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Complexity_ITS 2019-03-21 04.46 pair #429990512
details
property
value
status
complete
benchmark
fun2.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
61.1995 seconds
cpu usage
124.619
user time
122.789
system time
1.82976
max virtual memory
1.8881428E7
max residence set size
324192.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
124.37/60.72 WORST_CASE(Omega(n^1), O(n^1)) 124.37/60.74 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 124.37/60.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 124.37/60.74 124.37/60.74 124.37/60.74 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 124.37/60.74 124.37/60.74 (0) CpxIntTrs 124.37/60.74 (1) Koat Proof [FINISHED, 1469 ms] 124.37/60.74 (2) BOUNDS(1, n^1) 124.37/60.74 (3) Loat Proof [FINISHED, 59.1 s] 124.37/60.74 (4) BOUNDS(n^1, INF) 124.37/60.74 124.37/60.74 124.37/60.74 ---------------------------------------- 124.37/60.74 124.37/60.74 (0) 124.37/60.74 Obligation: 124.37/60.74 Complexity Int TRS consisting of the following rules: 124.37/60.74 f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N)) :|: TRUE 124.37/60.74 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, 0, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.37/60.74 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, 0, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.37/60.74 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 124.37/60.74 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, 3, P, 0, 0, 3, P, 2, M, N)) :|: 7 >= P && 3 >= P && P >= 1 124.37/60.74 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, 3, P, 0, 0, 3, P, 2, M, N)) :|: 7 >= P && P >= 5 124.37/60.74 f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C + 1, C + 1, E + 1, E + 1, 3, 4, 1, 0, 3, 4, 2, M, N)) :|: TRUE 124.37/60.74 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.37/60.74 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.37/60.74 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 124.37/60.74 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C, C, E, E, P, O, H, 0, P, O, 3, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.37/60.74 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C, C, E, E, P, O, H, 0, P, O, 3, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.37/60.74 f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f3(0, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 0, P, 4, 3, M, N)) :|: 7 >= P && P >= 1 124.37/60.74 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C, C, E, E, P, O, H, 1, P, O, 6, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.37/60.74 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C, C, E, E, P, O, H, 1, P, O, 6, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.37/60.74 f3(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f6(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 6, M, N)) :|: 7 >= P && P >= 1 124.37/60.74 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(P, C, C, E, E, O, 2, 0, P, O, 2, 4, M, N)) :|: 7 >= O && 1 >= P && P >= 0 && O >= 1 124.37/60.74 f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f4(P, C, C, E, E, O, 7, 1, P, O, 7, 4, M, N)) :|: 7 >= O && 1 >= P && P >= 0 && O >= 1 && H >= 1 && H <= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, P, O, 0, 0, P, O, 2, M, N)) :|: M >= 1 && M >= E + 1 && N >= 1 && N >= C + 1 && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H >= 1 && H <= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C, C, E, E, P, O, 0, 0, P, O, 2, M, N)) :|: M >= 1 && M >= E + 1 && N >= 1 && N >= C + 1 && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H >= 1 && H <= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f2(0, C + 1, C + 1, E + 1, E + 1, P, 4, 0, 0, P, 4, 2, M, N)) :|: M >= E + 2 && N >= C + 2 && M >= 1 && N >= 1 && 7 >= P && P >= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C, C, E, E, P, O, H, 0, P, O, 7, M, N)) :|: E >= M && C >= N && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C, C, E, E, P, O, H, 0, P, O, 7, M, N)) :|: E >= M && C >= N && 7 >= O && 7 >= P && O >= 5 && P >= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(0, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 0, P, 4, 7, M, N)) :|: E + 1 >= M && C + 1 >= N && 7 >= P && P >= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C, C, E, E, P, O, H, 1, P, O, 7, M, N)) :|: 7 >= O && 7 >= P && O >= 5 && P >= 1 124.37/60.74 f4(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f7(1, C + 1, C + 1, E + 1, E + 1, P, 4, 1, 1, P, 4, 7, M, N)) :|: 7 >= P && P >= 1 124.37/60.74 124.37/60.74 The start-symbols