details

property	value
status	complete
benchmark	ex22.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.20752 seconds
cpu usage	15.6345
user time	15.0244
system time	0.610124
max virtual memory	1.9248684E7
max residence set size	536904.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

15.44/6.14 WORST_CASE(?, O(1)) 15.44/6.16 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 15.44/6.16 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.44/6.16 15.44/6.16 15.44/6.16 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 15.44/6.16 15.44/6.16 (0) CpxIntTrs 15.44/6.16 (1) Koat Proof [FINISHED, 4405 ms] 15.44/6.16 (2) BOUNDS(1, 1) 15.44/6.16 15.44/6.16 15.44/6.16 ---------------------------------------- 15.44/6.16 15.44/6.16 (0) 15.44/6.16 Obligation: 15.44/6.16 Complexity Int TRS consisting of the following rules: 15.44/6.16 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f17(100, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f17(100, 10, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 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) -> Com_1(f20(A, B, B, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: 0 >= B + 1 15.44/6.16 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) -> Com_1(f20(A, B, B, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: B >= 1 15.44/6.16 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) -> Com_1(f45(A, 0, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: B >= 0 && B <= 0 15.44/6.16 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) -> Com_1(f26(A, B, C, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 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) -> Com_1(f26(A, B, C, 10, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f45(A, B, C, 0, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: D >= 0 && D <= 0 15.44/6.16 f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f29(A, B, C, D, D, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: 0 >= D + 1 15.44/6.16 f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f29(A, B, C, D, D, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: D >= 1 15.44/6.16 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f57(A, B, C, D, E, F, 200, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f57(A, B, C, D, E, F, 200, 10, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f57(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f60(A, B, C, D, E, F, G, H, H, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: 0 >= H + 1 15.44/6.16 f57(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f60(A, B, C, D, E, F, G, H, H, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: H >= 1 15.44/6.16 f57(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f85(A, B, C, D, E, F, G, 0, 0, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: H >= 0 && H <= 0 15.44/6.16 f60(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f66(A, B, C, D, E, F, G, H, I, 0, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f60(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f66(A, B, C, D, E, F, G, H, I, 10, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f66(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f85(A, B, C, D, E, F, G, H, I, 0, 0, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: J >= 0 && J <= 0 15.44/6.16 f66(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, J, 0, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: 0 >= J + 1 15.44/6.16 f66(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, J, 0, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: J >= 1 15.44/6.16 f85(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f97(A, B, C, D, E, F, G, H, I, J, K, L, 50, 0, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f85(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f97(A, B, C, D, E, F, G, H, I, J, K, L, 50, 10, O, P, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f97(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f100(A, B, C, D, E, F, G, H, I, J, K, L, M, N, N, P, Q, R, S, T, U, V, W, X)) :|: 0 >= N + 1 15.44/6.16 f97(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f100(A, B, C, D, E, F, G, H, I, J, K, L, M, N, N, P, Q, R, S, T, U, V, W, X)) :|: N >= 1 15.44/6.16 f97(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f125(A, B, C, D, E, F, G, H, I, J, K, L, M, 0, 0, P, Q, R, S, T, U, V, W, X)) :|: N >= 0 && N <= 0 15.44/6.16 f100(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f106(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, 0, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f100(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f106(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, 10, Q, R, S, T, U, V, W, X)) :|: TRUE 15.44/6.16 f106(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f125(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, 0, 0, R, S, T, U, V, W, X)) :|: P >= 0 && P <= 0 15.44/6.16 f106(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f109(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, P, 0, S, T, U, V, W, X)) :|: 0 >= P + 1 15.44/6.16 f106(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f109(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, P, 0, S, T, U, V, W, X)) :|: P >= 1 15.44/6.16 f125(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, 20, 0, U, V, W, X)) :|: TRUE 15.44/6.16 f125(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, 20, 10, U, V, W, X)) :|: TRUE 15.44/6.16 f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f140(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, T, V, W, X)) :|: 0 >= T + 1 15.44/6.16 f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f140(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, T, V, W, X)) :|: T >= 1 15.44/6.16 f140(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f146(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, 0, W, X)) :|: TRUE 15.44/6.16 f140(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f146(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, 10, W, X)) :|: TRUE 15.44/6.16 f146(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f149(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, V, 0)) :|: 0 >= V + 1 15.44/6.16 f146(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f149(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, V, 0)) :|: V >= 1 15.44/6.16 f137(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f166(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, 0, 0, V, W, X)) :|: T >= 0 && T <= 0 15.44/6.16 f146(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f166(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, 0, 0, X)) :|: V >= 0 && V <= 0 15.44/6.16 f149(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f149(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X + 1)) :|: S >= X + 1 15.44/6.16 f149(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f166(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: X >= S 15.44/6.16 f109(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f109(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R + 1, S, T, U, V, W, X)) :|: M >= R + 1 15.44/6.16 f109(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f125(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: R >= M 15.44/6.16 f69(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, K, L + 1, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: G >= L + 1 15.44/6.16 f69(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f85(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: L >= G 15.44/6.16 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f29(A, B, C, D, E, F + 1, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: A >= F + 1 15.44/6.16 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) -> Com_1(f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X)) :|: F >= A 15.44/6.16 15.44/6.16 The start-symbols are:[f0_24] 15.44/6.16 15.44/6.16 15.44/6.16 ---------------------------------------- 15.44/6.16 15.44/6.16 (1) Koat Proof (FINISHED) 15.44/6.16 YES(?, 18136) 15.44/6.16 15.44/6.16 15.44/6.16 15.44/6.16 Initial complexity problem: 15.44/6.16 15.44/6.16 1: T: 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f17(100, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f17(100, 10, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f20(ar_0, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) [ 0 >= ar_1 + 1 ] 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f20(ar_0, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) [ ar_1 >= 1 ] 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f45(ar_0, 0, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) [ ar_1 = 0 ] 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f26(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f26(ar_0, ar_1, ar_2, 10, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f45(ar_0, ar_1, ar_2, 0, 0, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) [ ar_3 = 0 ] 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_3, 0, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) [ 0 >= ar_3 + 1 ] 15.44/6.16 15.44/6.16 (Comp: ?, Cost: 1) f26(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_3, 0, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23)) [ ar_3 >= 1 ] 15.44/6.16 popout

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all output return to Complexity_ITS 2019-03-21 04.46