2.16/1.36	WORST_CASE(?, O(1))
2.16/1.38	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.16/1.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.16/1.38	
2.16/1.38	
2.16/1.38	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
2.16/1.38	
2.16/1.38	(0) CpxIntTrs
2.16/1.38	(1) Koat Proof [FINISHED, 73 ms]
2.16/1.38	(2) BOUNDS(1, 1)
2.16/1.38	
2.16/1.38	
2.16/1.38	----------------------------------------
2.16/1.38	
2.16/1.38	(0)
2.16/1.38	Obligation:
2.16/1.38	Complexity Int TRS consisting of the following rules:
2.16/1.38	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
2.16/1.38	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
2.16/1.38	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
2.16/1.38	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
2.16/1.38	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
2.16/1.38	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
2.16/1.38	
2.16/1.38	The start-symbols are:[eval_foo_start_4]
2.16/1.38	
2.16/1.38	
2.16/1.38	----------------------------------------
2.16/1.38	
2.16/1.38	(1) Koat Proof (FINISHED)
2.16/1.38	YES(?, 8)
2.16/1.38	
2.16/1.38	
2.16/1.38	
2.16/1.38	Initial complexity problem:
2.16/1.38	
2.16/1.38	1:	T:
2.16/1.38	
2.16/1.38			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.16/1.38	
2.16/1.38			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.16/1.38	
2.16/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
2.16/1.38	
2.16/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
2.16/1.38	
2.16/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_2 + 1, ar_1, ar_2))
2.16/1.38	
2.16/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.16/1.38	
2.16/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.16/1.38	
2.16/1.38		start location:	koat_start
2.16/1.38	
2.16/1.38		leaf cost:	0
2.16/1.38	
2.16/1.38	
2.16/1.38	
2.16/1.38	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.16/1.38	
2.16/1.38	2:	T:
2.16/1.38	
2.16/1.38			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.16/1.38	
2.16/1.38			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2))
2.16/1.38	
2.16/1.38			(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 ]
2.16/1.38	
2.16/1.38			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
2.16/1.38	
2.16/1.38			(Comp: 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_2 + 1, ar_1, ar_2))
2.16/1.38	
2.16/1.38			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.16/1.38	
2.16/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.16/1.38	
2.16/1.38		start location:	koat_start
2.16/1.38	
2.16/1.38		leaf cost:	0
2.16/1.38	
2.16/1.38	
2.16/1.38	
2.16/1.38	Complexity upper bound 8
2.16/1.38	
2.16/1.38	
2.16/1.38	
2.16/1.38	Time: 0.035 sec (SMT: 0.033 sec)
2.16/1.38	
2.16/1.38	
2.16/1.38	----------------------------------------
2.16/1.38	
2.16/1.38	(2)
2.16/1.38	BOUNDS(1, 1)
2.25/1.40	EOF