are:[f8_14] 124.37/60.74 124.37/60.74 124.37/60.74 ---------------------------------------- 124.37/60.74 124.37/60.74 (1) Koat Proof (FINISHED) 124.37/60.74 YES(?, 23*ar_4 + 23*ar_12 + 44*ar_2 + 44*ar_13 + 82) 124.37/60.74 124.37/60.74 124.37/60.74 124.37/60.74 Initial complexity problem: 124.37/60.74 124.37/60.74 1: T: 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f8(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) -> Com_1(f1(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)) 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f1(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) -> Com_1(f7(1, ar_2, ar_2, ar_4, ar_4, p, o, 0, 1, p, o, 7, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f1(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) -> Com_1(f7(1, ar_2, ar_2, ar_4, ar_4, p, o, 0, 1, p, o, 7, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f1(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) -> Com_1(f7(1, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, p, 4, 1, 1, p, 4, 7, ar_12, ar_13)) [ 7 >= p /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f1(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) -> Com_1(f2(0, ar_2, ar_2, ar_4, ar_4, 3, p, 0, 0, 3, p, 2, ar_12, ar_13)) [ 7 >= p /\ 3 >= p /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f1(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) -> Com_1(f2(0, ar_2, ar_2, ar_4, ar_4, 3, p, 0, 0, 3, p, 2, ar_12, ar_13)) [ 7 >= p /\ p >= 5 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f1(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) -> Com_1(f2(0, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, 3, 4, 1, 0, 3, 4, 2, ar_12, ar_13)) 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f2(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) -> Com_1(f7(1, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 1, p, o, 7, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f2(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) -> Com_1(f7(1, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 1, p, o, 7, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f2(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) -> Com_1(f7(1, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, p, 4, 1, 1, p, 4, 7, ar_12, ar_13)) [ 7 >= p /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f2(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) -> Com_1(f3(0, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 0, p, o, 3, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f2(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) -> Com_1(f3(0, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 0, p, o, 3, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f2(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) -> Com_1(f3(0, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, p, 4, 1, 0, p, 4, 3, ar_12, ar_13)) [ 7 >= p /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f3(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) -> Com_1(f6(1, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 1, p, o, 6, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f3(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) -> Com_1(f6(1, ar_2, ar_2, ar_4, ar_4, p, o, ar_7, 1, p, o, 6, ar_12, ar_13)) [ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f3(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) -> Com_1(f6(1, ar_2 + 1, ar_2 + 1, ar_4 + 1, ar_4 + 1, p, 4, 1, 1, p, 4, 6, ar_12, ar_13)) [ 7 >= p /\ p >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f6(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) -> Com_1(f4(p, ar_2, ar_2, ar_4, ar_4, o, 2, 0, p, o, 2, 4, ar_12, ar_13)) [ 7 >= o /\ 1 >= p /\ p >= 0 /\ o >= 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f6(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) -> Com_1(f4(p, ar_2, ar_2, ar_4, ar_4, o, 7, 1, p, o, 7, 4, ar_12, ar_13)) [ 7 >= o /\ 1 >= p /\ p >= 0 /\ o >= 1 /\ ar_7 = 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f4(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) -> Com_1(f2(0, ar_2, ar_2, ar_4, ar_4, p, o, 0, 0, p, o, 2, ar_12, ar_13)) [ ar_12 >= 1 /\ ar_12 >= ar_4 + 1 /\ ar_13 >= 1 /\ ar_13 >= ar_2 + 1 /\ 7 >= o /\ 7 >= p /\ 3 >= o /\ o >= 1 /\ p >= 1 /\ ar_7 = 1 ] 124.37/60.74 124.37/60.74 (Comp: ?, Cost: 1) f4(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) -> Com_1(f2(0, ar_2, ar_2, ar_4, ar_4, p, o, 0, 0, p, o, 2, ar_12, ar_13)) [ ar_12 >= 1 /\ ar_12 >= ar_4 + 1 /\ ar_13 >= 1 /\ ar_13 >= ar_2 + 1 /\ 7 >= o /\ 7 >= p /\ o >= 5 /\ p >= 1 /\ ar_7 = 1 ]
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