2.12/1.28	WORST_CASE(?, O(1))
2.12/1.29	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.12/1.29	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.12/1.29	
2.12/1.29	
2.12/1.29	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
2.12/1.29	
2.12/1.29	(0) CpxIntTrs
2.12/1.29	(1) Koat Proof [FINISHED, 44 ms]
2.12/1.29	(2) BOUNDS(1, 1)
2.12/1.29	
2.12/1.29	
2.12/1.29	----------------------------------------
2.12/1.29	
2.12/1.29	(0)
2.12/1.29	Obligation:
2.12/1.29	Complexity Int TRS consisting of the following rules:
2.12/1.29	eval_foo_start(v_.0, v_.01, v_tmp, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_tmp, v_x, v_y)) :|: TRUE
2.12/1.29	eval_foo_bb0_in(v_.0, v_.01, v_tmp, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_tmp, v_x, v_y)) :|: TRUE
2.12/1.29	eval_foo_bb1_in(v_.0, v_.01, v_tmp, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.0, v_tmp, v_x, v_y)) :|: v_.0 > v_.01
2.12/1.29	eval_foo_bb1_in(v_.0, v_.01, v_tmp, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_tmp, v_x, v_y)) :|: v_.0 <= v_.01
2.12/1.29	eval_foo_bb2_in(v_.0, v_.01, v_tmp, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_tmp, v_x, v_y)) :|: TRUE
2.12/1.29	
2.12/1.29	The start-symbols are:[eval_foo_start_5]
2.12/1.29	
2.12/1.29	
2.12/1.29	----------------------------------------
2.12/1.29	
2.12/1.29	(1) Koat Proof (FINISHED)
2.12/1.29	YES(?, 7)
2.12/1.29	
2.12/1.29	
2.12/1.29	
2.12/1.29	Initial complexity problem:
2.12/1.29	
2.12/1.29	1:	T:
2.12/1.29	
2.12/1.29			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.12/1.29	
2.12/1.29			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.12/1.29	
2.12/1.29			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_0, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.12/1.29	
2.12/1.29			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.12/1.29	
2.12/1.29			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.12/1.29	
2.12/1.29			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.12/1.29	
2.12/1.29		start location:	koat_start
2.12/1.29	
2.12/1.29		leaf cost:	0
2.12/1.29	
2.12/1.29	
2.12/1.29	
2.12/1.29	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.12/1.29	
2.12/1.29	2:	T:
2.12/1.29	
2.12/1.29			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.12/1.29	
2.12/1.29			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.12/1.29	
2.12/1.29			(Comp: 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_0, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.12/1.29	
2.12/1.29			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.12/1.29	
2.12/1.29			(Comp: 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.12/1.29	
2.12/1.29			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.12/1.29	
2.12/1.29		start location:	koat_start
2.12/1.29	
2.12/1.29		leaf cost:	0
2.12/1.29	
2.12/1.29	
2.12/1.29	
2.12/1.29	Complexity upper bound 7
2.12/1.29	
2.12/1.29	
2.12/1.29	
2.12/1.29	Time: 0.033 sec (SMT: 0.031 sec)
2.12/1.29	
2.12/1.29	
2.12/1.29	----------------------------------------
2.12/1.29	
2.12/1.29	(2)
2.12/1.29	BOUNDS(1, 1)
2.19/1.31	EOF