details

property	value
status	complete
benchmark	traverse_seg2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n041.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	17.7143 seconds
cpu usage	52.127
user time	50.7617
system time	1.36532
max virtual memory	1.9048176E7
max residence set size	399408.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

51.96/17.65 WORST_CASE(NON_POLY, ?) 51.96/17.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 51.96/17.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 51.96/17.67 51.96/17.67 51.96/17.67 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 51.96/17.67 51.96/17.67 (0) CpxIntTrs 51.96/17.67 (1) Loat Proof [FINISHED, 15.5 s] 51.96/17.67 (2) BOUNDS(INF, INF) 51.96/17.67 51.96/17.67 51.96/17.67 ---------------------------------------- 51.96/17.67 51.96/17.67 (0) 51.96/17.67 Obligation: 51.96/17.67 Complexity Int TRS consisting of the following rules: 51.96/17.67 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, L1, M1, N1) -> Com_1(f9(A, 1 + B, D, O1, D, P1, B, 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)) :|: A >= B + 1 && B >= 0 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, S1, R1, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Q1 >= H + 1 && Q1 >= R1 + 1 && I >= 0 && P1 >= Q1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, S1, R1, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Q1 >= H + 1 && Q1 >= R1 + 1 && I >= 0 && Q1 >= P1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, S1, R1, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Q1 >= H + 1 && R1 >= Q1 + 1 && I >= 0 && P1 >= Q1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, S1, R1, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Q1 >= H + 1 && R1 >= Q1 + 1 && I >= 0 && Q1 >= P1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, S1, R1, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: H >= Q1 + 1 && Q1 >= R1 + 1 && I >= 0 && P1 >= Q1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, S1, R1, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: H >= Q1 + 1 && Q1 >= R1 + 1 && I >= 0 && Q1 >= P1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, S1, R1, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: H >= Q1 + 1 && R1 >= Q1 + 1 && I >= 0 && P1 >= Q1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, S1, R1, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: H >= Q1 + 1 && R1 >= Q1 + 1 && I >= 0 && Q1 >= P1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, O, P, 1 + Q, -(1) + R, S1, H, R1, 1 + Q, -(1) + R, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Q1 >= T1 + 1 && Q1 >= R1 + 1 && Q >= 0 && R >= 0 && P1 >= Q1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, O, P, 1 + Q, -(1) + R, S1, H, R1, 1 + Q, -(1) + R, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Q1 >= T1 + 1 && Q1 >= R1 + 1 && Q >= 0 && R >= 0 && Q1 >= P1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, O, P, 1 + Q, -(1) + R, S1, H, R1, 1 + Q, -(1) + R, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Q1 >= T1 + 1 && R1 >= Q1 + 1 && Q >= 0 && R >= 0 && P1 >= Q1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, O, P, 1 + Q, -(1) + R, S1, H, R1, 1 + Q, -(1) + R, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Q1 >= T1 + 1 && R1 >= Q1 + 1 && Q >= 0 && R >= 0 && Q1 >= P1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, O, P, 1 + Q, -(1) + R, S1, H, R1, 1 + Q, -(1) + R, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: T1 >= Q1 + 1 && Q1 >= R1 + 