2.43/1.48	WORST_CASE(?, O(n^2))
2.43/1.49	proof of /export/starexec/sandbox2/output/output_files/bench.koat
2.43/1.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.43/1.49	
2.43/1.49	
2.43/1.49	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.43/1.49	
2.43/1.49	(0) CpxIntTrs
2.43/1.49	(1) Koat Proof [FINISHED, 276 ms]
2.43/1.49	(2) BOUNDS(1, n^2)
2.43/1.49	
2.43/1.49	
2.43/1.49	----------------------------------------
2.43/1.49	
2.43/1.49	(0)
2.43/1.49	Obligation:
2.43/1.49	Complexity Int TRS consisting of the following rules:
2.43/1.49	eval_foo_start(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_c, v_n)) :|: TRUE
2.43/1.49	eval_foo_bb0_in(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_bb1_in(1, v_n, v_c, v_n)) :|: TRUE
2.43/1.49	eval_foo_bb1_in(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_c, v_n)) :|: v_.0 > 0
2.43/1.49	eval_foo_bb1_in(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_c, v_n)) :|: v_.0 <= 0
2.43/1.49	eval_foo_bb2_in(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_c, v_n)) :|: v_.01 > 100
2.43/1.49	eval_foo_bb2_in(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_c, v_n)) :|: v_.01 <= 100
2.43/1.49	eval_foo_bb3_in(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 10, v_c, v_n)) :|: TRUE
2.43/1.49	eval_foo_bb4_in(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01 + 11, v_c, v_n)) :|: TRUE
2.43/1.49	eval_foo_bb5_in(v_.0, v_.01, v_c, v_n) -> Com_1(eval_foo_stop(v_.0, v_.01, v_c, v_n)) :|: TRUE
2.43/1.49	
2.43/1.49	The start-symbols are:[eval_foo_start_4]
2.43/1.49	
2.43/1.49	
2.43/1.49	----------------------------------------
2.43/1.49	
2.43/1.49	(1) Koat Proof (FINISHED)
2.43/1.49	YES(?, 18256*ar_2 + 36*ar_2^2 + 1476635)
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	Initial complexity problem:
2.43/1.49	
2.43/1.49	1:	T:
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 >= 101 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_1 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.49	
2.43/1.49		start location:	koat_start
2.43/1.49	
2.43/1.49		leaf cost:	0
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.43/1.49	
2.43/1.49	2:	T:
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 >= 101 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_1 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.49	
2.43/1.49		start location:	koat_start
2.43/1.49	
2.43/1.49		leaf cost:	0
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	A polynomial rank function with
2.43/1.49	
2.43/1.49		Pol(evalfoostart) = 2
2.43/1.49	
2.43/1.49		Pol(evalfoobb0in) = 2
2.43/1.49	
2.43/1.49		Pol(evalfoobb1in) = 2
2.43/1.49	
2.43/1.49		Pol(evalfoobb2in) = 2
2.43/1.49	
2.43/1.49		Pol(evalfoobb5in) = 1
2.43/1.49	
2.43/1.49		Pol(evalfoobb3in) = 2
2.43/1.49	
2.43/1.49		Pol(evalfoobb4in) = 2
2.43/1.49	
2.43/1.49		Pol(evalfoostop) = 0
2.43/1.49	
2.43/1.49		Pol(koat_start) = 2
2.43/1.49	
2.43/1.49	orients all transitions weakly and the transitions
2.43/1.49	
2.43/1.49		evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.49	
2.43/1.49	strictly and produces the following problem:
2.43/1.49	
2.43/1.49	3:	T:
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
2.43/1.49	
2.43/1.49			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_1 >= 101 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_1 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2))
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.49	
2.43/1.49		start location:	koat_start
2.43/1.49	
2.43/1.49		leaf cost:	0
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.43/1.49	
2.43/1.49	  For symbol evalfoobb2in: X_1 - 1 >= 0
2.43/1.49	
2.43/1.49	  For symbol evalfoobb3in: X_2 - 101 >= 0 /\ X_1 + X_2 - 102 >= 0 /\ X_1 - 1 >= 0
2.43/1.49	
2.43/1.49	  For symbol evalfoobb4in: -X_2 + 100 >= 0 /\ X_1 - X_2 + 99 >= 0 /\ X_1 - 1 >= 0
2.43/1.49	
2.43/1.49	  For symbol evalfoobb5in: -X_1 >= 0
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	This yielded the following problem:
2.43/1.49	
2.43/1.49	4:	T:
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.49	
