2.00/1.42	WORST_CASE(?, O(n^1))
2.00/1.43	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.00/1.43	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.00/1.43	
2.00/1.43	
2.00/1.43	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.00/1.43	
2.00/1.43	(0) CpxIntTrs
2.00/1.43	(1) Koat Proof [FINISHED, 191 ms]
2.00/1.43	(2) BOUNDS(1, n^1)
2.00/1.43	
2.00/1.43	
2.00/1.43	----------------------------------------
2.00/1.43	
2.00/1.43	(0)
2.00/1.43	Obligation:
2.00/1.43	Complexity Int TRS consisting of the following rules:
2.00/1.43	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
2.00/1.43	eval_foo_bb0_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_c, v_x, v_c, v_x)) :|: v_c >= 2
2.00/1.43	eval_foo_bb0_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_c, v_x)) :|: v_c < 2
2.00/1.43	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 + v_.0 >= 0
2.00/1.43	eval_foo_bb1_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_c, v_x)) :|: v_.01 + v_.0 < 0
2.00/1.43	eval_foo_bb2_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01 - v_.0, v_c, v_x)) :|: TRUE
2.00/1.43	eval_foo_bb3_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_c, v_x)) :|: TRUE
2.00/1.43	
2.00/1.43	The start-symbols are:[eval_foo_start_4]
2.00/1.43	
2.00/1.43	
2.00/1.43	----------------------------------------
2.00/1.43	
2.00/1.43	(1) Koat Proof (FINISHED)
2.00/1.43	YES(?, 4*ar_0 + 4*ar_3 + 11)
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	Initial complexity problem:
2.00/1.43	
2.00/1.43	1:	T:
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]
2.00/1.43	
2.00/1.43			(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_1 >= 0 ]
2.00/1.43	
2.00/1.43			(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_2 + ar_1 + 1 ]
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3))
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43			(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 ]
2.00/1.43	
2.00/1.43		start location:	koat_start
2.00/1.43	
2.00/1.43		leaf cost:	0
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.00/1.43	
2.00/1.43	2:	T:
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]
2.00/1.43	
2.00/1.43			(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_1 >= 0 ]
2.00/1.43	
2.00/1.43			(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_2 + ar_1 + 1 ]
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3))
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43			(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 ]
2.00/1.43	
2.00/1.43		start location:	koat_start
2.00/1.43	
2.00/1.43		leaf cost:	0
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	A polynomial rank function with
2.00/1.43	
2.00/1.43		Pol(evalfoostart) = 2
2.00/1.43	
2.00/1.43		Pol(evalfoobb0in) = 2
2.00/1.43	
2.00/1.43		Pol(evalfoobb1in) = 2
2.00/1.43	
2.00/1.43		Pol(evalfoobb3in) = 1
2.00/1.43	
2.00/1.43		Pol(evalfoobb2in) = 2
2.00/1.43	
2.00/1.43		Pol(evalfoostop) = 0
2.00/1.43	
2.00/1.43		Pol(koat_start) = 2
2.00/1.43	
2.00/1.43	orients all transitions weakly and the transitions
2.00/1.43	
2.00/1.43		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + ar_1 + 1 ]
2.00/1.43	
2.00/1.43	strictly and produces the following problem:
2.00/1.43	
2.00/1.43	3:	T:
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]
2.00/1.43	
2.00/1.43			(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_1 >= 0 ]
2.00/1.43	
2.00/1.43			(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_2 + ar_1 + 1 ]
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3))
2.00/1.43	
2.00/1.43			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43			(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 ]
2.00/1.43	
2.00/1.43		start location:	koat_start
2.00/1.43	
2.00/1.43		leaf cost:	0
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.00/1.43	
2.00/1.43	  For symbol evalfoobb1in: -X_3 + X_4 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0
2.00/1.43	
2.00/1.43	  For symbol evalfoobb2in: -X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_2 + X_3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	This yielded the following problem:
2.00/1.43	
2.00/1.43	4:	T:
2.00/1.43	
2.00/1.43			(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 ]
2.00/1.43	
2.00/1.43			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_1 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ]
2.00/1.43	
2.00/1.43			(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 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ 0 >= ar_2 + ar_1 + 1 ]
2.00/1.43	
2.00/1.43			(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_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_2 + ar_1 >= 0 ]
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43		start location:	koat_start
2.00/1.43	
2.00/1.43		leaf cost:	0
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	A polynomial rank function with
2.00/1.43	
2.00/1.43		Pol(evalfoobb2in) = 2*V_2 + 2*V_3 + 1
2.00/1.43	
2.00/1.43		Pol(evalfoobb1in) = 2*V_2 + 2*V_3 + 2
2.00/1.43	
2.00/1.43	and size complexities
2.00/1.43	
2.00/1.43		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
2.00/1.43	
2.00/1.43		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
2.00/1.43	
2.00/1.43		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
2.00/1.43	
2.00/1.43		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
2.00/1.43	
2.00/1.43		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]", 0-0) = ar_0
2.00/1.43	
2.00/1.43		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]", 0-1) = ar_0
2.00/1.43	
2.00/1.43		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]", 0-2) = ar_3
2.00/1.43	
2.00/1.43		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]", 0-3) = ar_3
2.00/1.43	
2.00/1.43		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]", 0-0) = ar_0
2.00/1.43	
2.00/1.43		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]", 0-1) = ar_1
2.00/1.43	
2.00/1.43		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]", 0-2) = ar_2
2.00/1.43	
2.00/1.43		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]", 0-3) = ar_3
2.00/1.43	
2.00/1.43		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_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 + ar_1 >= 0 ]", 0-0) = ar_0
2.00/1.43	
2.00/1.43		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_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 + ar_1 >= 0 ]", 0-1) = ?