1 && Q >= 0 && R >= 0 && P1 >= Q1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, O, P, 1 + Q, -(1) + R, S1, H, R1, 1 + Q, -(1) + R, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: T1 >= Q1 + 1 && Q1 >= R1 + 1 && Q >= 0 && R >= 0 && Q1 >= P1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, O, P, 1 + Q, -(1) + R, S1, H, R1, 1 + Q, -(1) + R, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: T1 >= Q1 + 1 && R1 >= Q1 + 1 && Q >= 0 && R >= 0 && P1 >= Q1 + 1 && O1 >= 2 51.96/17.67 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) -> Com_1(f16(A, B, C, D, E, F, G, H, I, O1, L, L, P1, P1, O, P, 1 + Q, -(1) + R, S1, H, R1, 1 + Q, -(1) + R, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: T1 >= Q1 + 1 && R1 >= Q1 + 1 && Q >= 0 && R >= 0 && Q1 >= P1 + 1 && O1 >= 2 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, P1, X, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: S1 >= X + 1 && Y >= 0 && R >= 0 && O1 >= 2 && Z >= P1 + 1 && P1 >= S1 + 1 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, P1, X, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: S1 >= X + 1 && Y >= 0 && R >= 0 && O1 >= 2 && Z >= P1 + 1 && S1 >= P1 + 1 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, P1, X, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: S1 >= X + 1 && Y >= 0 && R >= 0 && O1 >= 2 && P1 >= Z + 1 && P1 >= S1 + 1 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, P1, X, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: S1 >= X + 1 && Y >= 0 && R >= 0 && O1 >= 2 && P1 >= Z + 1 && S1 >= P1 + 1 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, P1, X, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: X >= S1 + 1 && Y >= 0 && R >= 0 && O1 >= 2 && Z >= P1 + 1 && P1 >= S1 + 1 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, P1, X, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: X >= S1 + 1 && Y >= 0 && R >= 0 && O1 >= 2 && Z >= P1 + 1 && S1 >= P1 + 1 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, P1, X, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: X >= S1 + 1 && Y >= 0 && R >= 0 && O1 >= 2 && P1 >= Z + 1 && P1 >= S1 + 1 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, P1, X, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: X >= S1 + 1 && Y >= 0 && R >= 0 && O1 >= 2 && P1 >= Z + 1 && S1 >= P1 + 1 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f18(A, B, C, D, E, F, G, H, I, O1, P1, L, R1, N, O, P, Q, R, S, T, U, V, W, V1, Y, T1, Q1, W1, S1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Y >= 0 && R >= 0 && O1 >= 2 && P1 >= R1 + 1 && U1 >= 1 && Z >= X && Z <= X 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f18(A, B, C, D, E, F, G, H, I, O1, P1, L, R1, N, O, P, Q, R, S, T, U, V, W, V1, Y, T1, Q1, W1, S1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Y >= 0 && R >= 0 && O1 >= 2 && P1 >= R1 + 1 && 0 >= U1 + 1 && Z >= X && Z <= X 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f18(A, B, C, D, E, F, G, H, I, O1, P1, L, R1, N, O, P, Q, R, S, T, U, V, W, V1, Y, T1, Q1, W1, S1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Y >= 0 && R >= 0 && O1 >= 2 && R1 >= P1 + 1 && U1 >= 1 && Z >= X && Z <= X 51.96/17.67 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1) -> Com_1(f18(A, B, C, D, E, F, G, H, I, O1, P1, L, R1, N, O, P, Q, R, S, T, U, V, W, V1, Y, T1, Q1, W1, S1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: Y >= 0 && R >= 0 && O1 >= 2 && R1 >= P1 + 1 && 0 >= U1 + 1 && Z >= X && Z <= X 51.96/17.67 