2.43/1.49			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2)) [ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 99 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2)) [ ar_1 - 101 >= 0 /\ ar_0 + ar_1 - 102 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ 100 >= ar_1 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ ar_1 >= 101 ]
2.43/1.49	
2.43/1.49			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49		start location:	koat_start
2.43/1.49	
2.43/1.49		leaf cost:	0
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	A polynomial rank function with
2.43/1.49	
2.43/1.49		Pol(koat_start) = -2*V_3 + 202
2.43/1.49	
2.43/1.49		Pol(evalfoostart) = -2*V_3 + 202
2.43/1.49	
2.43/1.49		Pol(evalfoobb5in) = 20*V_1 - 2*V_2
2.43/1.49	
2.43/1.49		Pol(evalfoostop) = 20*V_1 - 2*V_2
2.43/1.49	
2.43/1.49		Pol(evalfoobb4in) = 20*V_1 - 2*V_2 + 181
2.43/1.49	
2.43/1.49		Pol(evalfoobb1in) = 20*V_1 - 2*V_2 + 182
2.43/1.49	
2.43/1.49		Pol(evalfoobb3in) = 20*V_1 - 2*V_2 + 182
2.43/1.49	
2.43/1.49		Pol(evalfoobb2in) = 20*V_1 - 2*V_2 + 182
2.43/1.49	
2.43/1.49		Pol(evalfoobb0in) = -2*V_3 + 202
2.43/1.49	
2.43/1.49	orients all transitions weakly and the transitions
2.43/1.49	
2.43/1.49		evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2)) [ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 99 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ 100 >= ar_1 ]
2.43/1.49	
2.43/1.49	strictly and produces the following problem:
2.43/1.49	
2.43/1.49	5:	T:
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.49	
2.43/1.49			(Comp: 2, Cost: 1)               evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: 2*ar_2 + 202, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2)) [ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 99 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)               evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2)) [ ar_1 - 101 >= 0 /\ ar_0 + ar_1 - 102 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: 2*ar_2 + 202, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ 100 >= ar_1 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)               evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ ar_1 >= 101 ]
2.43/1.49	
2.43/1.49			(Comp: 2, Cost: 1)               evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.49	
2.43/1.49			(Comp: ?, Cost: 1)               evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)               evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)               evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49		start location:	koat_start
2.43/1.49	
2.43/1.49		leaf cost:	0
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	A polynomial rank function with
2.43/1.49	
2.43/1.49		Pol(evalfoobb3in) = 3*V_1 - 2
2.43/1.49	
2.43/1.49		Pol(evalfoobb1in) = 3*V_1
2.43/1.49	
2.43/1.49		Pol(evalfoobb2in) = 3*V_1 - 1
2.43/1.49	
2.43/1.49	and size complexities
2.43/1.49	
2.43/1.49		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.43/1.49	
2.43/1.49		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.43/1.49	
2.43/1.49		S("evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))", 0-0) = 1
2.43/1.49	
2.43/1.49		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))", 0-1) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]", 0-0) = 2*ar_2 + 812
2.43/1.49	
2.43/1.49		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]", 0-1) = ar_2 + 111
2.43/1.49	
2.43/1.49		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-0) = 2*ar_2 + 1624
2.43/1.49	
2.43/1.49		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_2 + 111
2.43/1.49	
2.43/1.49		S("evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\\ ar_1 >= 101 ]", 0-0) = 2*ar_2 + 812
2.43/1.49	
2.43/1.49		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\\ ar_1 >= 101 ]", 0-1) = ar_2 + 111
2.43/1.49	
2.43/1.49		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\\ ar_1 >= 101 ]", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\\ 100 >= ar_1 ]", 0-0) = 2*ar_2 + 812
2.43/1.49	
2.43/1.49		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\\ 100 >= ar_1 ]", 0-1) = ar_2 + 111
2.43/1.49	
