2.33/1.46	WORST_CASE(?, O(n^2))
2.33/1.47	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.33/1.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.33/1.47	
2.33/1.47	
2.33/1.47	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.33/1.47	
2.33/1.47	(0) CpxIntTrs
2.33/1.47	(1) Koat Proof [FINISHED, 285 ms]
2.33/1.47	(2) BOUNDS(1, n^2)
2.33/1.47	
2.33/1.47	
2.33/1.47	----------------------------------------
2.33/1.47	
2.33/1.47	(0)
2.33/1.47	Obligation:
2.33/1.47	Complexity Int TRS consisting of the following rules:
2.33/1.47	eval_foo_start(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_c, v_x)) :|: TRUE
2.33/1.47	eval_foo_bb0_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_x, 1, v_c, v_x)) :|: TRUE
2.33/1.47	eval_foo_bb1_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_c, v_x)) :|: v_.01 > 0
2.33/1.47	eval_foo_bb1_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_c, v_x)) :|: v_.01 <= 0
2.33/1.47	eval_foo_bb2_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_c, v_x)) :|: v_.0 > 100
2.33/1.47	eval_foo_bb2_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_c, v_x)) :|: v_.0 <= 100
2.33/1.47	eval_foo_bb3_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_.0 - 10, v_.01 - 1, v_c, v_x)) :|: TRUE
2.33/1.47	eval_foo_bb4_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_.0 + 11, v_.01 + 1, v_c, v_x)) :|: TRUE
2.33/1.47	eval_foo_bb5_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_c, v_x)) :|: TRUE
2.33/1.47	
2.33/1.47	The start-symbols are:[eval_foo_start_4]
2.33/1.47	
2.33/1.47	
2.33/1.47	----------------------------------------
2.33/1.47	
2.33/1.47	(1) Koat Proof (FINISHED)
2.33/1.47	YES(?, 18256*ar_1 + 36*ar_1^2 + 1476635)
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	Initial complexity problem:
2.33/1.47	
2.33/1.47	1:	T:
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.33/1.47	
2.33/1.47		start location:	koat_start
2.33/1.47	
2.33/1.47		leaf cost:	0
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.33/1.47	
2.33/1.47	2:	T:
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.33/1.47	
2.33/1.47		start location:	koat_start
2.33/1.47	
2.33/1.47		leaf cost:	0
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	A polynomial rank function with
2.33/1.47	
2.33/1.47		Pol(evalfoostart) = 2
2.33/1.47	
2.33/1.47		Pol(evalfoobb0in) = 2
2.33/1.47	
2.33/1.47		Pol(evalfoobb1in) = 2
2.33/1.47	
2.33/1.47		Pol(evalfoobb2in) = 2
2.33/1.47	
2.33/1.47		Pol(evalfoobb5in) = 1
2.33/1.47	
2.33/1.47		Pol(evalfoobb3in) = 2
2.33/1.47	
2.33/1.47		Pol(evalfoobb4in) = 2
2.33/1.47	
2.33/1.47		Pol(evalfoostop) = 0
2.33/1.47	
2.33/1.47		Pol(koat_start) = 2
2.33/1.47	
2.33/1.47	orients all transitions weakly and the transitions
2.33/1.47	
2.33/1.47		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.33/1.47	
2.33/1.47	strictly and produces the following problem:
2.33/1.47	
2.33/1.47	3:	T:
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]
2.33/1.47	
2.33/1.47			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1))
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1))
2.33/1.47	
2.33/1.47			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.33/1.47	
2.33/1.47		start location:	koat_start
2.33/1.47	
2.33/1.47		leaf cost:	0
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.33/1.47	
2.33/1.47	  For symbol evalfoobb2in: X_3 - 1 >= 0
2.33/1.47	
2.33/1.47	  For symbol evalfoobb3in: X_3 - 1 >= 0 /\ X_1 + X_3 - 102 >= 0 /\ X_1 - 101 >= 0
2.33/1.47	
2.33/1.47	  For symbol evalfoobb4in: X_3 - 1 >= 0 /\ -X_1 + X_3 + 99 >= 0 /\ -X_1 + 100 >= 0
2.33/1.47	
2.33/1.47	  For symbol evalfoobb5in: -X_3 >= 0
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	This yielded the following problem:
2.33/1.47	
2.33/1.47	4:	T:
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.33/1.47	
2.33/1.47			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 99 >= 0 /\ -ar_0 + 100 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ 100 >= ar_0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ]
2.33/1.47	
2.33/1.47			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47		start location:	koat_start
2.33/1.47	
2.33/1.47		leaf cost:	0
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	A polynomial rank function with
2.33/1.47	
2.33/1.47		Pol(koat_start) = -2*V_2 + 202
2.33/1.47	
2.33/1.47		Pol(evalfoostart) = -2*V_2 + 202
2.33/1.47	
2.33/1.47		Pol(evalfoobb5in) = -2*V_1 + 20*V_3
2.33/1.47	
2.33/1.47		Pol(evalfoostop) = -2*V_1 + 20*V_3
2.33/1.47	
2.33/1.47		Pol(evalfoobb4in) = -2*V_1 + 20*V_3 + 181
2.33/1.47	
2.33/1.47		Pol(evalfoobb1in) = -2*V_1 + 20*V_3 + 182
2.33/1.47	
2.33/1.47		Pol(evalfoobb3in) = -2*V_1 + 20*V_3 + 182
2.33/1.47	
2.33/1.47		Pol(evalfoobb2in) = -2*V_1 + 20*V_3 + 182
2.33/1.47	
2.33/1.47		Pol(evalfoobb0in) = -2*V_2 + 202
2.33/1.47	
2.33/1.47	orients all transitions weakly and the transitions
2.33/1.47	
2.33/1.47		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 99 >= 0 /\ -ar_0 + 100 >= 0 ]
2.33/1.47	
2.33/1.47		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ 100 >= ar_0 ]
2.33/1.47	
2.33/1.47	strictly and produces the following problem:
2.33/1.47	
2.33/1.47	5:	T:
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.33/1.47	
2.33/1.47			(Comp: 2, Cost: 1)               evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: 2*ar_1 + 202, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 99 >= 0 /\ -ar_0 + 100 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)               evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: 2*ar_1 + 202, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ 100 >= ar_0 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)               evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ]
