2.12/1.52	WORST_CASE(?, O(n^3))
2.12/1.53	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.12/1.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.12/1.53	
2.12/1.53	
2.12/1.53	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3).
2.12/1.53	
2.12/1.53	(0) CpxIntTrs
2.12/1.53	(1) Koat Proof [FINISHED, 284 ms]
2.12/1.53	(2) BOUNDS(1, n^3)
2.12/1.53	
2.12/1.53	
2.12/1.53	----------------------------------------
2.12/1.53	
2.12/1.53	(0)
2.12/1.53	Obligation:
2.12/1.53	Complexity Int TRS consisting of the following rules:
2.12/1.53	eval_foo_start(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_a, v_b)) :|: TRUE
2.12/1.53	eval_foo_bb0_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb1_in(v_a, v_b, v_a, v_b)) :|: TRUE
2.12/1.53	eval_foo_bb1_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_a, v_b)) :|: v_.0 >= 0
2.12/1.53	eval_foo_bb1_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_a, v_b)) :|: v_.0 < 0
2.12/1.53	eval_foo_bb2_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, -(v_.01) - 1, v_a, v_b)) :|: v_.01 >= 0
2.12/1.53	eval_foo_bb2_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_bb1_in(v_.0 + v_.01, -(v_.01), v_a, v_b)) :|: v_.01 < 0
2.12/1.53	eval_foo_bb3_in(v_.0, v_.01, v_a, v_b) -> Com_1(eval_foo_stop(v_.0, v_.01, v_a, v_b)) :|: TRUE
2.12/1.53	
2.12/1.53	The start-symbols are:[eval_foo_start_4]
2.12/1.53	
2.12/1.53	
2.12/1.53	----------------------------------------
2.12/1.53	
2.12/1.53	(1) Koat Proof (FINISHED)
2.12/1.53	YES(?, 198*ar_1 + 200*ar_1^2 + 228*ar_1*ar_3 + 64*ar_3^2 + 48*ar_1^3 + 96*ar_1^2*ar_3 + 60*ar_1*ar_3^2 + 12*ar_3^3 + 105*ar_3 + 63)
2.12/1.53	
2.12/1.53	
2.12/1.53	
2.12/1.53	Initial complexity problem:
2.12/1.53	
2.12/1.53	1:	T:
2.12/1.53	
2.12/1.53			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.12/1.53	
2.12/1.53			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.12/1.53	
2.12/1.53			(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 ]
2.12/1.53	
2.12/1.53			(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 ]
2.12/1.53	
2.12/1.53			(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 ]
2.12/1.53	
2.12/1.53			(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 ]
2.12/1.54	
2.12/1.54			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54		start location:	koat_start
2.12/1.54	
2.12/1.54		leaf cost:	0
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.12/1.54	
2.12/1.54	2:	T:
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54		start location:	koat_start
2.12/1.54	
2.12/1.54		leaf cost:	0
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	A polynomial rank function with
2.12/1.54	
2.12/1.54		Pol(evalfoostart) = 2
2.12/1.54	
2.12/1.54		Pol(evalfoobb0in) = 2
2.12/1.54	
2.12/1.54		Pol(evalfoobb1in) = 2
2.12/1.54	
2.12/1.54		Pol(evalfoobb2in) = 2
2.12/1.54	
2.12/1.54		Pol(evalfoobb3in) = 1
2.12/1.54	
2.12/1.54		Pol(evalfoostop) = 0
2.12/1.54	
2.12/1.54		Pol(koat_start) = 2
2.12/1.54	
2.12/1.54	orients all transitions weakly and the transitions
2.12/1.54	
2.12/1.54		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]
2.12/1.54	
2.12/1.54	strictly and produces the following problem:
2.12/1.54	
2.12/1.54	3:	T:
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54		start location:	koat_start
2.12/1.54	
2.12/1.54		leaf cost:	0
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.12/1.54	
2.12/1.54	  For symbol evalfoobb2in: X_1 >= 0
2.12/1.54	
2.12/1.54	  For symbol evalfoobb3in: -X_1 - 1 >= 0
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	This yielded the following problem:
2.12/1.54	
2.12/1.54	4:	T:
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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_0 - 1 >= 0 ]
2.12/1.54	
2.12/1.54			(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_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.12/1.54	
2.12/1.54			(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_0 >= 0 /\ ar_2 >= 0 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54		start location:	koat_start
2.12/1.54	
2.12/1.54		leaf cost:	0
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	A polynomial rank function with
2.12/1.54	
2.12/1.54		Pol(koat_start) = 2*V_2 + V_4 + 1
2.12/1.54	
2.12/1.54		Pol(evalfoostart) = 2*V_2 + V_4 + 1
2.12/1.54	
2.12/1.54		Pol(evalfoobb3in) = 2*V_1 + V_3
2.12/1.54	
2.12/1.54		Pol(evalfoostop) = 2*V_1 + V_3
2.12/1.54	
2.12/1.54		Pol(evalfoobb2in) = 2*V_1 + V_3 + 1
2.12/1.54	
2.12/1.54		Pol(evalfoobb1in) = 2*V_1 + V_3 + 1
2.12/1.54	
2.12/1.54		Pol(evalfoobb0in) = 2*V_2 + V_4 + 1
2.12/1.54	
2.12/1.54	orients all transitions weakly and the transition
2.12/1.54	
2.12/1.54		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2 - 1, ar_3)) [ ar_0 >= 0 /\ ar_2 >= 0 ]
2.12/1.54	
2.12/1.54	strictly and produces the following problem:
2.12/1.54	
2.12/1.54	5:	T:
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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_0 - 1 >= 0 ]
2.12/1.54	
2.12/1.54			(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_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.12/1.54	
2.12/1.54			(Comp: 2*ar_1 + 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_0 >= 0 /\ ar_2 >= 0 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)                    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)                    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54		start location:	koat_start
