: 2 35: f19 -> [16] : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 && 0>=free_78 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: f19 3: f18 -> f27 : D'=free_12, H'=free_11, T'=free_12, U'=free_11, [ D>=0 && H>=0 && 0>=C ], cost: 1 32: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, J1'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, S1'=-1, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 && J1>=0 ], cost: 2+J1 5: f27 -> f18 : A1'=D, B1'=H, C'=free_14, Z'=free_13, [ A>=2 && D>=0 && 0>=Y && H>=0 ], cost: 1 33: 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, U1'=-1, W1'=-1, [ free_69>=0 && A>=2 && 0>=C && D>=0 && H>=0 && Q1_1==0 && U1>=0 ], cost: 2+U1 16: f1 -> f18 : A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, F1'=free_52, P1'=free_55, Q1_1'=D1, R1'=D1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_61>=A && B>=C1 && A>=2 && H>=A && B>=0 && D==0 ], cost: 1 21: f19 -> f1 : A'=free_71, A2'=E1, B'=2, C1'=free_71, D1'=E1, E1'=free_72, E2'=free_74, F1'=E1, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ free_71>=2 && E1==A2 ], cost: 1 31: f19 -> f1 : A'=free_71, A2'=E1, B'=free_71, C1'=free_71, D1'=free_15, E1'=free_15, E2'=free_74, F1'=free_15, L2'=free_73, M2'=2, N2'=free_75, Z'=free_70, [ E1==A2 && free_71>=3 ], cost: -1+free_71 35: f19 -> [16] : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 && 0>=free_78 ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: f19 32: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, J1'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, S1'=-1, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 && J1>=0 ], cost: 2+J1 38: f18 -> f18 : A1'=free_12, B1'=free_11, C'=free_14, D'=free_12, H'=free_11, T'=free_12, U'=free_11, Z'=free_13, [ D>=0 && H>=0 && 0>=C && A>=2 && free_12>=0 && 0>=Y && free_11>=0 ], cost: 2 39: f18 -> f13 : D'=1+U1, H'=free_11, H1'=R1, Q1'=R1, J2'=free_69, K2'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, [ D>=0 && H>=0 && 0>=C && free_69>=0 && A>=2 && free_12>=0 && free_11>=0 && Q1_1==0 && U1>=0 ], cost: 3+U1 35: f19 -> [16] : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 && 0>=free_78 ], cost: NONTERM 36: f19 -> f18 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=E1, R1'=E1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_71>=2 && E1==A2 && free_61>=free_71 && 2>=free_71 && H>=free_71 && D==0 ], cost: 2 37: f19 -> f18 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=free_15, R1'=free_15, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 ], cost: free_71 Accelerating simple loops of location 2. Accelerating the following rules: 38: f18 -> f18 : A1'=free_12, B1'=free_11, C'=free_14, D'=free_12, H'=free_11, T'=free_12, U'=free_11, Z'=free_13, [ D>=0 && H>=0 && 0>=C && A>=2 && free_12>=0 && 0>=Y && free_11>=0 ], cost: 2 Accelerated rule 38 with NONTERM (after strengthening guard), yielding the new rule 40. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: f19 32: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, J1'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, S1'=-1, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 && J1>=0 ], cost: 2+J1 38: f18 -> f18 : A1'=free_12, B1'=free_11, C'=free_14, D'=free_12, H'=free_11, T'=free_12, U'=free_11, Z'=free_13, [ D>=0 && H>=0 && 0>=C && A>=2 && free_12>=0 && 0>=Y && free_11>=0 ], cost: 2 39: f18 -> f13 : D'=1+U1, H'=free_11, H1'=R1, Q1'=R1, J2'=free_69, K2'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, [ D>=0 && H>=0 && 0>=C && free_69>=0 && A>=2 && free_12>=0 && free_11>=0 && Q1_1==0 && U1>=0 ], cost: 3+U1 40: f18 -> [17] : [ D>=0 && H>=0 && 0>=C && A>=2 && free_12>=0 && 0>=Y && free_11>=0 && 0>=free_14 ], cost: NONTERM 35: f19 -> [16] : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 && 0>=free_78 ], cost: NONTERM 36: f19 -> f18 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=E1, R1'=E1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_71>=2 && E1==A2 && free_61>=free_71 && 2>=free_71 && H>=free_71 && D==0 ], cost: 2 37: f19 -> f18 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=free_15, R1'=free_15, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 ], cost: free_71 Chained accelerated rules (with incoming rules): Start location: f19 32: f18 -> f11 : D'=1+J1, G1'=J1, G2'=free_68, H1'=R1, H2'=-1, Q1'=R1, Q2'=free_67, J1'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, S1'=-1, [ free_68>=0 && free_67>=0 && A>=2 && C>=1 && D>=0 && H>=0 && Q1_1==0 && J1>=0 ], cost: 2+J1 39: f18 -> f13 : D'=1+U1, H'=free_11, H1'=R1, Q1'=R1, J2'=free_69, K2'=-1, L1'=0, M1'=R1, N1'=0, O1'=R1, Q1_1'=0, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, [ D>=0 && H>=0 && 0>=C && free_69>=0 && A>=2 && free_12>=0 && free_11>=0 && Q1_1==0 && U1>=0 ], cost: 3+U1 35: f19 -> [16] : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 && 0>=free_78 ], cost: NONTERM 36: f19 -> f18 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=E1, R1'=E1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_71>=2 && E1==A2 && free_61>=free_71 && 2>=free_71 && H>=free_71 && D==0 ], cost: 2 37: f19 -> f18 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=free_15, R1'=free_15, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 ], cost: free_71 41: f19 -> f18 : A'=2, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=free_12, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=E1, R1'=E1, T'=free_12, U'=free_11, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_61>=2 && H>=2 && D==0 && free_12>=0 && 0>=Y && free_11>=0 ], cost: 4 42: f19 -> f18 : A'=free_71, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=free_12, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=free_15, R1'=free_15, T'=free_12, U'=free_11, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && free_12>=0 && 0>=Y && free_11>=0 ], cost: 2+free_71 43: f19 -> [17] : A'=2, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=E1, R1'=E1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_61>=2 && H>=2 && D==0 && 0>=free_53 && 0>=Y ], cost: NONTERM 44: f19 -> [17] : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=free_15, R1'=free_15, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && 0>=free_53 && 0>=Y ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: f19 35: f19 -> [16] : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 && 0>=free_78 ], cost: NONTERM 43: f19 -> [17] : A'=2, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=E1, R1'=E1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_61>=2 && H>=2 && D==0 && 0>=free_53 && 0>=Y ], cost: NONTERM 44: f19 -> [17] : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=free_15, R1'=free_15, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && 0>=free_53 && 0>=Y ], cost: NONTERM 45: f19 -> f11 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=1+J1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, G1'=J1, G2'=free_68, H1'=E1, H2'=-1, Q1'=E1, Q2'=free_67, J1'=-1, L1'=0, L2'=free_73, M1'=E1, M2'=2, N1'=0, N2'=free_75, O1'=E1, P1'=free_55, Q1_1'=0, R1'=E1, S1'=-1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_71>=2 && E1==A2 && free_61>=free_71 && 2>=free_71 && H>=free_71 && D==0 && free_68>=0 && free_67>=0 && free_53>=1 && H>=0 && E1==0 && J1>=0 ], cost: 4+J1 46: f19 -> f13 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=1+U1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, H1'=E1, Q1'=E1, J2'=free_69, K2'=-1, L1'=0, L2'=free_73, M1'=E1, M2'=2, N1'=0, N2'=free_75, O1'=E1, P1'=free_55, Q1_1'=0, R1'=E1, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_71>=2 && E1==A2 && free_61>=free_71 && 2>=free_71 && H>=free_71 && D==0 && H>=0 && 0>=free_53 && free_69>=0 && free_12>=0 && free_11>=0 && E1==0 && U1>=0 ], cost: 5+U1 47: f19 -> f11 