details

property	value
status	complete
benchmark	traverse.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n127.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	14.5619 seconds
cpu usage	38.4611
user time	37.4994
system time	0.961747
max virtual memory	1.8994336E7
max residence set size	412164.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

38.27/14.51 WORST_CASE(NON_POLY, ?) 38.39/14.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 38.39/14.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 38.39/14.53 38.39/14.53 38.39/14.53 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 38.39/14.53 38.39/14.53 (0) CpxIntTrs 38.39/14.53 (1) Loat Proof [FINISHED, 12.6 s] 38.39/14.53 (2) BOUNDS(INF, INF) 38.39/14.53 38.39/14.53 38.39/14.53 ---------------------------------------- 38.39/14.53 38.39/14.53 (0) 38.39/14.53 Obligation: 38.39/14.53 Complexity Int TRS consisting of the following rules: 38.39/14.53 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) -> Com_1(f14(D, O1, P1, D, 0, M1, Q1, R1, S1, T1, U1, C, C, C, N1, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: A >= B && A >= 0 && M1 >= 2 && 0 >= C + 1 && N1 >= M1 && D >= M1 && E >= 0 && E <= 0 38.39/14.53 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) -> Com_1(f14(D, O1, P1, D, 0, M1, Q1, R1, S1, T1, U1, C, C, C, N1, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: A >= B && A >= 0 && M1 >= 2 && C >= 1 && N1 >= M1 && D >= M1 && E >= 0 && E <= 0 38.39/14.53 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) -> Com_1(f1(1 + A, B, K, D, E, F, G, H, I, K, M1, L, M, N, O, O1, A, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: B >= A + 1 && A >= 0 38.39/14.53 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) -> Com_1(f14(A, B, C, D, 1, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, 1 + D, Q1, D, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: A >= 0 && M1 >= 2 && 0 >= N + 1 && R1 >= M1 && 0 >= O1 + 1 && E >= 1 && E <= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, 1, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, 1 + D, Q1, D, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: A >= 0 && M1 >= 2 && 0 >= N + 1 && R1 >= M1 && O1 >= 1 && E >= 1 && E <= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, 1, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, 1 + D, Q1, D, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: A >= 0 && M1 >= 2 && N >= 1 && R1 >= M1 && 0 >= O1 + 1 && E >= 1 && E <= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, 1, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, 1 + D, Q1, D, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: A >= 0 && M1 >= 2 && N >= 1 && R1 >= M1 && O1 >= 1 && E >= 1 && E <= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, R, S, T, U, P1, Q1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: U >= 0 && M1 >= 2 && 0 >= N + 1 && 0 >= O1 + 1 && 0 >= Q1 + 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, R, S, T, U, P1, Q1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: U >= 0 && M1 >= 2 && 0 >= N + 1 && 0 >= O1 + 1 && Q1 >= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, R, S, T, U, P1, Q1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: U >= 0 && M1 >= 2 && 0 >= N + 1 && O1 >= 1 && 0 >= Q1 + 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, R, S, T, U, P1, Q1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: U >= 0 && M1 >= 2 && 0 >= N + 1 && O1 >= 1 && Q1 >= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, R, S, T, U, P1, Q1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: U >= 0 && M1 >= 2 && N >= 1 && 0 >= O1 + 1 && 0 >= Q1 + 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, R, S, T, U, P1, Q1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: U >= 0 && M1 >= 2 && N >= 1 && 0 >= O1 + 1 && Q1 >= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, R, S, T, U, P1, Q1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: U >= 0 && M1 >= 2 && N >= 1 && O1 >= 1 && 0 >= Q1 + 1 38.39/14.53 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) -> Com_1(f14(A, B, C, D, E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, R, S, T, U, P1, Q1, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: U >= 0 && M1 >= 2 && N >= 1 && O1 >= 1 && Q1 >= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, -(1) + D, 1 + E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, S, T, U, V, W, N, Q1, 1 + E, -(1) + D, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: E >= 0 && D >= 0 && M1 >= 2 && 0 >= R1 + 1 && 0 >= O1 + 1 && 0 >= Q1 + 1 38.39/14.53 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) -> Com_1(f14(A, B, C, -(1) + D, 1 + E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, S, T, U, V, W, N, Q1, 1 + E, -(1) + D, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: E >= 0 && D >= 0 && M1 >= 2 && 0 >= R1 + 1 && 0 >= O1 + 1 && Q1 >= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, -(1) + D, 1 + E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, S, T, U, V, W, N, Q1, 1 + E, -(1) + D, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: E >= 0 && D >= 0 && M1 >= 2 && 0 >= R1 + 1 && O1 >= 1 && 0 >= Q1 + 1 38.39/14.53 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) -> Com_1(f14(A, B, C, -(1) + D, 1 + E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, S, T, U, V, W, N, Q1, 1 + E, -(1) + D, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: E >= 0 && D >= 0 && M1 >= 2 && 0 >= R1 + 1 && O1 >= 1 && Q1 >= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, -(1) + D, 1 + E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, S, T, U, V, W, N, Q1, 1 + E, -(1) + D, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: E >= 0 && D >= 0 && M1 >= 2 && R1 >= 1 && 0 >= O1 + 1 && 0 >= Q1 + 1 38.39/14.53 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) -> Com_1(f14(A, B, C, -(1) + D, 1 + E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, S, T, U, V, W, N, Q1, 1 + E, -(1) + D, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: E >= 0 && D >= 0 && M1 >= 2 && R1 >= 1 && 0 >= O1 + 1 && Q1 >= 1 38.39/14.53 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) -> Com_1(f14(A, B, C, -(1) + D, 1 + E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, S, T, U, V, W, N, Q1, 1 + E, -(1) + D, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: E >= 0 && D >= 0 && M1 >= 2 && R1 >= 1 && O1 >= 1 && 0 >= Q1 + 1 38.39/14.53 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) -> Com_1(f14(A, B, C, -(1) + D, 1 + E, M1, G, H, I, J, K, O1, O1, N, O, P, Q, P1, S, T, U, V, W, N, Q1, 1 + E, -(1) + D, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1)) :|: E >= 0 && D >= 0 && M1 >= 2 && R1 >= 1 && O1 >= 1 && Q1 >= 1 38.39/14.53 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) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, I1, J1, K1, L1)) :|: P1 >= B1 + 1 && C1 >= 0 && M1 >= 2 && O1 >= P1 + 1 && 0 >= O1 + 1 && D1 >= 0 && D1 <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, I1, J1, K1, L1)) :|: P1 >= B1 + 1 && C1 >= 0 && M1 >= 2 && O1 >= P1 + 1 && O1 >= 1 && D1 >= 0 && D1 <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, I1, J1, K1, L1)) :|: P1 >= B1 + 1 && C1 >= 0 && M1 >= 2 && P1 >= O1 + 1 && 0 >= O1 + 1 && D1 >= 0 && D1 <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, I1, J1, K1, L1)) :|: P1 >= B1 + 1 && C1 >= 0 && M1 >= 2 && P1 >= O1 + 1 && O1 >= 1 && D1 >= 0 && D1 <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, I1, J1, K1, L1)) :|: B1 >= P1 + 1 && C1 >= 0 && M1 >= 2 && O1 >= P1 + 1 && 0 >= O1 + 1 && D1 >= 0 && D1 <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, I1, J1, K1, L1)) :|: B1 >= P1 + 1 && C1 >= 0 && M1 >= 2 && O1 >= P1 + 1 && O1 >= 1 && D1 >= 0 && D1 <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, I1, J1, K1, L1)) :|: B1 >= P1 + 1 && C1 >= 0 && M1 >= 2 && P1 >= O1 + 1 && 0 >= O1 + 1 && D1 >= 0 && D1 <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, I1, J1, K1, L1)) :|: B1 >= P1 + 1 && C1 >= 0 && M1 >= 2 && P1 >= O1 + 1 && O1 >= 1 && D1 >= 0 && D1 <= 0 38.39/14.53 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) -> Com_1(f16(A, B, C, D, E, M1, G, O1, I, J, K, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, U1, C1, T1, Q1, R1, S1, N1, I1, J1, K1, L1)) :|: C1 >= 0 && 0 >= P1 + 1 && M1 >= 2 && D1 >= B1 && D1 <= B1 38.39/14.53 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) -> Com_1(f16(A, B, C, D, E, M1, G, O1, I, J, K, P1, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, U1, C1, T1, Q1, R1, S1, N1, I1, J1, K1, L1)) :|: C1 >= 0 && P1 >= 1 && M1 >= 2 && D1 >= B1 && D1 <= B1 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, P1, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, -(1) + I1, -(1) + I1, K1, L1)) :|: Q1 >= B1 + 1 && I1 >= 0 && M1 >= 2 && O1 >= Q1 + 1 && 0 >= O1 + 1 && D1 >= 0 && D1 <= 0 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, P1, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, -(1) + I1, -(1) + I1, K1, L1)) :|: Q1 >= B1 + 1 && I1 >= 0 && M1 >= 2 && O1 >= Q1 + 1 && O1 >= 1 && D1 >= 0 && D1 <= 0 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, P1, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, -(1) + I1, -(1) + I1, K1, L1)) :|: Q1 >= B1 + 1 && I1 >= 0 && M1 >= 2 && Q1 >= O1 + 1 && 0 >= O1 + 1 && D1 >= 0 && D1 <= 0 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, P1, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, -(1) + I1, -(1) + I1, K1, L1)) :|: Q1 >= B1 + 1 && I1 >= 0 && M1 >= 2 && Q1 >= O1 + 1 && O1 >= 1 && D1 >= 0 && D1 <= 0 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, P1, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, -(1) + I1, -(1) + I1, K1, L1)) :|: B1 >= Q1 + 1 && I1 >= 0 && M1 >= 2 && O1 >= Q1 + 1 && 0 >= O1 + 1 && D1 >= 0 && D1 <= 0 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, P1, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, -(1) + I1, -(1) + I1, K1, L1)) :|: B1 >= Q1 + 1 && I1 >= 0 && M1 >= 2 && O1 >= Q1 + 1 && O1 >= 1 && D1 >= 0 && D1 <= 0 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, P1, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, -(1) + I1, -(1) + I1, K1, L1)) :|: B1 >= Q1 + 1 && I1 >= 0 && M1 >= 2 && Q1 >= O1 + 1 && 0 >= O1 + 1 && D1 >= 0 && D1 <= 0 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f8(A, B, C, D, E, M1, G, H, I, J, K, O1, M, N, O, P, Q, P1, S, T, U, V, W, X, Y, Z, A1, B1, C1, 0, O1, 0, O1, B1, -(1) + I1, -(1) + I1, K1, L1)) :|: B1 >= Q1 + 1 && I1 >= 0 && M1 >= 2 && Q1 >= O1 + 1 && O1 >= 1 && D1 >= 0 && D1 <= 0 38.39/14.53 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1) -> Com_1(f16(A, B, C, D, E, M1, G, O1, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, T1, C1, S1, P1, Q1, R1, U1, I1, J1, K1, L1)) :|: M1 >= 2 && I1 >= 0 && D1 >= B1 && D1 <= B1 38.39/14.53 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) -> Com_1(f1(2, O1, P1, D, E, O1, G, H, P1, P1, Q1, 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, M1, R1)) :|: O1 >= 2 38.39/14.53 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) -> Com_1(f16(R1, P1, Q1, D, E, O1, S1, T1, U1, N1, Y1, 0, Z1, A2, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, F2, C1, E2, B2, C2, D2, G2, I1, J1, M1, L1)) :|: 0 >= V1 && 0 >= W1 && 0 >= O1 && 0 >= X1 38.39/14.53 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) -> Com_1(f8(A, B, C, D, I1 + 1, M1, G, H, I, J, K, L, O1, P1, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, L, I1, 0, L, 0, L, L, I1, J1, K1, L1)) :|: Q1 >= 2 && M1 >= 2 && U >= 0 && L >= 1 && 0 >= L + 1 && N >= 0 && N <= 0 && E >= 1 && E <= 1 38.39/14.53 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) -> Com_1(f8(A, B, C, D, I1 + 1, M1, G, H, I, J, K, L, O1, P1, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, L, I1, 0, L, 0, L, L, I1, J1, K1, L1)) :|: Q1 >= 2 && M1 >= 2 && U >= 0 && L >= 1 && N >= 0 && N <= 0 && E >= 1 && E <= 1 38.39/14.53 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) -> Com_1(f8(A, B, C, D, I1 + 1, M1, G, H, I, J, K, L, O1, P1, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, L, I1, 0, L, 0, L, L, I1, J1, K1, L1)) :|: Q1 >= 2 && M1 >= 2 && U >= 0 && 0 >= L + 1 && N >= 0 && N <= 0 && E >= 1 && E <= 1 38.39/14.53 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) -> Com_1(f8(A, B, C, D, I1 + 1, M1, G, H, I, J, K, L, O1, P1, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, L, I1, 0, L, 0, L, L, I1, J1, K1, L1)) :|: Q1 >= 2 && M1 >= 2 && D >= 0 && E >= 0 && L >= 1 && 0 >= L + 1 && N >= 0 && N <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, I1 + 1, M1, G, H, I, J, K, L, O1, P1, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, L, I1, 0, L, 0, L, L, I1, J1, K1, L1)) :|: Q1 >= 2 && M1 >= 2 && D >= 0 && E >= 0 && L >= 1 && N >= 0 && N <= 0 38.39/14.53 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) -> Com_1(f8(A, B, C, D, I1 + 1, M1, G, H, I, J, K, L, O1, P1, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, L, I1, 0, L, 0, L, L, I1, J1, K1, L1)) :|: Q1 >= 2 && M1 >= 2 && D >= 0 && E >= 0 && 0 >= L + 1 && N >= 0 && N <= 0 38.39/14.53 38.39/14.53 The start-symbols are:[f15_38] 38.39/14.53 38.39/14.53 38.39/14.53 ---------------------------------------- 38.39/14.53 38.39/14.53 (1) Loat Proof (FINISHED) 38.39/14.53 38.39/14.53 38.39/14.53 ### Pre-processing the ITS problem ### 38.39/14.53 38.39/14.53 38.39/14.53 38.39/14.53 Initial linear ITS problem 38.39/14.53 38.39/14.53 Start location: f15 38.39/14.53 38.39/14.53 0: f1 -> f14 : A'=D, B'=free, C'=free_5, E'=0, F'=free_7, G'=free_2, H'=free_8, Q'=free_4, J'=free_1, K'=free_6, L'=C, M'=C, N'=C, O'=free_3, [ A>=B && A>=0 && free_7>=2 && 0>=1+C && free_3>=free_7 && D>=free_7 && E==0 ], cost: 1 38.39/14.53 38.39/14.53 1: f1 -> f14 : A'=D, B'=free_9, C'=free_14, E'=0, F'=free_16, G'=free_11, H'=free_17, Q'=free_13, J'=free_10, K'=free_15, L'=C, M'=C, N'=C, O'=free_12, [ A>=B && A>=0 && free_16>=2 && C>=1 && free_12>=free_16 && D>=free_16 && E==0 ], cost: 1 38.39/14.53 38.39/14.53 2: f1 -> f1 : A'=1+A, C'=K, J'=K, K'=free_18, P'=free_19, Q_1'=A, [ B>=1+A && A>=0 ], cost: 1 38.39/14.53 38.39/14.53 3: f10 -> f14 : E'=1, F'=free_20, L'=free_22, M'=free_22, R'=free_23, S'=1+D, T'=free_21, U'=D, [ A>=0 && free_20>=2 && 0>=1+N && free_24>=free_20 && 0>=1+free_22 && E==1 ], cost: 1 38.39/14.53 38.39/14.53 4: f10 -> f14 : E'=1, F'=free_25, L'=free_27, M'=free_27, R'=free_28, S'=1+D, T'=free_26, U'=D, [ A>=0 && free_25>=2 && 0>=1+N && free_29>=free_25 && free_27>=1 && E==1 ], cost: 1 38.39/14.53 38.39/14.53 5: f10 -> f14 : E'=1, F'=free_30, L'=free_32, M'=free_32, R'=free_33, S'=1+D, T'=free_31, U'=D, [ A>=0 && free_30>=2 && N>=1 && free_34>=free_30 && 0>=1+free_32 && E==1 ], cost: 1 38.39/14.53 38.39/14.53 6: f10 -> f14 : E'=1, F'=free_35, L'=free_37, M'=free_37, R'=free_38, S'=1+D, T'=free_36, U'=D, [ A>=0 && free_35>=2 && N>=1 && free_39>=free_35 && free_37>=1 && E==1 ], cost: 1 38.39/14.53 38.39/14.53 7: f11 -> f14 : F'=free_40, L'=free_42, M'=free_42, V'=free_43, W'=free_41, [ U>=0 && free_40>=2 && 0>=1+N && 0>=1+free_42 && 0>=1+free_41 ], cost: 1 38.39/14.53 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