2.12/1.54	
2.12/1.54		leaf cost:	0
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	A polynomial rank function with
2.12/1.54	
2.12/1.54		Pol(evalfoobb2in) = 2*V_1 + 1
2.12/1.54	
2.12/1.54		Pol(evalfoobb1in) = 2*V_1 + 2
2.12/1.54	
2.12/1.54	and size complexities
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-0) = 22*ar_1 + 13*ar_3 + 6*ar_1^2 + 9*ar_1*ar_3 + 3*ar_3^2 + 12
2.12/1.54	
2.12/1.54		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-1) = ar_1
2.12/1.54	
2.12/1.54		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-2) = 3*ar_1 + 3*ar_3 + 9
2.12/1.54	
2.12/1.54		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]", 0-3) = ar_3
2.12/1.54	
2.12/1.54		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-0) = 22*ar_1 + 13*ar_3 + 6*ar_1^2 + 9*ar_1*ar_3 + 3*ar_3^2 + 12
2.12/1.54	
2.12/1.54		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
2.12/1.54	
2.12/1.54		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-2) = 3*ar_1 + 3*ar_3 + 27
2.12/1.54	
2.12/1.54		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3
2.12/1.54	
2.12/1.54		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_0 >= 0 /\\ ar_2 >= 0 ]", 0-0) = 22*ar_1 + 13*ar_3 + 6*ar_1^2 + 9*ar_1*ar_3 + 3*ar_3^2 + 12
2.12/1.54	
2.12/1.54		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_0 >= 0 /\\ ar_2 >= 0 ]", 0-1) = ar_1
2.12/1.54	
2.12/1.54		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_0 >= 0 /\\ ar_2 >= 0 ]", 0-2) = 3*ar_1 + 3*ar_3 + 9
2.12/1.54	
2.12/1.54		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_0 >= 0 /\\ ar_2 >= 0 ]", 0-3) = ar_3
2.12/1.54	
2.12/1.54		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2, ar_3)) [ ar_0 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-0) = 22*ar_1 + 13*ar_3 + 6*ar_1^2 + 9*ar_1*ar_3 + 3*ar_3^2 + 12
2.12/1.54	
2.12/1.54		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2, ar_3)) [ ar_0 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-1) = ar_1
2.12/1.54	
2.12/1.54		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2, ar_3)) [ ar_0 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-2) = 3*ar_1 + 3*ar_3 + 9
2.12/1.54	
2.12/1.54		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2, ar_3)) [ ar_0 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-3) = ar_3
2.12/1.54	
2.12/1.54		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 - 1 >= 0 ]", 0-0) = 22*ar_1 + 13*ar_3 + 6*ar_1^2 + 9*ar_1*ar_3 + 3*ar_3^2 + 12
2.12/1.54	
2.12/1.54		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 - 1 >= 0 ]", 0-1) = ar_1
2.12/1.54	
2.12/1.54		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 - 1 >= 0 ]", 0-2) = 3*ar_1 + 3*ar_3 + 81
2.12/1.54	
2.12/1.54		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 - 1 >= 0 ]", 0-3) = ar_3
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54		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
2.12/1.54	
2.12/1.54	orients the transitions
2.12/1.54	
2.12/1.54		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2, ar_3)) [ ar_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.12/1.54	
2.12/1.54		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.12/1.54	
2.12/1.54	weakly and the transitions
2.12/1.54	
2.12/1.54		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + ar_2, ar_1, -ar_2, ar_3)) [ ar_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.12/1.54	
2.12/1.54		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ]
2.12/1.54	
2.12/1.54	strictly and produces the following problem:
2.12/1.54	
2.12/1.54	6:	T:
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(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_0 - 1 >= 0 ]
2.12/1.54	
2.12/1.54			(Comp: 98*ar_1 + 100*ar_1^2 + 114*ar_1*ar_3 + 32*ar_3^2 + 24*ar_1^3 + 48*ar_1^2*ar_3 + 30*ar_1*ar_3^2 + 6*ar_3^3 + 52*ar_3 + 28, 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_0 >= 0 /\ 0 >= ar_2 + 1 ]
2.12/1.54	
2.12/1.54			(Comp: 2*ar_1 + 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_0 >= 0 /\ ar_2 >= 0 ]
2.12/1.54	
2.12/1.54			(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 ]
2.12/1.54	
2.12/1.54			(Comp: 98*ar_1 + 100*ar_1^2 + 114*ar_1*ar_3 + 32*ar_3^2 + 24*ar_1^3 + 48*ar_1^2*ar_3 + 30*ar_1*ar_3^2 + 6*ar_3^3 + 52*ar_3 + 28, 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 ]
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)                                                                                                                           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.12/1.54	
2.12/1.54			(Comp: 1, Cost: 1)                                                                                                                           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.12/1.54	
2.12/1.54		start location:	koat_start
2.12/1.54	
2.12/1.54		leaf cost:	0
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	Complexity upper bound 198*ar_1 + 200*ar_1^2 + 228*ar_1*ar_3 + 64*ar_3^2 + 48*ar_1^3 + 96*ar_1^2*ar_3 + 60*ar_1*ar_3^2 + 12*ar_3^3 + 105*ar_3 + 63
2.12/1.54	
2.12/1.54	
2.12/1.54	
2.12/1.54	Time: 0.316 sec (SMT: 0.292 sec)
2.12/1.54	
2.12/1.54	
2.12/1.54	----------------------------------------
2.12/1.54	
2.12/1.54	(2)
2.12/1.54	BOUNDS(1, n^3)
2.12/1.56	EOF