2.33/1.47	
2.33/1.47			(Comp: 2, Cost: 1)               evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.33/1.47	
2.33/1.47			(Comp: ?, Cost: 1)               evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)               evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)               evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47		start location:	koat_start
2.33/1.47	
2.33/1.47		leaf cost:	0
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	A polynomial rank function with
2.33/1.47	
2.33/1.47		Pol(evalfoobb3in) = 3*V_3 - 2
2.33/1.47	
2.33/1.47		Pol(evalfoobb1in) = 3*V_3
2.33/1.47	
2.33/1.47		Pol(evalfoobb2in) = 3*V_3 - 1
2.33/1.47	
2.33/1.47	and size complexities
2.33/1.47	
2.33/1.47		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.33/1.47	
2.33/1.47		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.33/1.47	
2.33/1.47		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))", 0-0) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))", 0-2) = 1
2.33/1.47	
2.33/1.47		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]", 0-0) = ar_1 + 111
2.33/1.47	
2.33/1.47		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]", 0-2) = 2*ar_1 + 812
2.33/1.47	
2.33/1.47		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-0) = ar_1 + 111
2.33/1.47	
2.33/1.47		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]", 0-2) = 2*ar_1 + 1624
2.33/1.47	
2.33/1.47		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_0 >= 101 ]", 0-0) = ar_1 + 111
2.33/1.47	
2.33/1.47		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_0 >= 101 ]", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_0 >= 101 ]", 0-2) = 2*ar_1 + 812
2.33/1.47	
2.33/1.47		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ 100 >= ar_0 ]", 0-0) = ar_1 + 111
2.33/1.47	
2.33/1.47		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ 100 >= ar_0 ]", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ 100 >= ar_0 ]", 0-2) = 2*ar_1 + 812
2.33/1.47	
2.33/1.47		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - 101 >= 0 ]", 0-0) = ar_1 + 111
2.33/1.47	
2.33/1.47		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - 101 >= 0 ]", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 102 >= 0 /\\ ar_0 - 101 >= 0 ]", 0-2) = 2*ar_1 + 812
2.33/1.47	
2.33/1.47		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 99 >= 0 /\\ -ar_0 + 100 >= 0 ]", 0-0) = ar_1 + 111
2.33/1.47	
2.33/1.47		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 99 >= 0 /\\ -ar_0 + 100 >= 0 ]", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 99 >= 0 /\\ -ar_0 + 100 >= 0 ]", 0-2) = 2*ar_1 + 812
2.33/1.47	
2.33/1.47		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]", 0-0) = ar_1 + 111
2.33/1.47	
2.33/1.47		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]", 0-2) = 2*ar_1 + 3248
2.33/1.47	
2.33/1.47		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.33/1.47	
2.33/1.47		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.33/1.47	
2.33/1.47		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.33/1.47	
2.33/1.47	orients the transitions
2.33/1.47	
2.33/1.47		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ]
2.33/1.47	
2.33/1.47		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ]
2.33/1.47	
2.33/1.47		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]
2.33/1.47	
2.33/1.47	weakly and the transitions
2.33/1.47	
2.33/1.47		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ]
2.33/1.47	
2.33/1.47		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ]
2.33/1.47	
2.33/1.47		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]
2.33/1.47	
2.33/1.47	strictly and produces the following problem:
2.33/1.47	
2.33/1.47	6:	T:
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 0)                                 koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.33/1.47	
2.33/1.47			(Comp: 2, Cost: 1)                                 evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_2 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: 2*ar_1 + 202, Cost: 1)                      evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) [ ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 99 >= 0 /\ -ar_0 + 100 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: 12*ar_1^2 + 6084*ar_1 + 492075, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) [ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 102 >= 0 /\ ar_0 - 101 >= 0 ]
2.33/1.47	
2.33/1.47			(Comp: 2*ar_1 + 202, Cost: 1)                      evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ 100 >= ar_0 ]
2.33/1.47	
2.33/1.47			(Comp: 12*ar_1^2 + 6084*ar_1 + 492075, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_0 >= 101 ]
2.33/1.47	
2.33/1.47			(Comp: 2, Cost: 1)                                 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
2.33/1.47	
2.33/1.47			(Comp: 12*ar_1^2 + 6084*ar_1 + 492075, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ]
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)                                 evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1))
2.33/1.47	
2.33/1.47			(Comp: 1, Cost: 1)                                 evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.33/1.47	
2.33/1.47		start location:	koat_start
2.33/1.47	
2.33/1.47		leaf cost:	0
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	Complexity upper bound 18256*ar_1 + 36*ar_1^2 + 1476635
2.33/1.47	
2.33/1.47	
2.33/1.47	
2.33/1.47	Time: 0.236 sec (SMT: 0.214 sec)
2.33/1.47	
2.33/1.47	
2.33/1.47	----------------------------------------
2.33/1.47	
2.33/1.47	(2)
2.33/1.47	BOUNDS(1, n^2)
2.33/1.49	EOF