details

property	value
status	complete
benchmark	qrdcmp.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.83336 seconds
cpu usage	16.3762
user time	15.8812
system time	0.495052
max virtual memory	1.8730204E7
max residence set size	247056.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

16.20/7.46 WORST_CASE(Omega(n^1), O(n^1)) 16.20/7.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 16.20/7.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.20/7.48 16.20/7.48 16.20/7.48 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 16.20/7.48 16.20/7.48 (0) CpxIntTrs 16.20/7.48 (1) Koat Proof [FINISHED, 391 ms] 16.20/7.48 (2) BOUNDS(1, n^1) 16.20/7.48 (3) Loat Proof [FINISHED, 5821 ms] 16.20/7.48 (4) BOUNDS(n^1, INF) 16.20/7.48 16.20/7.48 16.20/7.48 ---------------------------------------- 16.20/7.48 16.20/7.48 (0) 16.20/7.48 Obligation: 16.20/7.48 Complexity Int TRS consisting of the following rules: 16.20/7.48 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= 2 16.20/7.48 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= B + 1 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, C, D + 1, C, S, S, H, I, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 + S && A >= D 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, S, D + 1, C, S, S, H, I, J, K, L, M, N, O, P, Q, R)) :|: S >= C && A >= D 16.20/7.48 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D + 1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, 0, 0, J, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, S, T, J + T, K, L, M, N, O, P, Q, R)) :|: 0 >= S + 1 && A >= D 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, S, T, J + T, K, L, M, N, O, P, Q, R)) :|: S >= 1 && A >= D 16.20/7.48 f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= K 16.20/7.48 f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f55(A, B, C, D + 1, E, F, G, H, I, S, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.48 f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f61(A, B, C, D + 1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= D 16.20/7.48 f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K + 1, L, M, N, O, P, Q, R)) :|: D >= 1 + A 16.20/7.48 f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f61(A, B, C, D, E, F, G, H, I, J, K, S, M, N, O, P, Q, R)) :|: D >= 1 + A 16.20/7.48 f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: K >= 1 + A 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K, L, S, T, T, P, Q, R)) :|: D >= 1 + A 16.20/7.48 f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, -(S), T, S, R)) :|: 0 >= U + 1 && D >= 1 + A 16.20/7.48 f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: D >= 1 + A 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B + 1, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, 0)) :|: D >= 1 + A && C >= 0 && C <= 0 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: 0 >= C + 1 && D >= 1 + A 16.20/7.48 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 && D >= 1 + A 16.20/7.48 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f73(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A && 0 >= S + 1 16.20/7.48 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f73(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A 16.20/7.48 16.20/7.48 The start-symbols are:[f0_18] 16.20/7.48 16.20/7.48 16.20/7.48 ---------------------------------------- 16.20/7.48 16.20/7.48 (1) Koat Proof (FINISHED) 16.20/7.48 YES(?, 37*ar_0 + 3*ar_10 + 32*ar_3 + 2*ar_1 + 38) 16.20/7.48 16.20/7.48 16.20/7.48 16.20/7.48 Initial complexity problem: 16.20/7.48 16.20/7.48 1: T: 16.20/7.48 16.20/7.48 (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) -> Com_1(f10(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_0 >= 2 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(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) -> Com_1(f13(ar_0, ar_1, 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_0 >= ar_1 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(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) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_2, s, s, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_2 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(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) -> Com_1(f13(ar_0, ar_1, s, ar_3 + 1, ar_2, s, s, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ s >= ar_2 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(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) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3 + 1, 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_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(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) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, 0, 0, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(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) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, s, t, ar_9 + t, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ 0 >= s + 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(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) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, s, t, ar_9 + t, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ s >= 1 /\ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(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) -> Com_1(f55(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_0 >= ar_10 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(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) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, s, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(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) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, 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_0 >= ar_3 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f61(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) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10 + 1, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f55(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) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, s, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f53(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) -> Com_1(f10(ar_0, ar_1 + 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_10 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(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) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, s, t, t, ar_15, ar_16, ar_17)) [ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f34(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) -> Com_1(f53(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, -s, t, s, ar_17)) [ 0 >= u + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f29(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) -> Com_1(f34(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_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(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) -> Com_1(f10(ar_0, ar_1 + 1, 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, 0)) [ ar_3 >= ar_0 + 1 /\ ar_2 = 0 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(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) -> Com_1(f29(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)) [ 0 >= ar_2 + 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f13(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) -> Com_1(f29(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_2 >= 1 /\ ar_3 >= ar_0 + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(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) -> Com_1(f73(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_1 >= ar_0 /\ 0 >= s + 1 ] 16.20/7.48 16.20/7.48 (Comp: ?, Cost: 1) f10(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) -> Com_1(f73(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_1 >= ar_0 ] 16.20/7.48 popout

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actions

all output return to Complexity_ITS 2019-03-21 04.46