2.48/1.55	WORST_CASE(?, O(n^3))
2.48/1.56	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.48/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.48/1.56	
2.48/1.56	
2.48/1.56	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3).
2.48/1.56	
2.48/1.56	(0) CpxIntTrs
2.48/1.56	(1) Koat Proof [FINISHED, 274 ms]
2.48/1.56	(2) BOUNDS(1, n^3)
2.48/1.56	
2.48/1.56	
2.48/1.56	----------------------------------------
2.48/1.56	
2.48/1.56	(0)
2.48/1.56	Obligation:
2.48/1.56	Complexity Int TRS consisting of the following rules:
2.48/1.56	eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.48/1.56	eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE
2.48/1.56	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= 0
2.48/1.56	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < 0
2.48/1.56	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, v_.01 - 1, v_x, v_y)) :|: v_.01 >= 0
2.48/1.56	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, v_.01, v_x, v_y)) :|: v_.01 < 0
2.48/1.56	eval_foo_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.48/1.56	
2.48/1.56	The start-symbols are:[eval_foo_start_4]
2.48/1.56	
2.48/1.56	
2.48/1.56	----------------------------------------
2.48/1.56	
2.48/1.56	(1) Koat Proof (FINISHED)
2.48/1.56	YES(?, 8*ar_1 + 4*ar_1*ar_3 + 16*ar_3^2 + 4*ar_3^3 + 25*ar_3 + 23)
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	Initial complexity problem:
2.48/1.56	
2.48/1.56	1:	T:
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56			(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 ]
2.48/1.56	
2.48/1.56		start location:	koat_start
2.48/1.56	
2.48/1.56		leaf cost:	0
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.48/1.56	
2.48/1.56	2:	T:
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56			(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 ]
2.48/1.56	
2.48/1.56		start location:	koat_start
2.48/1.56	
2.48/1.56		leaf cost:	0
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	A polynomial rank function with
2.48/1.56	
2.48/1.56		Pol(evalfoostart) = 2
2.48/1.56	
2.48/1.56		Pol(evalfoobb0in) = 2
2.48/1.56	
2.48/1.56		Pol(evalfoobb1in) = 2
2.48/1.56	
2.48/1.56		Pol(evalfoobb2in) = 2
2.48/1.56	
2.48/1.56		Pol(evalfoobb3in) = 1
2.48/1.56	
2.48/1.56		Pol(evalfoostop) = 0
2.48/1.56	
2.48/1.56		Pol(koat_start) = 2
2.48/1.56	
2.48/1.56	orients all transitions weakly and the transitions
2.48/1.56	
2.48/1.56		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.48/1.56	
2.48/1.56	strictly and produces the following problem:
2.48/1.56	
2.48/1.56	3:	T:
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56			(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 ]
2.48/1.56	
2.48/1.56		start location:	koat_start
2.48/1.56	
2.48/1.56		leaf cost:	0
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	A polynomial rank function with
2.48/1.56	
2.48/1.56		Pol(evalfoostart) = V_4 + 1
2.48/1.56	
2.48/1.56		Pol(evalfoobb0in) = V_4 + 1
2.48/1.56	
2.48/1.56		Pol(evalfoobb1in) = V_3 + 1
2.48/1.56	
2.48/1.56		Pol(evalfoobb2in) = V_3 + 1
2.48/1.56	
2.48/1.56		Pol(evalfoobb3in) = V_3
2.48/1.56	
2.48/1.56		Pol(evalfoostop) = V_3
2.48/1.56	
2.48/1.56		Pol(koat_start) = V_4 + 1
2.48/1.56	
2.48/1.56	orients all transitions weakly and the transition
2.48/1.56	
2.48/1.56		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 0 ]
2.48/1.56	
2.48/1.56	strictly and produces the following problem:
2.48/1.56	
2.48/1.56	4:	T:
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: ar_3 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56			(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 ]
2.48/1.56	
2.48/1.56		start location:	koat_start
2.48/1.56	
2.48/1.56		leaf cost:	0
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.48/1.56	
2.48/1.56	  For symbol evalfoobb1in: -X_3 + X_4 >= 0
2.48/1.56	
2.48/1.56	  For symbol evalfoobb2in: -X_3 + X_4 >= 0 /\ X_1 >= 0
2.48/1.56	
2.48/1.56	  For symbol evalfoobb3in: -X_3 + X_4 >= 0 /\ -X_1 - 1 >= 0
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	This yielded the following problem:
2.48/1.56	
2.48/1.56	5:	T:
2.48/1.56	
2.48/1.56			(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 ]
2.48/1.56	
2.48/1.56			(Comp: 2, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 - 1 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: ar_3 + 1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_0 + 1 ]
2.48/1.56	
2.48/1.56			(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_3 >= 0 /\ ar_0 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56		start location:	koat_start
2.48/1.56	
2.48/1.56		leaf cost:	0
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	A polynomial rank function with
2.48/1.56	
2.48/1.56		Pol(evalfoobb2in) = 2*V_1 + 1
2.48/1.56	
2.48/1.56		Pol(evalfoobb1in) = 2*V_1 + 2
2.48/1.56	
2.48/1.56	and size complexities
2.48/1.56	
2.48/1.56		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.48/1.56	
2.48/1.56		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.48/1.56	