2.43/1.49		S("evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\\ 100 >= ar_1 ]", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2)) [ ar_1 - 101 >= 0 /\\ ar_0 + ar_1 - 102 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = 2*ar_2 + 812
2.43/1.49	
2.43/1.49		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2)) [ ar_1 - 101 >= 0 /\\ ar_0 + ar_1 - 102 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2 + 111
2.43/1.49	
2.43/1.49		S("evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2)) [ ar_1 - 101 >= 0 /\\ ar_0 + ar_1 - 102 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2)) [ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 99 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = 2*ar_2 + 812
2.43/1.49	
2.43/1.49		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2)) [ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 99 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2 + 111
2.43/1.49	
2.43/1.49		S("evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2)) [ -ar_1 + 100 >= 0 /\\ ar_0 - ar_1 + 99 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 >= 0 ]", 0-0) = 2*ar_2 + 3248
2.43/1.49	
2.43/1.49		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 >= 0 ]", 0-1) = ar_2 + 111
2.43/1.49	
2.43/1.49		S("evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 >= 0 ]", 0-2) = ar_2
2.43/1.49	
2.43/1.49		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.43/1.49	
2.43/1.49		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.43/1.49	
2.43/1.49		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.43/1.49	
2.43/1.49	orients the transitions
2.43/1.49	
2.43/1.49		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2)) [ ar_1 - 101 >= 0 /\ ar_0 + ar_1 - 102 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ ar_1 >= 101 ]
2.43/1.49	
2.43/1.49		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
2.43/1.49	
2.43/1.49	weakly and the transitions
2.43/1.49	
2.43/1.49		evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2)) [ ar_1 - 101 >= 0 /\ ar_0 + ar_1 - 102 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49		evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ ar_1 >= 101 ]
2.43/1.49	
2.43/1.49		evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
2.43/1.49	
2.43/1.49	strictly and produces the following problem:
2.43/1.49	
2.43/1.49	6:	T:
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 0)                                 koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.49	
2.43/1.49			(Comp: 2, Cost: 1)                                 evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) [ -ar_0 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: 2*ar_2 + 202, Cost: 1)                      evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1 + 11, ar_2)) [ -ar_1 + 100 >= 0 /\ ar_0 - ar_1 + 99 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: 12*ar_2^2 + 6084*ar_2 + 492075, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1 - 10, ar_2)) [ ar_1 - 101 >= 0 /\ ar_0 + ar_1 - 102 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.49	
2.43/1.49			(Comp: 2*ar_2 + 202, Cost: 1)                      evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ 100 >= ar_1 ]
2.43/1.49	
2.43/1.49			(Comp: 12*ar_2^2 + 6084*ar_2 + 492075, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 - 1 >= 0 /\ ar_1 >= 101 ]
2.43/1.49	
2.43/1.49			(Comp: 2, Cost: 1)                                 evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.49	
2.43/1.49			(Comp: 12*ar_2^2 + 6084*ar_2 + 492075, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)                                 evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(1, ar_2, ar_2))
2.43/1.49	
2.43/1.49			(Comp: 1, Cost: 1)                                 evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2))
2.43/1.49	
2.43/1.49		start location:	koat_start
2.43/1.49	
2.43/1.49		leaf cost:	0
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	Complexity upper bound 18256*ar_2 + 36*ar_2^2 + 1476635
2.43/1.49	
2.43/1.49	
2.43/1.49	
2.43/1.49	Time: 0.234 sec (SMT: 0.212 sec)
2.43/1.49	
2.43/1.49	
2.43/1.49	----------------------------------------
2.43/1.49	
2.43/1.49	(2)
2.43/1.49	BOUNDS(1, n^2)
2.43/1.50	EOF