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, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, 0, S1, T, U, V, W, X, Y, Z, P1, X, C1, R - 1 + D1, 0, R - 1 + D1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: R1 >= X + 1 && D1 >= 0 && Q1 >= 0 && O1 >= 2 && Z >= P1 + 1 && P1 >= R1 + 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, 0, S1, T, U, V, W, X, Y, Z, P1, X, C1, R - 1 + D1, 0, R - 1 + D1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: R1 >= X + 1 && D1 >= 0 && Q1 >= 0 && O1 >= 2 && Z >= P1 + 1 && R1 >= P1 + 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, 0, S1, T, U, V, W, X, Y, Z, P1, X, C1, R - 1 + D1, 0, R - 1 + D1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: R1 >= X + 1 && D1 >= 0 && Q1 >= 0 && O1 >= 2 && P1 >= Z + 1 && P1 >= R1 + 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, 0, S1, T, U, V, W, X, Y, Z, P1, X, C1, R - 1 + D1, 0, R - 1 + D1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: R1 >= X + 1 && D1 >= 0 && Q1 >= 0 && O1 >= 2 && P1 >= Z + 1 && R1 >= P1 + 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, 0, S1, T, U, V, W, X, Y, Z, P1, X, C1, R - 1 + D1, 0, R - 1 + D1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: X >= R1 + 1 && D1 >= 0 && Q1 >= 0 && O1 >= 2 && Z >= P1 + 1 && P1 >= R1 + 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, 0, S1, T, U, V, W, X, Y, Z, P1, X, C1, R - 1 + D1, 0, R - 1 + D1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: X >= R1 + 1 && D1 >= 0 && Q1 >= 0 && O1 >= 2 && Z >= P1 + 1 && R1 >= P1 + 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, 0, S1, T, U, V, W, X, Y, Z, P1, X, C1, R - 1 + D1, 0, R - 1 + D1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: X >= R1 + 1 && D1 >= 0 && Q1 >= 0 && O1 >= 2 && P1 >= Z + 1 && P1 >= R1 + 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f7(A, B, C, D, E, F, G, H, I, O1, Z, L, P1, N, O, P, Q, 0, S1, T, U, V, W, X, Y, Z, P1, X, C1, R - 1 + D1, 0, R - 1 + D1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: X >= R1 + 1 && D1 >= 0 && Q1 >= 0 && O1 >= 2 && P1 >= Z + 1 && R1 >= P1 + 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f18(A, B, C, D, E, F, G, H, I, O1, K, L, M, N, O, P, Q, R, S, T, U, V, W, Q1, Y, R1, S1, T1, P1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: D1 >= 0 && R >= 0 && V1 >= 1 && O1 >= 2 && Z >= X && Z <= X 51.96/17.67 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, L1, M1, N1) -> Com_1(f18(A, B, C, D, E, F, G, H, I, O1, K, L, M, N, O, P, Q, R, S, T, U, V, W, Q1, Y, R1, S1, T1, P1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1)) :|: D1 >= 0 && R >= 0 && 0 >= V1 + 1 && O1 >= 2 && Z >= X && Z <= X 51.96/17.67 f17(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) -> Com_1(f9(P1, 2, R1, Q1, R1, F, G, H, I, P1, S1, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, O1, S1, R1, T1, K1, L1, M1, N1)) :|: P1 >= 2 51.96/17.67 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, L1, M1, N1) -> Com_1(f16(P1, Q1, R1, A2, U1, F, G, C, R, O1, K, K, Z1, Z1, O, P, 1, R, B2, T, U, V, W, X, Y, Z, A1, B1, V1, D1, E1, F1, G1, S1, W1, J1, T1, R + 1, C2, N1)) :|: X1 >= O1 && Y1 >= 2 && Q1 >= Y1 && Z1 >= K + 1 && B >= A && B >= 0 && K >= C + 1 && Q1 >= 0 && O1 >= 2 && Q >= 1 && Q <= 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f16(P1, Q1, R1, A2, U1, F, G, C, R, O1, K, K, Z1, Z1, O, P, 1, R, B2, T, U, V, W, X, Y, Z, A1, B1, V1, D1, E1, F1, G1, S1, W1, J1, T1, R + 1, C2, N1)) :|: X1 >= O1 && Y1 >= 2 && Q1 >= Y1 && Z1 >= K + 1 && B >= A && B >= 0 && C >= K + 1 && Q1 >= 0 && O1 >= 2 && Q >= 1 && Q <= 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f16(P1, Q1, R1, A2, U1, F, G, C, R, O1, K, K, Z1, Z1, O, P, 1, R, B2, T, U, V, W, X, Y, Z, A1, B1, V1, D1, E1, F1, G1, S1, W1, J1, T1, R + 1, C2, N1)) :|: X1 >= O1 && Y1 >= 2 && Q1 >= Y1 && K >= Z1 + 1 && B >= A && B >= 0 && K >= C + 1 && Q1 >= 0 && O1 >= 2 && Q >= 1 && Q <= 1 51.96/17.67 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, L1, M1, N1) -> Com_1(f16(P1, Q1, R1, A2, U1, F, G, C, R, O1, K, K, Z1, Z1, O, P, 1, R, B2, T, U, V, W, X, Y, Z, A1, B1, V1, D1, E1, F1, G1, S1, W1, J1, T1, R + 1, C2, N1)) :|: X1 >= O1 && Y1 >= 2 && Q1 >= Y1 && K >= Z1 + 1 && B >= A && B >= 0 && C >= K + 1 && Q1 >= 0 && O1 >= 2 && Q >= 1 && Q <= 1 51.96/17.67 f17(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) -> Com_1(f18(S1, T1, Q1, Z1, A2, F, G, X1, I, P1, K, C2, K, B2, O, P, Q, R, S, T, U, V, W, H2, Y, G2, Y1, I2, W1, D1, E1, F1, O1, R1, U1, J1, V1, L1, M1, N1)) :|: 0 >= D2 && 0 >= E2 && 0 >= P1 && 0 >= F2 51.96/17.67 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, L1, M1, N1) -> Com_1(f18(P1, Q1, R1, A2, U1, F, G, C2, I, O1, C, B2, C, Z1, O, P, Q, R, S, T, U, V, W, G2, Y, Y1, X1, H2, V1, D1, E1, F1, G1, S1, W1, J1, T1, L1, M1, N1)) :|: I2 >= 2 && Q1 >= I2 && D2 >= 2 && Q1 >= D2 && B >= A && B >= 0 && Q1 >= O1 && O1 >= 2 && Q1 >= 0 && C >= K && C <= K 51.96/17.67 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) -> Com_1(f7(A, B, C, D, E, F, G, R1, -(1) + Q, O1, K, S1, M, P1, O, P, 1 + D1, 0, S, T, U, V, W, M, D1, K, M, M, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, 0)) :|: Q1 >= 2 && K >= M + 1 && O1 >= 2 && Q >= 1 && M >= K + 1 && I + 1 >= Q && I + 1 <= Q && R >= 0 && R <= 0 && L >= H && L <= H 51.96/17.67 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) -> Com_1(f7(A, B, C, D, E, F, G, R1, -(1) + Q, O1, K, S1, M, P1, O, P, 1 + D1, 0, S, T, U, V, W, M, D1, K, M, M, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, 0)) :|: Q1 >= 2 && K >= M + 1 && O1 >= 2 && Q >= 1 && I + 1 >= Q && I + 1 <= Q && R >= 0 && R <= 0 && L >= H && L <= H 51.96/17.67 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) -> Com_1(f7(A, B, C, D, E, F, G, R1, -(1) + Q, O1, K, S1, M, P1, O, P, 1 + D1, 0, S, T, U, V, W, M, D1, K, M, M, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, 0)) :|: Q1 >= 2 && M >= K + 1 && O1 >= 2 && Q >= 1 && I + 1 >= Q && I + 1 <= Q && R >= 0 && R <= 0 && L >= H && L <= H 51.96/17.67 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) -> Com_1(f7(A, B, C, D, E, F, G, R1, I, O1, K, S1, M, P1, O, P, -(R) + 1 + D1, R, S, T, U, V, W, M, -(R) + D1, K, M, M, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, 0)) :|: Q1 >= 2 && K >= M + 1 && O1 >= 2 && Q >= 0 && R >= 0 && M >= K + 1 && L >= H && L <= H 51.96/17.67 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) -> Com_1(f7(A, B, C, D, E, F, G, R1, I, O1, K, S1, M, P1, O, P, -(R) + 1 + D1, R, S, T, U, V, W, M, -(R) + D1, K, M, M, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, 0)) :|: Q1 >= 2 && K >= M + 1 && O1 >= 2 && Q >= 0 && R >= 0 && L >= H && L <= H 51.96/17.67 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) -> Com_1(f7(A, B, C, D, E, F, G, R1, I, O1, K, S1, M, P1, O, P, -(R) + 1 + D1, R, S, T, U, V, W, M, -(R) + D1, K, M, M, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, 0)) :|: Q1 >= 2 && M >= K + 1 && O1 >= 2 && Q >= 0 && R >= 0 && L >= H && L <= H 51.96/17.67 f17(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) -> Com_1(f18(P1, Q1, R1, A2, U1, F, G, C2, I, 