2.48/1.56		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.48/1.56	
2.48/1.56		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.48/1.56	
2.48/1.56		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-0) = ar_1
2.48/1.56	
2.48/1.56		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-1) = ar_1
2.48/1.56	
2.48/1.56		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-2) = ar_3
2.48/1.56	
2.48/1.56		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-3) = ar_3
2.48/1.56	
2.48/1.56		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_1 + 3*ar_3 + ar_3^2 + 2
2.48/1.56	
2.48/1.56		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_1
2.48/1.56	
2.48/1.56		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_3 + 1
2.48/1.56	
2.48/1.56		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_3
2.48/1.56	
2.48/1.56		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ 0 >= ar_0 + 1 ]", 0-0) = ar_1 + 3*ar_3 + ar_3^2 + 2
2.48/1.56	
2.48/1.56		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.48/1.56	
2.48/1.56		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ 0 >= ar_0 + 1 ]", 0-2) = ar_3 + 1
2.48/1.56	
2.48/1.56		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ 0 >= ar_0 + 1 ]", 0-3) = ar_3
2.48/1.56	
2.48/1.56		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= 0 ]", 0-0) = ar_1 + 3*ar_3 + ar_3^2 + 2
2.48/1.56	
2.48/1.56		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= 0 ]", 0-1) = ar_1
2.48/1.56	
2.48/1.56		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= 0 ]", 0-2) = ar_3 + 1
2.48/1.56	
2.48/1.56		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= 0 ]", 0-3) = ar_3
2.48/1.56	
2.48/1.56		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-0) = ar_1 + 3*ar_3 + ar_3^2 + 2
2.48/1.56	
2.48/1.56		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-1) = ar_1
2.48/1.56	
2.48/1.56		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-2) = ar_3 + 1
2.48/1.56	
2.48/1.56		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-3) = ar_3
2.48/1.56	
2.48/1.56		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ -ar_0 - 1 >= 0 ]", 0-0) = ar_1 + 3*ar_3 + ar_3^2 + 2
2.48/1.56	
2.48/1.56		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ -ar_0 - 1 >= 0 ]", 0-1) = ar_1
2.48/1.56	
2.48/1.56		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ -ar_0 - 1 >= 0 ]", 0-2) = ar_3 + 1
2.48/1.56	
2.48/1.56		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ -ar_0 - 1 >= 0 ]", 0-3) = ar_3
2.48/1.56	
2.48/1.56		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.48/1.56	
2.48/1.56		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.48/1.56	
2.48/1.56		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.48/1.56	
2.48/1.56		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.48/1.56	
2.48/1.56	orients the transitions
2.48/1.56	
2.48/1.56		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.48/1.56	
2.48/1.56		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 0 ]
2.48/1.56	
2.48/1.56	weakly and the transitions
2.48/1.56	
2.48/1.56		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.48/1.56	
2.48/1.56		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 0 ]
2.48/1.56	
2.48/1.56	strictly and produces the following problem:
2.48/1.56	
2.48/1.56	6:	T:
2.48/1.56	
2.48/1.56			(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 ]
2.48/1.56	
2.48/1.56			(Comp: 2, Cost: 1)                                                           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 - 1 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: 4*ar_1 + 2*ar_1*ar_3 + 8*ar_3^2 + 2*ar_3^3 + 12*ar_3 + 8, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: ar_3 + 1, Cost: 1)                                                    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, ar_2 - 1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: 2, Cost: 1)                                                           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ 0 >= ar_0 + 1 ]
2.48/1.56	
2.48/1.56			(Comp: 4*ar_1 + 2*ar_1*ar_3 + 8*ar_3^2 + 2*ar_3^3 + 12*ar_3 + 8, 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_3 >= 0 /\ ar_0 >= 0 ]
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)                                                           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.48/1.56	
2.48/1.56			(Comp: 1, Cost: 1)                                                           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.48/1.56	
2.48/1.56		start location:	koat_start
2.48/1.56	
2.48/1.56		leaf cost:	0
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	Complexity upper bound 8*ar_1 + 4*ar_1*ar_3 + 16*ar_3^2 + 4*ar_3^3 + 25*ar_3 + 23
2.48/1.56	
2.48/1.56	
2.48/1.56	
2.48/1.56	Time: 0.295 sec (SMT: 0.270 sec)
2.48/1.56	
2.48/1.56	
2.48/1.56	----------------------------------------
2.48/1.56	
2.48/1.56	(2)
2.48/1.56	BOUNDS(1, n^3)
2.48/1.57	EOF