2.07/1.18	WORST_CASE(?, O(1))
2.20/1.19	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.20/1.19	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.20/1.19	
2.20/1.19	
2.20/1.19	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
2.20/1.19	
2.20/1.19	(0) CpxIntTrs
2.20/1.19	(1) Koat Proof [FINISHED, 0 ms]
2.20/1.19	(2) BOUNDS(1, 1)
2.20/1.19	
2.20/1.19	
2.20/1.19	----------------------------------------
2.20/1.19	
2.20/1.19	(0)
2.20/1.19	Obligation:
2.20/1.19	Complexity Int TRS consisting of the following rules:
2.20/1.19	eval_relation1_start(v_x, v_y) -> Com_1(eval_relation1_bb0_in(v_x, v_y)) :|: TRUE
2.20/1.19	eval_relation1_bb0_in(v_x, v_y) -> Com_1(eval_relation1_bb1_in(v_x, v_y)) :|: TRUE
2.20/1.19	eval_relation1_bb1_in(v_x, v_y) -> Com_1(eval_relation1_0(v_x, v_y)) :|: TRUE
2.20/1.19	eval_relation1_0(v_x, v_y) -> Com_2(eval_nondet_start(v_x, v_y), eval_relation1_1(v_x, v_y)) :|: TRUE
2.20/1.19	eval_relation1_1(v_x, v_y) -> Com_1(eval_relation1_bb2_in(v_x, v_y)) :|: TRUE
2.20/1.19	eval_relation1_bb2_in(v_x, v_y) -> Com_1(eval_relation1_stop(v_x, v_y)) :|: TRUE
2.20/1.19	
2.20/1.19	The start-symbols are:[eval_relation1_start_2]
2.20/1.19	
2.20/1.19	
2.20/1.19	----------------------------------------
2.20/1.19	
2.20/1.19	(1) Koat Proof (FINISHED)
2.20/1.19	YES(?, 6)
2.20/1.19	
2.20/1.19	
2.20/1.19	
2.20/1.19	Initial complexity problem:
2.20/1.19	
2.20/1.19	1:	T:
2.20/1.19	
2.20/1.19			(Comp: ?, Cost: 1)    evalrelation1start() -> Com_1(evalrelation1bb0in())
2.20/1.19	
2.20/1.19			(Comp: ?, Cost: 1)    evalrelation1bb0in() -> Com_1(evalrelation1bb1in())
2.20/1.19	
2.20/1.19			(Comp: ?, Cost: 1)    evalrelation1bb1in() -> Com_1(evalrelation10())
2.20/1.19	
2.20/1.19			(Comp: ?, Cost: 1)    evalrelation10() -> Com_2(evalnondetstart(), evalrelation11())
2.20/1.19	
2.20/1.19			(Comp: ?, Cost: 1)    evalrelation11() -> Com_1(evalrelation1bb2in())
2.20/1.19	
2.20/1.19			(Comp: ?, Cost: 1)    evalrelation1bb2in() -> Com_1(evalrelation1stop())
2.20/1.19	
2.20/1.19			(Comp: 1, Cost: 0)    koat_start() -> Com_1(evalrelation1start()) [ 0 <= 0 ]
2.20/1.19	
2.20/1.19		start location:	koat_start
2.20/1.19	
2.20/1.19		leaf cost:	0
2.20/1.19	
2.20/1.19	
2.20/1.19	
2.20/1.19	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.20/1.19	
2.20/1.19	2:	T:
2.20/1.19	
2.20/1.19			(Comp: 1, Cost: 1)    evalrelation1start() -> Com_1(evalrelation1bb0in())
2.20/1.19	
2.20/1.19			(Comp: 1, Cost: 1)    evalrelation1bb0in() -> Com_1(evalrelation1bb1in())
2.20/1.19	
2.20/1.19			(Comp: 1, Cost: 1)    evalrelation1bb1in() -> Com_1(evalrelation10())
2.20/1.19	
2.20/1.19			(Comp: 1, Cost: 1)    evalrelation10() -> Com_2(evalnondetstart(), evalrelation11())
2.20/1.19	
2.20/1.19			(Comp: 1, Cost: 1)    evalrelation11() -> Com_1(evalrelation1bb2in())
2.20/1.19	
2.20/1.19			(Comp: 1, Cost: 1)    evalrelation1bb2in() -> Com_1(evalrelation1stop())
2.20/1.19	
2.20/1.19			(Comp: 1, Cost: 0)    koat_start() -> Com_1(evalrelation1start()) [ 0 <= 0 ]
2.20/1.19	
2.20/1.19		start location:	koat_start
2.20/1.19	
2.20/1.19		leaf cost:	0
2.20/1.19	
2.20/1.19	
2.20/1.19	
2.20/1.19	Complexity upper bound 6
2.20/1.19	
2.20/1.19	
2.20/1.19	
2.20/1.19	Time: 0.005 sec (SMT: 0.005 sec)
2.20/1.19	
2.20/1.19	
2.20/1.19	----------------------------------------
2.20/1.19	
2.20/1.19	(2)
2.20/1.19	BOUNDS(1, 1)
2.21/1.22	EOF