1, D, B2, D, Z1, O, P, Q, R, S, T, U, V, W, G2, Y, Y1, X1, H2, V1, D1, E1, F1, O1, S1, W1, J1, T1, L1, M1, N1)) :|: TRUE 51.96/17.67 f17(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) -> Com_1(f18(P1, Q1, R1, Z1, A2, F, G, Y1, I, 1, T1, X1, B2, C2, O, P, Q, R, S, T, U, V, W, I2, Y, H2, G2, D2, W1, D1, E1, F1, O1, S1, U1, J1, V1, L1, M1, N1)) :|: 0 >= 1 && T1 >= B2 + 1 51.96/17.67 f17(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) -> Com_1(f18(P1, Q1, R1, Z1, A2, F, G, Y1, I, 1, T1, X1, B2, C2, O, P, Q, R, S, T, U, V, W, I2, Y, H2, G2, D2, W1, D1, E1, F1, O1, S1, U1, J1, V1, L1, M1, N1)) :|: 0 >= 1 && B2 >= T1 + 1 51.96/17.67 51.96/17.67 The start-symbols are:[f17_40] 51.96/17.67 51.96/17.67 51.96/17.67 ---------------------------------------- 51.96/17.67 51.96/17.67 (1) Loat Proof (FINISHED) 51.96/17.67 51.96/17.67 51.96/17.67 ### Pre-processing the ITS problem ### 51.96/17.67 51.96/17.67 51.96/17.67 51.96/17.67 Initial linear ITS problem 51.96/17.67 51.96/17.67 Start location: f17 51.96/17.67 51.96/17.67 0: f9 -> f9 : B'=1+B, C'=D, D'=free_1, E'=D, F'=free, G'=B, [ A>=1+B && B>=0 ], cost: 1 51.96/17.67 51.96/17.67 40: f9 -> f16 : A'=free_220, B'=free_214, C'=free_210, C1'=free_216, D'=free_218, E'=free_223, H'=C, H1'=free_217, Q'=R, Q1'=free_215, J'=free_221, K1'=free_213, L'=K, L1'=1+R, M'=free_224, M1'=free_211, N'=free_224, Q_1'=1, S'=free_219, [ free_212>=free_221 && free_222>=2 && free_214>=free_222 && free_224>=1+K && B>=A && B>=0 && K>=1+C && free_214>=0 && free_221>=2 && Q_1==1 ], cost: 1 51.96/17.67 51.96/17.67 41: f9 -> f16 : A'=free_235, B'=free_229, C'=free_225, C1'=free_231, D'=free_233, E'=free_238, H'=C, H1'=free_232, Q'=R, Q1'=free_230, J'=free_236, K1'=free_228, L'=K, L1'=1+R, M'=free_239, M1'=free_226, N'=free_239, Q_1'=1, S'=free_234, [ free_227>=free_236 && free_237>=2 && free_229>=free_237 && free_239>=1+K && B>=A && B>=0 && C>=1+K && free_229>=0 && free_236>=2 && Q_1==1 ], cost: 1 51.96/17.67 51.96/17.67 42: f9 -> f16 : A'=free_250, B'=free_244, C'=free_240, C1'=free_246, D'=free_248, E'=free_253, H'=C, H1'=free_247, Q'=R, Q1'=free_245, J'=free_251, K1'=free_243, L'=K, L1'=1+R, M'=free_254, M1'=free_241, N'=free_254, Q_1'=1, S'=free_249, [ free_242>=free_251 && free_252>=2 && free_244>=free_252 && K>=1+free_254 && B>=A && B>=0 && K>=1+C && free_244>=0 && free_251>=2 && Q_1==1 ], cost: 1 51.96/17.67 51.96/17.67 43: f9 -> f16 : A'=free_265, B'=free_259, C'=free_255, C1'=free_261, D'=free_263, E'=free_268, H'=C, H1'=free_262, Q'=R, Q1'=free_260, J'=free_266, K1'=free_258, L'=K, L1'=1+R, M'=free_269, M1'=free_256, N'=free_269, Q_1'=1, S'=free_264, [ free_257>=free_266 && free_267>=2 && free_259>=free_267 && K>=1+free_269 && B>=A && B>=0 && C>=1+K && free_259>=0 && free_266>=2 && Q_1==1 ], cost: 1 51.96/17.67 51.96/17.67 45: f9 -> f18 : A'=free_302, A1'=free_296, A2'=free_292, B'=free_300, B1'=free_308, B2'=F, C'=G, C1'=free_304, C2'=Q, D'=free_309, D1'=C, D2'=free_301, E'=C, E1'=free_298, E2'=O, F'=P, F1'=Q_1, F2'=R, G'=S, G1'=T, G2'=U, H'=V, H1'=W, H2'=free_299, Q'=Y, Q1'=free_297, Q2'=free_295, J'=free_293, J1'=free_294, K'=D1, K1'=E1, L'=F1, L1'=G1, M'=free_306, M1'=free_307, N'=J1, N1'=free_305, O'=L1, O1'=M1, P'=N1, [ free_303>=2 && free_296>=free_303 && free_291>=2 && free_296>=free_291 && B>=A && B>=0 && free_296>=free_309 && free_309>=2 && free_296>=0 && C==K ], cost: 1 popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Complexity_ITS 2019-03-21 04.46