/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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:
eval_relation1_start(v_x, v_y) -> Com_1(eval_relation1_bb0_in(v_x, v_y)) :|: TRUE
eval_relation1_bb0_in(v_x, v_y) -> Com_1(eval_relation1_0(v_x, v_y)) :|: TRUE
eval_relation1_0(v_x, v_y) -> Com_1(eval_relation1_1(v_x, v_y)) :|: TRUE
eval_relation1_1(v_x, v_y) -> Com_1(eval_relation1_2(v_x, v_y)) :|: TRUE
eval_relation1_2(v_x, v_y) -> Com_1(eval_relation1_3(v_x, v_y)) :|: TRUE
eval_relation1_3(v_x, v_y) -> Com_1(eval_relation1_4(v_x, v_y)) :|: TRUE
eval_relation1_4(v_x, v_y) -> Com_1(eval_relation1_5(v_x, v_y)) :|: TRUE
eval_relation1_5(v_x, v_y) -> Com_1(eval_relation1_bb1_in(v_x, v_y)) :|: TRUE
eval_relation1_bb1_in(v_x, v_y) -> Com_1(eval_relation1_6(v_x, v_y)) :|: TRUE
eval_relation1_6(v_x, v_y) -> Com_1(eval_relation1_7(v_x, v_y)) :|: TRUE
eval_relation1_7(v_x, v_y) -> Com_1(eval_relation1_bb2_in(v_x, v_y)) :|: TRUE
eval_relation1_bb2_in(v_x, v_y) -> Com_1(eval_relation1_stop(v_x, v_y)) :|: TRUE

The start-symbols are:[eval_relation1_start_2]


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(1) Koat Proof (FINISHED)
YES(?, 12)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalrelation1start() -> Com_1(evalrelation1bb0in())

		(Comp: ?, Cost: 1)    evalrelation1bb0in() -> Com_1(evalrelation10())

		(Comp: ?, Cost: 1)    evalrelation10() -> Com_1(evalrelation11())

		(Comp: ?, Cost: 1)    evalrelation11() -> Com_1(evalrelation12())

		(Comp: ?, Cost: 1)    evalrelation12() -> Com_1(evalrelation13())

		(Comp: ?, Cost: 1)    evalrelation13() -> Com_1(evalrelation14())

		(Comp: ?, Cost: 1)    evalrelation14() -> Com_1(evalrelation15())

		(Comp: ?, Cost: 1)    evalrelation15() -> Com_1(evalrelation1bb1in())

		(Comp: ?, Cost: 1)    evalrelation1bb1in() -> Com_1(evalrelation16())

		(Comp: ?, Cost: 1)    evalrelation16() -> Com_1(evalrelation17())

		(Comp: ?, Cost: 1)    evalrelation17() -> Com_1(evalrelation1bb2in())

		(Comp: ?, Cost: 1)    evalrelation1bb2in() -> Com_1(evalrelation1stop())

		(Comp: 1, Cost: 0)    koat_start() -> Com_1(evalrelation1start()) [ 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)    evalrelation1start() -> Com_1(evalrelation1bb0in())

		(Comp: 1, Cost: 1)    evalrelation1bb0in() -> Com_1(evalrelation10())

		(Comp: 1, Cost: 1)    evalrelation10() -> Com_1(evalrelation11())

		(Comp: 1, Cost: 1)    evalrelation11() -> Com_1(evalrelation12())

		(Comp: 1, Cost: 1)    evalrelation12() -> Com_1(evalrelation13())

		(Comp: 1, Cost: 1)    evalrelation13() -> Com_1(evalrelation14())

		(Comp: 1, Cost: 1)    evalrelation14() -> Com_1(evalrelation15())

		(Comp: 1, Cost: 1)    evalrelation15() -> Com_1(evalrelation1bb1in())

		(Comp: 1, Cost: 1)    evalrelation1bb1in() -> Com_1(evalrelation16())

		(Comp: 1, Cost: 1)    evalrelation16() -> Com_1(evalrelation17())

		(Comp: 1, Cost: 1)    evalrelation17() -> Com_1(evalrelation1bb2in())

		(Comp: 1, Cost: 1)    evalrelation1bb2in() -> Com_1(evalrelation1stop())

		(Comp: 1, Cost: 0)    koat_start() -> Com_1(evalrelation1start()) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 12



Time: 0.009 sec (SMT: 0.009 sec)


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(2)
BOUNDS(1, 1)