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


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WORST_CASE(?, O(1))
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 13 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
start(A, B, C, D) -> Com_1(lbl41(E, B, C, D)) :|: A >= B && A <= B && C >= D && C <= D
lbl41(A, B, C, D) -> Com_1(stop(A, B, A, D)) :|: C >= D && C <= D
start0(A, B, C, D) -> Com_1(start(B, B, D, D)) :|: TRUE

The start-symbols are:[start0_4]


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(1) Koat Proof (FINISHED)
YES(?, 3)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3) -> Com_1(lbl41(e, ar_1, ar_2, ar_3)) [ ar_0 = ar_1 /\ ar_2 = ar_3 ]

		(Comp: ?, Cost: 1)    lbl41(ar_0, ar_1, ar_2, ar_3) -> Com_1(stop(ar_0, ar_1, ar_0, ar_3)) [ ar_2 = ar_3 ]

		(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3) -> Com_1(start(ar_1, ar_1, ar_3, ar_3))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 1 produces the following problem:

2:	T:

		(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3) -> Com_1(lbl41(e, ar_1, ar_2, ar_3)) [ ar_0 = ar_1 /\ ar_2 = ar_3 ]

		(Comp: 1, Cost: 1)    lbl41(ar_0, ar_1, ar_2, ar_3) -> Com_1(stop(ar_0, ar_1, ar_0, ar_3)) [ ar_2 = ar_3 ]

		(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3) -> Com_1(start(ar_1, ar_1, ar_3, ar_3))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 3



Time: 0.019 sec (SMT: 0.018 sec)


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(2)
BOUNDS(1, 1)