2.00/1.43	
2.00/1.43		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_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 + ar_1 >= 0 ]", 0-2) = ?
2.00/1.43	
2.00/1.43		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_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 + ar_1 >= 0 ]", 0-3) = ar_3
2.00/1.43	
2.00/1.43		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 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 /\\ 0 >= ar_2 + ar_1 + 1 ]", 0-0) = ar_0
2.00/1.43	
2.00/1.43		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 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 /\\ 0 >= ar_2 + ar_1 + 1 ]", 0-1) = ?
2.00/1.43	
2.00/1.43		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 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 /\\ 0 >= ar_2 + ar_1 + 1 ]", 0-2) = ?
2.00/1.43	
2.00/1.43		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 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 /\\ 0 >= ar_2 + ar_1 + 1 ]", 0-3) = ar_3
2.00/1.43	
2.00/1.43		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_1 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-0) = ar_0
2.00/1.43	
2.00/1.43		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_1 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-1) = ?
2.00/1.43	
2.00/1.43		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_1 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-2) = ?
2.00/1.43	
2.00/1.43		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3)) [ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_1 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-3) = ar_3
2.00/1.43	
2.00/1.43		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.00/1.43	
2.00/1.43		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
2.00/1.43	
2.00/1.43		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.00/1.43	
2.00/1.43		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.00/1.43	
2.00/1.43		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
2.00/1.43	
2.00/1.43		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
2.00/1.43	
2.00/1.43		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
2.00/1.43	
2.00/1.43		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
2.00/1.43	
2.00/1.43	orients the transitions
2.00/1.43	
2.00/1.43		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_1 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ]
2.00/1.43	
2.00/1.43		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_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_2 + ar_1 >= 0 ]
2.00/1.43	
2.00/1.43	weakly and the transitions
2.00/1.43	
2.00/1.43		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_1 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ]
2.00/1.43	
2.00/1.43		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_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_2 + ar_1 >= 0 ]
2.00/1.43	
2.00/1.43	strictly and produces the following problem:
2.00/1.43	
2.00/1.43	5:	T:
2.00/1.43	
2.00/1.43			(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 ]
2.00/1.43	
2.00/1.43			(Comp: 2, Cost: 1)                      evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43			(Comp: 2*ar_0 + 2*ar_3 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2 - ar_1, ar_3)) [ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_1 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ]
2.00/1.43	
2.00/1.43			(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 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ 0 >= ar_2 + ar_1 + 1 ]
2.00/1.43	
2.00/1.43			(Comp: 2*ar_0 + 2*ar_3 + 2, 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_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_2 + ar_1 >= 0 ]
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ]
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_0, ar_3, ar_3)) [ ar_0 >= 2 ]
2.00/1.43	
2.00/1.43			(Comp: 1, Cost: 1)                      evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.00/1.43	
2.00/1.43		start location:	koat_start
2.00/1.43	
2.00/1.43		leaf cost:	0
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	Complexity upper bound 4*ar_0 + 4*ar_3 + 11
2.00/1.43	
2.00/1.43	
2.00/1.43	
2.00/1.43	Time: 0.223 sec (SMT: 0.202 sec)
2.00/1.43	
2.00/1.43	
2.00/1.43	----------------------------------------
2.00/1.43	
2.00/1.43	(2)
2.00/1.43	BOUNDS(1, n^1)
2.00/1.45	EOF