/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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WORST_CASE(?, O(1))
proof of /export/starexec/sandbox/output/output_files/bench.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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:
eval_foo_start(v_.0, v_res, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_res, v_x, v_y)) :|: TRUE
eval_foo_bb0_in(v_.0, v_res, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_y, v_res, v_x, v_y)) :|: TRUE
eval_foo_bb1_in(v_.0, v_res, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_res, v_x, v_y)) :|: v_x > v_.0
eval_foo_bb1_in(v_.0, v_res, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_res, v_x, v_y)) :|: v_x <= v_.0
eval_foo_bb2_in(v_.0, v_res, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x + 1, v_res, v_x, v_y)) :|: TRUE
eval_foo_bb3_in(v_.0, v_res, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_res, v_x, v_y)) :|: TRUE

The start-symbols are:[eval_foo_start_4]


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(1) Koat Proof (FINISHED)
YES(?, 8)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalfoostart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2))

		(Comp: ?, Cost: 1)    evalfoobb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_2))

		(Comp: ?, Cost: 1)    evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_2 + 1, Ar_1, Ar_2))

		(Comp: ?, Cost: 1)    evalfoobb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2)) [ 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)    evalfoostart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2))

		(Comp: 1, Cost: 1)    evalfoobb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_2))

		(Comp: 1, Cost: 1)    evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)    evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ]

		(Comp: 1, Cost: 1)    evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_2 + 1, Ar_1, Ar_2))

		(Comp: 2, Cost: 1)    evalfoobb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 8



Time: 0.026 sec (SMT: 0.024 sec)


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(2)
BOUNDS(1, 1)