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


--------------------------------------------------------------------------------


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval(A, B) -> Com_1(eval(B, A)) :|: A >= B + 1
start(A, B) -> Com_1(eval(A, B)) :|: TRUE

The start-symbols are:[start_2]


----------------------------------------

(1) Koat Proof (FINISHED)
YES(?, 2)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    eval(ar_0, ar_1) -> Com_1(eval(ar_1, ar_0)) [ ar_0 >= ar_1 + 1 ]

		(Comp: ?, Cost: 1)    start(ar_0, ar_1) -> Com_1(eval(ar_0, ar_1))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(start(ar_0, ar_1)) [ 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)    eval(ar_0, ar_1) -> Com_1(eval(ar_1, ar_0)) [ ar_0 >= ar_1 + 1 ]

		(Comp: 1, Cost: 1)    start(ar_0, ar_1) -> Com_1(eval(ar_0, ar_1))

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

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 2



Time: 0.009 sec (SMT: 0.009 sec)


----------------------------------------

(2)
BOUNDS(1, 1)