2.24/1.37	WORST_CASE(?, O(n^1))
2.24/1.38	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.24/1.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.24/1.38	
2.24/1.38	
2.24/1.38	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.24/1.38	
2.24/1.38	(0) CpxIntTrs
2.24/1.38	(1) Koat Proof [FINISHED, 76 ms]
2.24/1.38	(2) BOUNDS(1, n^1)
2.24/1.38	
2.24/1.38	
2.24/1.38	----------------------------------------
2.24/1.38	
2.24/1.38	(0)
2.24/1.38	Obligation:
2.24/1.38	Complexity Int TRS consisting of the following rules:
2.24/1.38	eval_foo_start(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp)) :|: TRUE
2.24/1.38	eval_foo_bb0_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp) -> Com_1(eval_foo_bb1_in(v_k, v_i, v_j, v_i, v_j, v_k, v_tmp)) :|: TRUE
2.24/1.38	eval_foo_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp)) :|: v_.01 <= 100 && v_.02 <= v_.0
2.24/1.38	eval_foo_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp)) :|: v_.01 > 100
2.24/1.38	eval_foo_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp)) :|: v_.02 > v_.0
2.24/1.38	eval_foo_bb2_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.02, v_.01 + 1, v_i, v_j, v_k, v_tmp)) :|: TRUE
2.24/1.38	eval_foo_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.02, v_i, v_j, v_k, v_tmp)) :|: TRUE
2.24/1.38	
2.24/1.38	The start-symbols are:[eval_foo_start_7]
2.24/1.38	
2.24/1.38	
2.24/1.38	----------------------------------------
2.24/1.38	
2.24/1.38	(1) Koat Proof (FINISHED)
2.24/1.38	YES(?, 2*ar_1 + 2*ar_3 + 2*ar_5 + 210)
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	Initial complexity problem:
2.24/1.38	
2.24/1.38	1:	T:
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_2 /\ ar_0 >= ar_4 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 101 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_2 + 1, ar_5))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.24/1.38	
2.24/1.38	2:	T:
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_2 /\ ar_0 >= ar_4 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 101 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_2 + 1, ar_5))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	A polynomial rank function with
2.24/1.38	
2.24/1.38		Pol(evalfoostart) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb0in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb1in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb2in) = 2
2.24/1.38	
2.24/1.38		Pol(evalfoobb3in) = 1
2.24/1.38	
2.24/1.38		Pol(evalfoostop) = 0
2.24/1.38	
2.24/1.38		Pol(koat_start) = 2
2.24/1.38	
2.24/1.38	orients all transitions weakly and the transitions
2.24/1.38	
2.24/1.38		evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.38	
2.24/1.38		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.24/1.38	
2.24/1.38		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 101 ]
2.24/1.38	
2.24/1.38	strictly and produces the following problem:
2.24/1.38	
2.24/1.38	3:	T:
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_2 /\ ar_0 >= ar_4 ]
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 101 ]
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.24/1.38	
2.24/1.38			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_2 + 1, ar_5))
2.24/1.38	
2.24/1.38			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.38	
2.24/1.38			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.24/1.38	
2.24/1.38		start location:	koat_start
2.24/1.38	
2.24/1.38		leaf cost:	0
2.24/1.38	
2.24/1.38	
2.24/1.38	
2.24/1.38	A polynomial rank function with
2.24/1.38	
2.24/1.38		Pol(evalfoostart) = V_2 - V_4 - V_6 + 101
2.24/1.38	
2.24/1.38		Pol(evalfoobb0in) = V_2 - V_4 - V_6 + 101
2.24/1.38	
2.24/1.38		Pol(evalfoobb1in) = V_1 - V_3 - V_5 + 101
2.24/1.38	
2.24/1.38		Pol(evalfoobb2in) = V_1 - V_3 - V_5 + 99
2.24/1.39	
2.24/1.39		Pol(evalfoobb3in) = V_1 - V_3 - V_5
2.24/1.39	
2.24/1.39		Pol(evalfoostop) = V_1 - V_3 - V_5
2.24/1.39	
2.24/1.39		Pol(koat_start) = V_2 - V_4 - V_6 + 101
2.24/1.39	
2.24/1.39	orients all transitions weakly and the transition
2.24/1.39	
2.24/1.39		evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_2 /\ ar_0 >= ar_4 ]
2.24/1.39	
2.24/1.39	strictly and produces the following problem:
2.24/1.39	
2.24/1.39	4:	T:
2.24/1.39	
2.24/1.39			(Comp: 1, Cost: 1)                           evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.39	
2.24/1.39			(Comp: 1, Cost: 1)                           evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.24/1.39	
2.24/1.39			(Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_2 /\ ar_0 >= ar_4 ]
2.24/1.39	
2.24/1.39			(Comp: 2, Cost: 1)                           evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 101 ]
2.24/1.39	
2.24/1.39			(Comp: 2, Cost: 1)                           evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.24/1.39	
2.24/1.39			(Comp: ?, Cost: 1)                           evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_2 + 1, ar_5))
2.24/1.39	
2.24/1.39			(Comp: 2, Cost: 1)                           evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.39	
2.24/1.39			(Comp: 1, Cost: 0)                           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.24/1.39	
2.24/1.39		start location:	koat_start
2.24/1.39	
2.24/1.39		leaf cost:	0
2.24/1.39	
2.24/1.39	
2.24/1.39	
2.24/1.39	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.24/1.39	
2.24/1.39	5:	T:
2.24/1.39	
2.24/1.39			(Comp: 1, Cost: 1)                           evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.39	
2.24/1.39			(Comp: 1, Cost: 1)                           evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5))
2.24/1.39	
2.24/1.39			(Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_2 /\ ar_0 >= ar_4 ]
2.24/1.39	
2.24/1.39			(Comp: 2, Cost: 1)                           evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 101 ]
2.24/1.39	
2.24/1.39			(Comp: 2, Cost: 1)                           evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ]
2.24/1.39	
2.24/1.39			(Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_4, ar_3, ar_2 + 1, ar_5))
2.24/1.39	
2.24/1.39			(Comp: 2, Cost: 1)                           evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
2.24/1.39	
2.24/1.39			(Comp: 1, Cost: 0)                           koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
2.24/1.39	
2.24/1.39		start location:	koat_start
2.24/1.39	
2.24/1.39		leaf cost:	0
2.24/1.39	
2.24/1.39	
2.24/1.39	
2.24/1.39	Complexity upper bound 2*ar_1 + 2*ar_3 + 2*ar_5 + 210
2.24/1.39	
2.24/1.39	
2.24/1.39	
2.24/1.39	Time: 0.093 sec (SMT: 0.079 sec)
2.24/1.39	
2.24/1.39	
2.24/1.39	----------------------------------------
2.24/1.39	
2.24/1.39	(2)
2.24/1.39	BOUNDS(1, n^1)
2.24/1.40	EOF