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=1+J1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, G1'=J1, G2'=free_68, H1'=free_15, H2'=-1, Q1'=free_15, Q2'=free_67, J1'=-1, L1'=0, L2'=free_73, M1'=free_15, M2'=2, N1'=0, N2'=free_75, O1'=free_15, P1'=free_55, Q1_1'=0, R1'=free_15, S1'=-1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && free_68>=0 && free_67>=0 && free_53>=1 && H>=0 && free_15==0 && J1>=0 ], cost: 2+free_71+J1 48: f19 -> f13 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=1+U1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, H1'=free_15, Q1'=free_15, J2'=free_69, K2'=-1, L1'=0, L2'=free_73, M1'=free_15, M2'=2, N1'=0, N2'=free_75, O1'=free_15, P1'=free_55, Q1_1'=0, R1'=free_15, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && 0>=free_53 && free_69>=0 && free_12>=0 && free_11>=0 && free_15==0 && U1>=0 ], cost: 3+U1+free_71 49: f19 -> f11 : A'=2, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=1+J1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, G1'=J1, G2'=free_68, H'=free_11, H1'=E1, H2'=-1, Q1'=E1, Q2'=free_67, J1'=-1, L1'=0, L2'=free_73, M1'=E1, M2'=2, N1'=0, N2'=free_75, O1'=E1, P1'=free_55, Q1_1'=0, R1'=E1, S1'=-1, T'=free_12, U'=free_11, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_61>=2 && H>=2 && D==0 && free_12>=0 && 0>=Y && free_11>=0 && free_68>=0 && free_67>=0 && free_14>=1 && E1==0 && J1>=0 ], cost: 6+J1 50: f19 -> f13 : A'=2, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=1+U1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, H1'=E1, Q1'=E1, J2'=free_69, K2'=-1, L1'=0, L2'=free_73, M1'=E1, M2'=2, N1'=0, N2'=free_75, O1'=E1, P1'=free_55, Q1_1'=0, R1'=E1, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_61>=2 && H>=2 && D==0 && free_12>=0 && 0>=Y && free_11>=0 && 0>=free_14 && free_69>=0 && E1==0 && U1>=0 ], cost: 7+U1 51: f19 -> f11 : A'=free_71, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=1+J1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, G1'=J1, G2'=free_68, H'=free_11, H1'=free_15, H2'=-1, Q1'=free_15, Q2'=free_67, J1'=-1, L1'=0, L2'=free_73, M1'=free_15, M2'=2, N1'=0, N2'=free_75, O1'=free_15, P1'=free_55, Q1_1'=0, R1'=free_15, S1'=-1, T'=free_12, U'=free_11, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && free_12>=0 && 0>=Y && free_11>=0 && free_68>=0 && free_67>=0 && free_14>=1 && free_15==0 && J1>=0 ], cost: 4+free_71+J1 52: f19 -> f13 : A'=free_71, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=1+U1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, H1'=free_15, Q1'=free_15, J2'=free_69, K2'=-1, L1'=0, L2'=free_73, M1'=free_15, M2'=2, N1'=0, N2'=free_75, O1'=free_15, P1'=free_55, Q1_1'=0, R1'=free_15, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && free_12>=0 && 0>=Y && free_11>=0 && 0>=free_14 && free_69>=0 && free_15==0 && U1>=0 ], cost: 5+U1+free_71 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f19 35: f19 -> [16] : A'=1, A2'=free_87, B'=free_81, B2'=free_76, C'=free_78, C1'=free_86, D1'=free_83, E1'=free_88, E2'=free_79, F1'=free_77, F2'=free_79, L2'=free_85, O2'=free_84, P1'=free_80, Q1_1'=E1, R1'=E1, Z'=free_82, [ E1==A2 && 0>=free_78 ], cost: NONTERM 43: f19 -> [17] : A'=2, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=E1, R1'=E1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_61>=2 && H>=2 && D==0 && 0>=free_53 && 0>=Y ], cost: NONTERM 44: f19 -> [17] : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=0, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, L2'=free_73, M2'=2, N2'=free_75, P1'=free_55, Q1_1'=free_15, R1'=free_15, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && 0>=free_53 && 0>=Y ], cost: NONTERM 45: f19 -> f11 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=1+J1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, G1'=J1, G2'=free_68, H1'=E1, H2'=-1, Q1'=E1, Q2'=free_67, J1'=-1, L1'=0, L2'=free_73, M1'=E1, M2'=2, N1'=0, N2'=free_75, O1'=E1, P1'=free_55, Q1_1'=0, R1'=E1, S1'=-1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_71>=2 && E1==A2 && free_61>=free_71 && 2>=free_71 && H>=free_71 && D==0 && free_68>=0 && free_67>=0 && free_53>=1 && H>=0 && E1==0 && J1>=0 ], cost: 4+J1 46: f19 -> f13 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=1+U1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, H1'=E1, Q1'=E1, J2'=free_69, K2'=-1, L1'=0, L2'=free_73, M1'=E1, M2'=2, N1'=0, N2'=free_75, O1'=E1, P1'=free_55, Q1_1'=0, R1'=E1, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ free_71>=2 && E1==A2 && free_61>=free_71 && 2>=free_71 && H>=free_71 && D==0 && H>=0 && 0>=free_53 && free_69>=0 && free_12>=0 && free_11>=0 && E1==0 && U1>=0 ], cost: 5+U1 47: f19 -> f11 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=1+J1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, G1'=J1, G2'=free_68, H1'=free_15, H2'=-1, Q1'=free_15, Q2'=free_67, J1'=-1, L1'=0, L2'=free_73, M1'=free_15, M2'=2, N1'=0, N2'=free_75, O1'=free_15, P1'=free_55, Q1_1'=0, R1'=free_15, S1'=-1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && free_68>=0 && free_67>=0 && free_53>=1 && H>=0 && free_15==0 && J1>=0 ], cost: 2+free_71+J1 48: f19 -> f13 : A'=free_71, A2'=free_51, B'=free_56, B2'=free_54, C'=free_53, C1'=free_60, C2'=H, D'=1+U1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, H1'=free_15, Q1'=free_15, J2'=free_69, K2'=-1, L1'=0, L2'=free_73, M1'=free_15, M2'=2, N1'=0, N2'=free_75, O1'=free_15, P1'=free_55, Q1_1'=0, R1'=free_15, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, Y1'=free_56, Z'=free_57, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && 0>=free_53 && free_69>=0 && free_12>=0 && free_11>=0 && free_15==0 && U1>=0 ], cost: 3+U1+free_71 49: f19 -> f11 : A'=2, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=1+J1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, G1'=J1, G2'=free_68, H'=free_11, H1'=E1, H2'=-1, Q1'=E1, Q2'=free_67, J1'=-1, L1'=0, L2'=free_73, M1'=E1, M2'=2, N1'=0, N2'=free_75, O1'=E1, P1'=free_55, Q1_1'=0, R1'=E1, S1'=-1, T'=free_12, U'=free_11, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_61>=2 && H>=2 && D==0 && free_12>=0 && 0>=Y && free_11>=0 && free_68>=0 && free_67>=0 && free_14>=1 && E1==0 && J1>=0 ], cost: 6+J1 50: f19 -> f13 : A'=2, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=1+U1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, H1'=E1, Q1'=E1, J2'=free_69, K2'=-1, L1'=0, L2'=free_73, M1'=E1, M2'=2, N1'=0, N2'=free_75, O1'=E1, P1'=free_55, Q1_1'=0, R1'=E1, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_61>=2 && H>=2 && D==0 && free_12>=0 && 0>=Y && free_11>=0 && 0>=free_14 && free_69>=0 && E1==0 && U1>=0 ], cost: 7+U1 51: f19 -> f11 : A'=free_71, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=1+J1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, G1'=J1, G2'=free_68, H'=free_11, H1'=free_15, H2'=-1, Q1'=free_15, Q2'=free_67, J1'=-1, L1'=0, L2'=free_73, M1'=free_15, M2'=2, N1'=0, N2'=free_75, O1'=free_15, P1'=free_55, Q1_1'=0, R1'=free_15, S1'=-1, T'=free_12, U'=free_11, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && free_12>=0 && 0>=Y && free_11>=0 && free_68>=0 && free_67>=0 && free_14>=1 && free_15==0 && J1>=0 ], cost: 4+free_71+J1 52: f19 -> f13 : A'=free_71, A1'=free_12, A2'=free_51, B'=free_56, B1'=free_11, B2'=free_54, C'=free_14, C1'=free_60, C2'=H, D'=1+U1, D1'=free_58, E1'=free_62, E2'=free_74, F1'=free_52, H'=free_11, H1'=free_15, Q1'=free_15, J2'=free_69, K2'=-1, L1'=0, L2'=free_73, M1'=free_15, M2'=2, N1'=0, N2'=free_75, O1'=free_15, P1'=free_55, Q1_1'=0, R1'=free_15, T'=free_12, T1'=U1, U'=free_11, U1'=-1, W1'=-1, Y1'=free_56, Z'=free_13, Z1'=free_61, [ E1==A2 && free_71>=3 && free_61>=free_71 && H>=free_71 && D==0 && H>=0 && free_12>=0 && 0>=Y && free_11>=0 && 0>=free_14 && free_69>=0 && free_15==0 && U1>=0 ], cost: 5+U1+free_71 Computing asymptotic complexity for rule 35 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ E1==A2 && 0>=free_78 ] NO ---------------------------------------- (2) BOUNDS(INF, INF)