/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?, O(1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 0 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f8(A, B, C) -> Com_1(f12(2, 1, C)) :|: A >= 2 && A <= 2
f8(A, B, C) -> Com_1(f12(A, 0, C)) :|: 1 >= A
f8(A, B, C) -> Com_1(f12(A, 0, C)) :|: A >= 3
f0(A, B, C) -> Com_1(f12(1, 1, 1)) :|: TRUE

The start-symbols are:[f0_3]


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(1) Koat Proof (FINISHED)
YES(?, 1)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f12(2, 1, ar_2)) [ ar_0 = 2 ]

		(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f12(ar_0, 0, ar_2)) [ 1 >= ar_0 ]

		(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f12(ar_0, 0, ar_2)) [ ar_0 >= 3 ]

		(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f12(1, 1, 1))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Testing for reachability in the complexity graph removes the following transitions from problem 1:

	f8(ar_0, ar_1, ar_2) -> Com_1(f12(2, 1, ar_2)) [ ar_0 = 2 ]

	f8(ar_0, ar_1, ar_2) -> Com_1(f12(ar_0, 0, ar_2)) [ 1 >= ar_0 ]

	f8(ar_0, ar_1, ar_2) -> Com_1(f12(ar_0, 0, ar_2)) [ ar_0 >= 3 ]

We thus obtain the following problem:

2:	T:

		(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f12(1, 1, 1))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 2 produces the following problem:

3:	T:

		(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f12(1, 1, 1))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 1



Time: 0.007 sec (SMT: 0.006 sec)


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(2)
BOUNDS(1, 1)