Complexity_ITS 2019-03-21 04.46 pair #429990056

details
property	value
status	complete
benchmark	queens.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	T2
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.53315 seconds
cpu usage	6.50545
user time	6.08169
system time	0.423751
max virtual memory	1.875468E7
max residence set size	245568.0
stage attributes
key	value
starexec-result	WORST_CASE(?, O(1))
output
6.17/2.48	WORST_CASE(?, O(1))
6.17/2.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.17/2.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.17/2.49	
6.17/2.49	
6.17/2.49	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
6.17/2.49	
6.17/2.49	(0) CpxIntTrs
6.17/2.49	(1) Koat Proof [FINISHED, 784 ms]
6.17/2.49	(2) BOUNDS(1, 1)
6.17/2.49	
6.17/2.49	
6.17/2.49	----------------------------------------
6.17/2.49	
6.17/2.49	(0)
6.17/2.49	Obligation:
6.17/2.49	Complexity Int TRS consisting of the following rules:
6.17/2.49	f30(A, B, C, D, E, F, G, H, I, J) -> Com_1(f31(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= A + 1
6.17/2.49	f30(A, B, C, D, E, F, G, H, I, J) -> Com_1(f31(A, B, C, D, E, F, G, H, I, J)) :|: A >= 1
6.17/2.49	f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= A + 1
6.17/2.49	f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J)) :|: A >= 1
6.17/2.49	f37(A, B, C, D, E, F, G, H, I, J) -> Com_1(f38(A, B, C, D, E, F, G, H, I, J)) :|: B + K >= C + L + 1
6.17/2.49	f37(A, B, C, D, E, F, G, H, I, J) -> Com_1(f38(A, B, C, D, E, F, G, H, I, J)) :|: C + K >= 1 + B + L
6.17/2.49	f0(A, B, C, D, E, F, G, H, I, J) -> Com_1(f10(1, B, 0, 9, 1, K, G, H, I, J)) :|: TRUE
6.17/2.49	f10(A, B, C, D, E, F, G, H, I, J) -> Com_1(f10(A, B, C + 1, D, E, F, G, H, I, J)) :|: D >= C + 1
6.17/2.49	f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f19(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= E + 1 && D >= C + 1
6.17/2.49	f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f19(A, B, C, D, E, F, G, H, I, J)) :|: E >= 1 && D >= C + 1
6.17/2.49	f19(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, 0, C, D, 1, F, 1, H, I, J)) :|: D >= K + 1
6.17/2.49	f19(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, 0, C, D, 0, F, 0, H, I, J)) :|: TRUE
6.17/2.49	f19(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, 0, C, D, 0, F, 0, H, I, J)) :|: 0 >= K + 1
6.17/2.49	f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, 0, C, D, 0, F, 0, H, I, J)) :|: D >= C + 1 && E >= 0 && E <= 0
6.17/2.49	f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f30(A, B, C, D, E, F, G, H, I, J)) :|: D >= B + 1 && B >= C + 1
6.17/2.49	f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f30(A, B, C, D, E, F, G, H, I, J)) :|: C >= 1 + B && D >= B + 1
6.17/2.49	f31(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(1, B, C, D, E, F, G, 1, I, J)) :|: K >= L + 1
6.17/2.49	f31(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(1, B, C, D, E, F, G, 1, I, J)) :|: TRUE
6.17/2.49	f31(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(0, B, C, D, E, F, G, 0, I, J)) :|: TRUE
6.17/2.49	f30(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(0, B, C, D, E, F, G, 0, I, J)) :|: A >= 0 && A <= 0
6.17/2.49	f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, C + 1, C, D, E, F, G, H, I, J)) :|: D >= B + 1 && C >= B && C <= B
6.17/2.49	f38(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(1, B + 1, C, D, E, F, G, H, 1, J)) :|: B + K >= C + L + 1
6.17/2.49	f38(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(1, B + 1, C, D, E, F, G, H, 1, J)) :|: C + K >= 1 + B + L
6.17/2.49	f38(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(0, B + 1, C, D, E, F, G, H, 0, J)) :|: TRUE
6.17/2.49	f37(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(0, B + 1, C, D, E, F, G, H, 0, J)) :|: TRUE
6.17/2.49	f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(0, B + 1, C, D, E, F, G, H, 0, J)) :|: A >= 0 && A <= 0
6.17/2.49	f49(A, B, C, D, E, F, G, H, I, J) -> Com_1(f56(A, B, C, D, E, F, G, H, I, 0)) :|: 0 >= A + 1
6.17/2.49	f49(A, B, C, D, E, F, G, H, I, J) -> Com_1(f56(A, B, C, D, E, F, G, H, I, 0)) :|: A >= 1
6.17/2.49	f49(A, B, C, D, E, F, G, H, I, J) -> Com_1(f56(0, B, C, D, E, F, G, H, I, 1)) :|: A >= 0 && A <= 0
6.17/2.49	f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f16(A, B, C + 1, D, E, F, G, H, I, J)) :|: B >= D
6.17/2.49	f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f49(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= E + 1 && C >= D
6.17/2.49	f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f49(A, B, C, D, E, F, G, H, I, J)) :|: E >= 1 && C >= D
6.17/2.49	f16(A, B, C, D, E, F, G, H, I, J) -> Com_1(f56(A, B, C, D, 0, F, G, H, I, 1)) :|: C >= D && E >= 0 && E <= 0
6.17/2.49	f10(A, B, C, D, E, F, G, H, I, J) -> Com_1(f16(A, B, 0, D, E, F, G, H, I, J)) :|: C >= D
6.17/2.49	
6.17/2.49	The start-symbols are:[f0_10]
6.17/2.49	
6.17/2.49	
6.17/2.49	----------------------------------------
6.17/2.49	
6.17/2.49	(1) Koat Proof (FINISHED)
6.17/2.49	YES(?, 76754)
6.17/2.49	
6.17/2.49	
6.17/2.49	
6.17/2.49	Initial complexity problem:
6.17/2.49	
6.17/2.49	1:	T:
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f38(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_1 + k >= ar_2 + l + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f38(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 + k >= ar_1 + l + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f10(1, ar_1, 0, 9, 1, k, ar_6, ar_7, ar_8, ar_9))
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_2 + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_4 + 1 /\ ar_3 >= ar_2 + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= 1 /\ ar_3 >= ar_2 + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, 0, ar_2, ar_3, 1, ar_5, 1, ar_7, ar_8, ar_9)) [ ar_3 >= k + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, 0, ar_2, ar_3, 0, ar_5, 0, ar_7, ar_8, ar_9))
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, 0, ar_2, ar_3, 0, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= k + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, 0, ar_2, ar_3, 0, ar_5, 0, ar_7, ar_8, ar_9)) [ ar_3 >= ar_2 + 1 /\ ar_4 = 0 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_1 + 1 /\ ar_1 >= ar_2 + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f30(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 + 1 /\ ar_3 >= ar_1 + 1 ]
6.17/2.49	
6.17/2.49			(Comp: ?, Cost: 1)    f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f36(1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, 1, ar_8, ar_9)) [ k >= l + 1 ]
6.17/2.49
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